Atlas › Modular forms › Weight 2 › Level 925 › 925.2.a

Newspace 925.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(925))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Elliptic curve
925.2.a.a	1	$\mathbb{Q}$	$q - q^{2} + 2q^{3} - q^{4} - 2q^{6} + 2q^{7} + O(q^{8})$	−	925c1 rank 0
925.2.a.b	1	$\mathbb{Q}$	$q - q^{3} - 2q^{4} + q^{7} + O(q^{8})$	+	925b1 rank 1
925.2.a.c	1	$\mathbb{Q}$	$q + q^{3} - 2q^{4} + 3q^{7} + O(q^{8})$	+	925a1 rank 1
925.2.a.d	1	$\mathbb{Q}$	$q + 2q^{2} - q^{3} + 2q^{4} - 2q^{6} + 5q^{7} + O(q^{8})$	−	925d1 rank 0
925.2.a.e	1	$\mathbb{Q}$	$q + 2q^{2} + 3q^{3} + 2q^{4} + 6q^{6} + q^{7} + O(q^{8})$	−	925e1 rank 0
925.2.a.f	5	degree 5	$5q - 2q^{2} - 3q^{3} + 10q^{4} - 6q^{6} - 11q^{7} + O(q^{8})$	+
925.2.a.g	5	degree 5	$5q - q^{2} + q^{3} + q^{4} - 6q^{6} + O(q^{8})$	−
925.2.a.h	5	degree 5	$5q + q^{3} + 6q^{4} - 2q^{6} - 7q^{7} + O(q^{8})$	−
925.2.a.i	5	degree 5	$5q + q^{2} - q^{3} + q^{4} - 6q^{6} + O(q^{8})$	+
925.2.a.j	7	degree 7	$7q - q^{2} + q^{3} + 7q^{4} + 6q^{6} + O(q^{8})$	+
925.2.a.k	7	degree 7	$7q + q^{2} - q^{3} + 7q^{4} + 6q^{6} + O(q^{8})$	−
925.2.a.l	9	degree 9	$9q - 5q^{2} - 8q^{3} + 11q^{4} + 2q^{6} - 8q^{7} + O(q^{8})$	−
925.2.a.m	9	degree 9	$9q + 5q^{2} + 8q^{3} + 11q^{4} + 2q^{6} + 8q^{7} + O(q^{8})$	+

Hecke characteristic polynomials

The eigenvalue of $T = T_{2} + 3T_{3} + 5T_{7} + 7T_{11}$ 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 $T$
925.2.a.a	$x - 15$
925.2.a.b	$x - 23$
925.2.a.c	$x + 17$
925.2.a.d	$x - 45$
925.2.a.e	$x + 19$
925.2.a.f	$x^{5} + 101x^{4} + 2746x^{3} + 9006x^{2} - 47575x - 184543$
925.2.a.g	$x^{5} + 110x^{4} + 3697x^{3} + 7272x^{2} - 1715862x - 23000053$
925.2.a.h	$x^{5} - 17x^{4} - 2742x^{3} + 70170x^{2} + 15353x - 7051229$
925.2.a.i	$x^{5} + 114x^{4} + 3851x^{3} + 27714x^{2} - 240220x + 36469$
925.2.a.j	$x^{7} - 114x^{6} + 2938x^{5} + 5254x^{4} - 479431x^{3} + 1870835x^{2} + 11510670x - 57398967$
925.2.a.k	$x^{7} - 110x^{6} + 3876x^{5} - 25428x^{4} - 1312123x^{3} + 28868671x^{2} - 202488108x + 393056163$
925.2.a.l	$x^{9} + 69x^{8} + 40x^{7} - 90216x^{6} - 1562918x^{5} + 26580646x^{4} + 797567608x^{3} + 717992432x^{2} - 102742080027x - 647652543331$
925.2.a.m	$x^{9} - 69x^{8} - 1276x^{7} + 158228x^{6} - 876722x^{5} - 99022274x^{4} + 1327506444x^{3} + 10237391364x^{2} - 224942594015x + 853483919711$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(925))$	57
Old forms	32
Cusp forms $S_{2}(\Gamma_0(925))$	89
Eisenstein series $E_{2}(\Gamma_0(925))$	11
Modular forms $M_{2}(\Gamma_0(925))$	100

Decomposition of the old subspace

$S_{2}^{\mathrm{old}}(\Gamma_0(925)) =$ $S_{2}^{\mathrm{new}}(\Gamma_0(37))^{\oplus 3}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(185))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.457 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, 25, 37, 185, 925]: [0, 1, 3, 3, 20, 96] (certified at ell = 2147482801)
T = [(2, 1), (3, 3), (7, 5), (11, 7)]; h of degree 57 = 1 x 57 (phi(ord eps) x dim S_k^new); 13 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(925, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 925:2 1000

← 924.2.a · 926.2.a →