Atlas › Modular forms › Weight 2 › Level 955 › 955.2.a

Newspace 955.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(955))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	Elliptic curve
955.2.a.a	1	$\mathbb{Q}$	$q - q^{2} - q^{4} - q^{5} + 2q^{7} + O(q^{8})$	+ −	$+1$	955a1 rank 0
955.2.a.b	2	$\mathbb{Q}(\sqrt{5})$	$2q + q^{2} - 2q^{3} - q^{4} + 2q^{5} - q^{6} + q^{7} + O(q^{8})$	− −	$-1$
955.2.a.c	12	degree 12	$12q - 9q^{2} - 5q^{3} + 15q^{4} + 12q^{5} - q^{6} - 11q^{7} + O(q^{8})$	− −	$-1$
955.2.a.d	14	degree 14	$14q - 4q^{2} - q^{3} + 10q^{4} - 14q^{5} - 10q^{6} - 2q^{7} + O(q^{8})$	+ +	$-1$
955.2.a.e	17	degree 17	$17q + 7q^{2} - q^{3} + 21q^{4} - 17q^{5} + 2q^{6} - 2q^{7} + O(q^{8})$	+ −	$+1$
955.2.a.f	17	degree 17	$17q + 7q^{2} + 5q^{3} + 17q^{4} + 17q^{5} - 2q^{6} + 8q^{7} + O(q^{8})$	− +	$+1$

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 $T$
955.2.a.a	$x + 1$
955.2.a.b	$x^{2} + x - 1$
955.2.a.c	$x^{12} + 14x^{11} + 55x^{10} - 34x^{9} - 588x^{8} - 667x^{7} + 1279x^{6} + 2418x^{5} + 671x^{4} - 507x^{3} - 219x^{2} - 27x - 1$
955.2.a.d	$x^{14} + 5x^{13} - 20x^{12} - 113x^{11} + 155x^{10} + 983x^{9} - 580x^{8} - 4102x^{7} + 938x^{6} + 8356x^{5} - 107x^{4} - 7295x^{3} - 691x^{2} + 1562x - 191$
955.2.a.e	$x^{17} - 6x^{16} - 51x^{15} + 331x^{14} + 822x^{13} - 6098x^{12} - 5609x^{11} + 49346x^{10} + 18744x^{9} - 185850x^{8} - 38155x^{7} + 306922x^{6} + 72766x^{5} - 180045x^{4} - 69225x^{3} + 10985x^{2} + 5120x + 356$
955.2.a.f	$x^{17} - 12x^{16} + 15x^{15} + 331x^{14} - 1226x^{13} - 2142x^{12} + 15743x^{11} - 5264x^{10} - 75854x^{9} + 89076x^{8} + 133049x^{7} - 260116x^{6} - 18684x^{5} + 238149x^{4} - 98545x^{3} - 33975x^{2} + 21048x - 1436$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(955))$	63
Old forms	32
Cusp forms $S_{2}(\Gamma_0(955))$	95
Eisenstein series $E_{2}(\Gamma_0(955))$	3
Modular forms $M_{2}(\Gamma_0(955))$	98

Decomposition of the old subspace

$S_{2}^{\mathrm{old}}(\Gamma_0(955)) =$ $S_{2}^{\mathrm{new}}(\Gamma_0(191))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.276 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, 5, 191, 955]: [0, 1, 17, 98] (certified at ell = 2147476141)
T = [(2, 1), (3, 1)]; h of degree 63 = 1 x 63 (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(955, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 955:2 1000

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