Atlas › Modular forms › Weight 2 › Level 905 › 905.2.a

Newspace 905.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(905))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	Elliptic curve
905.2.a.a	1	$\mathbb{Q}$	$q + q^{2} + q^{3} - q^{4} + q^{5} + q^{6} + 2q^{7} + O(q^{8})$	− +	$+1$	905b1 rank 0
905.2.a.b	1	$\mathbb{Q}$	$q + q^{2} + 2q^{3} - q^{4} - q^{5} + 2q^{6} - 4q^{7} + O(q^{8})$	+ +	$-1$	905a1 rank 1
905.2.a.c	5	degree 5	$5q - 3q^{2} + q^{4} - 5q^{5} + 2q^{6} - q^{7} + O(q^{8})$	+ +	$-1$
905.2.a.d	6	degree 6	$6q + 3q^{2} + 5q^{4} - 6q^{5} - 12q^{6} - 9q^{7} + O(q^{8})$	+ +	$-1$
905.2.a.e	13	degree 13	$13q - 6q^{2} - 8q^{3} + 12q^{4} + 13q^{5} - 6q^{6} - 26q^{7} + O(q^{8})$	− −	$-1$
905.2.a.f	17	degree 17	$17q + 4q^{2} + 7q^{3} + 24q^{4} + 17q^{5} - q^{6} + 22q^{7} + O(q^{8})$	− +	$+1$
905.2.a.g	18	degree 18	$18q - 3q^{2} - 2q^{3} + 23q^{4} - 18q^{5} + 10q^{6} + 20q^{7} + O(q^{8})$	+ −	$+1$

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 $T$
905.2.a.a	$x - 2$
905.2.a.b	$x - 3$
905.2.a.c	$x^{5} + 3x^{4} - 8x^{3} - 17x^{2} + 15x + 23$
905.2.a.d	$x^{6} - 3x^{5} - 5x^{4} + 23x^{3} - 18x^{2} - x + 1$
905.2.a.e	$x^{13} + 14x^{12} + 59x^{11} + 3x^{10} - 511x^{9} - 769x^{8} + 942x^{7} + 2011x^{6} - 483x^{5} - 1407x^{4} - 142x^{3} + 205x^{2} + 34x + 1$
905.2.a.f	$x^{17} - 11x^{16} - 3x^{15} + 408x^{14} - 950x^{13} - 4736x^{12} + 17761x^{11} + 16827x^{10} - 117174x^{9} + 25452x^{8} + 296729x^{7} - 188841x^{6} - 247927x^{5} + 176447x^{4} + 65345x^{3} - 42782x^{2} - 3612x + 1568$
905.2.a.g	$x^{18} + 5x^{17} - 65x^{16} - 312x^{15} + 1576x^{14} + 7380x^{13} - 17209x^{12} - 83159x^{11} + 76148x^{10} + 461978x^{9} - 25739x^{8} - 1179469x^{7} - 598407x^{6} + 1021867x^{5} + 941791x^{4} - 9744x^{3} - 223152x^{2} - 69780x - 6236$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(905))$	61
Old forms	28
Cusp forms $S_{2}(\Gamma_0(905))$	89
Eisenstein series $E_{2}(\Gamma_0(905))$	3
Modular forms $M_{2}(\Gamma_0(905))$	92

Decomposition of the old subspace

$S_{2}^{\mathrm{old}}(\Gamma_0(905)) =$ $S_{2}^{\mathrm{new}}(\Gamma_0(181))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.263 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, 181, 905]: [0, 1, 15, 92] (certified at ell = 2147482801)
T = [(2, 1), (3, 1)]; h of degree 61 = 1 x 61 (phi(ord eps) x dim S_k^new); 6 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(905, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 905:2 1000

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