Atlas › Modular forms › Weight 2 › Level 887 › 887.2.a

Newspace 887.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(887))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign
887.2.a.a	2	$\mathbb{Q}(\sqrt{5})$	$2q + q^{2} + 2q^{3} - q^{4} - 3q^{5} + q^{6} - 2q^{7} + O(q^{8})$	+	$-1$
887.2.a.b	21	degree 21	$21q - 4q^{2} - 11q^{3} + 12q^{4} - 3q^{5} - 7q^{6} - 15q^{7} + O(q^{8})$	+	$-1$
887.2.a.c	51	degree 51	$51q + 4q^{2} + 11q^{3} + 62q^{4} + 8q^{5} - 2q^{6} + 23q^{7} + O(q^{8})$	−	$+1$

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 $T$
887.2.a.a	$x^{2} - 3x + 1$
887.2.a.b	$x^{21} + 15x^{20} + 59x^{19} - 160x^{18} - 1607x^{17} - 1636x^{16} + 12445x^{15} + 28357x^{14} - 38162x^{13} - 147746x^{12} + 37240x^{11} + 386966x^{10} + 40635x^{9} - 574889x^{8} - 101287x^{7} + 490174x^{6} + 42279x^{5} - 213973x^{4} + 16869x^{3} + 30778x^{2} - 6578x + 251$
887.2.a.c	$x^{51} - 15x^{50} - 81x^{49} + 2225x^{48} - 835x^{47} - 146192x^{46} + 375973x^{45} + 5603505x^{44} - 22530190x^{43} - 138488949x^{42} + 748929102x^{41} + 2287725269x^{40} - 16528911286x^{39} - 24869720163x^{38} + 260048329427x^{37} + 155838360042x^{36} - 3029443105889x^{35} - 93155991129x^{34} + 26757288361315x^{33} - 8901335370406x^{32} - 182111249243735x^{31} + 101006009932402x^{30} + 966275312561115x^{29} - 645850751647636x^{28} - 4028685596439187x^{27} + 2793715971179409x^{26} + 13247491429242222x^{25} - 8543801999847410x^{24} - 34296528816541874x^{23} + 18486458430936808x^{22} + 69293747684382404x^{21} - 27369863525913666x^{20} - 107393042294203556x^{19} + 25119305451301505x^{18} + 124307122604954567x^{17} - 9382306944325198x^{16} - 103579961522833748x^{15} - 6689777820854485x^{14} + 59307703578229026x^{13} + 10400490410117735x^{12} - 22150681162974407x^{11} - 5544060600107521x^{10} + 5159587370057368x^{9} + 1480635695970338x^{8} - 725450892908003x^{7} - 202535586681763x^{6} + 60821329046302x^{5} + 13098288943153x^{4} - 2987281941207x^{3} - 310027357611x^{2} + 67442015067x - 858608529$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(887))$	74
Old forms	0
Cusp forms $S_{2}(\Gamma_0(887))$	74
Eisenstein series $E_{2}(\Gamma_0(887))$	1
Modular forms $M_{2}(\Gamma_0(887))$	75

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.287 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, 887]: [0, 75] (certified at ell = 2147476169)
T = [(2, 1), (3, 1)]; h of degree 74 = 1 x 74 (phi(ord eps) x dim S_k^new); 8 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(887, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 887:2 1000

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