Atlas › Modular forms › Weight 2 › Level 839 › 839.2.a

Newspace 839.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(839))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
839.2.a.a	19	degree 19	$19q - 3q^{2} - 4q^{3} + 7q^{4} - 4q^{5} - 9q^{6} - 13q^{7} + O(q^{8})$	+	$-1$
839.2.a.b	51	degree 51	$51q + 4q^{2} + 4q^{3} + 66q^{4} + 6q^{5} + 15q^{6} + 19q^{7} + O(q^{8})$	−	$+1$

Hecke characteristic polynomials

The eigenvalue of $T = T_{2} + T_{3}$ generates each orbit's coefficient field; on the newspace its characteristic polynomial factors over $\mathbb{Q}$ as one irreducible factor per orbit:

Orbit	Characteristic polynomial of $T$
839.2.a.a	$x^{19} + 7x^{18} - 15x^{17} - 179x^{16} + x^{15} + 1728x^{14} + 845x^{13} - 8045x^{12} - 3834x^{11} + 19493x^{10} + 4887x^{9} - 23331x^{8} - 797x^{7} + 12253x^{6} - 1037x^{5} - 2314x^{4} + 202x^{3} + 140x^{2} - 2x - 1$
839.2.a.b	$x^{51} - 8x^{50} - 184x^{49} + 1594x^{48} + 14939x^{47} - 143395x^{46} - 704484x^{45} + 7737806x^{44} + 21318920x^{43} - 280879638x^{42} - 428803527x^{41} + 7296002219x^{40} + 5625262188x^{39} - 140927977357x^{38} - 41350682615x^{37} + 2077149411818x^{36} - 6706742626x^{35} - 23782554759826x^{34} + 4118634889627x^{33} + 214103188531135x^{32} - 53545723412869x^{31} - 1526675277659980x^{30} + 392950917282387x^{29} + 8648472158274589x^{28} - 1845518590234454x^{27} - 38878596935085263x^{26} + 5201987689936533x^{25} + 137973009584234672x^{24} - 4503357483218454x^{23} - 382979104904462344x^{22} - 29732591701361711x^{21} + 820657955453733510x^{20} + 152943352497620590x^{19} - 1335234492910897604x^{18} - 380458788351567455x^{17} + 1617914988314212893x^{16} + 593437402877227888x^{15} - 1429144421232849303x^{14} - 610171340623036888x^{13} + 899058834879418524x^{12} + 413978858978943828x^{11} - 392382466288302294x^{10} - 180531619155741397x^{9} + 115125210830184059x^{8} + 47762245460970539x^{7} - 21687950851813216x^{6} - 6801940095658336x^{5} + 2374583616112294x^{4} + 375350374227811x^{3} - 111604956059785x^{2} + 2468858826330x - 13560307155$

Orbit

Characteristic polynomial of

T

839.2.a.a

x^{19} + 7x^{18} - 15x^{17} - 179x^{16} + x^{15} + 1728x^{14} + 845x^{13} - 8045x^{12} - 3834x^{11} + 19493x^{10} + 4887x^{9} - 23331x^{8} - 797x^{7} + 12253x^{6} - 1037x^{5} - 2314x^{4} + 202x^{3} + 140x^{2} - 2x - 1

839.2.a.b

x^{51} - 8x^{50} - 184x^{49} + 1594x^{48} + 14939x^{47} - 143395x^{46} - 704484x^{45} + 7737806x^{44} + 21318920x^{43} - 280879638x^{42} - 428803527x^{41} + 7296002219x^{40} + 5625262188x^{39} - 140927977357x^{38} - 41350682615x^{37} + 2077149411818x^{36} - 6706742626x^{35} - 23782554759826x^{34} + 4118634889627x^{33} + 214103188531135x^{32} - 53545723412869x^{31} - 1526675277659980x^{30} + 392950917282387x^{29} + 8648472158274589x^{28} - 1845518590234454x^{27} - 38878596935085263x^{26} + 5201987689936533x^{25} + 137973009584234672x^{24} - 4503357483218454x^{23} - 382979104904462344x^{22} - 29732591701361711x^{21} + 820657955453733510x^{20} + 152943352497620590x^{19} - 1335234492910897604x^{18} - 380458788351567455x^{17} + 1617914988314212893x^{16} + 593437402877227888x^{15} - 1429144421232849303x^{14} - 610171340623036888x^{13} + 899058834879418524x^{12} + 413978858978943828x^{11} - 392382466288302294x^{10} - 180531619155741397x^{9} + 115125210830184059x^{8} + 47762245460970539x^{7} - 21687950851813216x^{6} - 6801940095658336x^{5} + 2374583616112294x^{4} + 375350374227811x^{3} - 111604956059785x^{2} + 2468858826330x - 13560307155

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(839))$	70
Old forms	0
Cusp forms $S_{2}(\Gamma_0(839))$	70
Eisenstein series $E_{2}(\Gamma_0(839))$	1
Modular forms $M_{2}(\Gamma_0(839))$	71

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.274 s (one thread) and proven: the dimensions are certified, and the characteristic polynomial of $T$ over $\mathbb{Z}$ is reconstructed by CRT past a rigorous coefficient bound.

The engine's checks

dim M^+ at levels [1, 839]: [0, 71] (certified at ell = 2147479751)
T = [(2, 1), (3, 1)]; h of degree 70 = 1 x 70 (phi(ord eps) x dim S_k^new); 7 primes, 0 rejected

Open in the notebook · JSON · stored data

Recompute it yourself

In Sage mode at sagebrush.space (or npx sagebrush --sage):

newform_orbits(839, 2)

With the Rust engine (source), in engine/:

cargo run --release -p sagebrush-web --example atlas -- 839:2 1000

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