Atlas › Modular forms › Weight 2 › Level 373 › 373.2.a

Newspace 373.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(373))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	Elliptic curve
373.2.a.a	1	$\mathbb{Q}$	$q - 2q^{2} + q^{3} + 2q^{4} + 2q^{5} - 2q^{6} - 4q^{7} + O(q^{8})$	+	$-1$	373a1 rank 1
373.2.a.b	12	degree 12	$12q - 4q^{2} - 15q^{3} + 8q^{4} - 11q^{5} + 4q^{6} - q^{7} + O(q^{8})$	+	$-1$
373.2.a.c	17	degree 17	$17q + 4q^{2} + 14q^{3} + 18q^{4} + 9q^{5} + 4q^{6} + 3q^{7} + O(q^{8})$	−	$+1$

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 $T$
373.2.a.a	$x + 1$
373.2.a.b	$x^{12} + 19x^{11} + 136x^{10} + 420x^{9} + 265x^{8} - 1547x^{7} - 3429x^{6} - 1037x^{5} + 3337x^{4} + 3049x^{3} + 401x^{2} - 175x + 7$
373.2.a.c	$x^{17} - 18x^{16} + 95x^{15} + 128x^{14} - 2854x^{13} + 6924x^{12} + 17361x^{11} - 98178x^{10} + 50931x^{9} + 426324x^{8} - 734186x^{7} - 409436x^{6} + 1976076x^{5} - 1183497x^{4} - 1145884x^{3} + 1805872x^{2} - 846056x + 136693$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(373))$	30
Old forms	0
Cusp forms $S_{2}(\Gamma_0(373))$	30
Eisenstein series $E_{2}(\Gamma_0(373))$	1
Modular forms $M_{2}(\Gamma_0(373))$	31

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.182 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, 373]: [0, 31] (certified at ell = 2147478997)
T = [(2, 1), (3, 1)]; h of degree 30 = 1 x 30 (phi(ord eps) x dim S_k^new); 3 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(373, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 373:2 1000

← 372.2.a · 374.2.a →