Atlas › Modular forms › Weight 2 › Level 901 › 901.2.a

Newspace 901.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(901))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	Elliptic curve
901.2.a.a	1	$\mathbb{Q}$	$q - 2q^{2} - q^{3} + 2q^{4} + 3q^{5} + 2q^{6} + 2q^{7} + O(q^{8})$	− −	$-1$	901f1 rank 1
901.2.a.b	1	$\mathbb{Q}$	$q - q^{2} - q^{4} + 2q^{7} + O(q^{8})$	+ +	$-1$	901a1 rank 1
901.2.a.c	1	$\mathbb{Q}$	$q - q^{2} - q^{4} + 3q^{5} - q^{7} + O(q^{8})$	− +	$+1$	901d1 rank 0
901.2.a.d	1	$\mathbb{Q}$	$q - q^{2} + 2q^{3} - q^{4} - 2q^{6} - 4q^{7} + O(q^{8})$	+ +	$-1$	901b1 rank 1
901.2.a.e	1	$\mathbb{Q}$	$q + q^{3} - 2q^{4} - 3q^{5} - 4q^{7} + O(q^{8})$	− +	$+1$	901c1 rank 0
901.2.a.f	1	$\mathbb{Q}$	$q + 2q^{2} - 3q^{3} + 2q^{4} + q^{5} - 6q^{6} - 2q^{7} + O(q^{8})$	− −	$-1$	901e1 rank 1
901.2.a.g	12	degree 12	$12q - q^{2} - 3q^{3} + 9q^{4} - 5q^{5} - 5q^{6} + 3q^{7} + O(q^{8})$	+ +	$-1$
901.2.a.h	13	degree 13	$13q - 2q^{2} - 7q^{3} + 10q^{4} - 11q^{5} + 3q^{6} - 7q^{7} + O(q^{8})$	− −	$-1$
901.2.a.i	18	degree 18	$18q + 4q^{2} + 8q^{3} + 28q^{4} + 7q^{5} + 3q^{6} + 14q^{7} + O(q^{8})$	− +	$+1$
901.2.a.j	20	degree 20	$20q + 5q^{2} + 3q^{3} + 25q^{4} + 7q^{5} - 3q^{6} - 7q^{7} + O(q^{8})$	+ −	$+1$

Hecke characteristic polynomials

The eigenvalue of $T = T_{2} + 3T_{3} + 5T_{5} + 7T_{7}$ 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 $T$
901.2.a.a	$x - 24$
901.2.a.b	$x - 13$
901.2.a.c	$x - 7$
901.2.a.d	$x + 23$
901.2.a.e	$x + 40$
901.2.a.f	$x + 16$
901.2.a.g	$x^{12} + 14x^{11} - 1318x^{10} - 25610x^{9} + 446755x^{8} + 14022557x^{7} + 36412095x^{6} - 2058132506x^{5} - 27078938060x^{4} - 142700839210x^{3} - 330194258349x^{2} - 229655245896x + 101954657884$
901.2.a.h	$x^{13} + 127x^{12} + 5331x^{11} + 51761x^{10} - 1883563x^{9} - 41182746x^{8} + 89871283x^{7} + 6616475521x^{6} + 15572581604x^{5} - 336907156249x^{4} - 505910983233x^{3} + 7290930210219x^{2} - 10416922731667x + 3377562192879$
901.2.a.i	$x^{18} - 161x^{17} + 7505x^{16} + 113975x^{15} - 19780240x^{14} + 401327667x^{13} + 12156364134x^{12} - 559769382750x^{11} + 1677415594251x^{10} + 229145717550745x^{9} - 3134390249054724x^{8} - 24473238921374068x^{7} + 642145590725431561x^{6} + 163554407036172306x^{5} - 48297444271892832423x^{4} + 11227733841924261235x^{3} + 1499176497920749630739x^{2} + 2929649693357771587611x + 435180186045612510860$
901.2.a.j	$x^{20} - 8180x^{18} + 24748x^{17} + 25612023x^{16} - 126996051x^{15} - 40169086461x^{14} + 247096688416x^{13} + 34713106677991x^{12} - 229761039254882x^{11} - 17289591886410447x^{10} + 110111148863132538x^{9} + 5045858848412706555x^{8} - 27405371524654192909x^{7} - 851840260341117931681x^{6} + 3322625274467773254990x^{5} + 77439464481633864244658x^{4} - 151076151204958485708878x^{3} - 2949027906650298113444927x^{2} - 561515747783174683266980x + 18468603393910316271284$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(901))$	69
Old forms	10
Cusp forms $S_{2}(\Gamma_0(901))$	79
Eisenstein series $E_{2}(\Gamma_0(901))$	3
Modular forms $M_{2}(\Gamma_0(901))$	82

Decomposition of the old subspace

$S_{2}^{\mathrm{old}}(\Gamma_0(901)) =$ $S_{2}^{\mathrm{new}}(\Gamma_0(17))^{\oplus 2}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(53))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.418 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, 17, 53, 901]: [0, 2, 5, 82] (certified at ell = 2147482481)
T = [(2, 1), (3, 3), (5, 5), (7, 7)]; h of degree 69 = 1 x 69 (phi(ord eps) x dim S_k^new); 15 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(901, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 901:2 1000

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