Atlas › Modular forms › Weight 2 › Level 379 › 379.2.a

Newspace 379.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(379))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
379.2.a.a	13	degree 13	$13q - 5q^{2} - 5q^{3} + 9q^{4} - 20q^{5} - 8q^{6} - 3q^{7} + O(q^{8})$	+	$-1$
379.2.a.b	18	degree 18	$18q + 3q^{2} + q^{3} + 17q^{4} + 22q^{5} + 8q^{6} + q^{7} + O(q^{8})$	−	$+1$

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 $T$
379.2.a.a	$x^{13} + 10x^{12} + 19x^{11} - 82x^{10} - 253x^{9} + 207x^{8} + 878x^{7} - 318x^{6} - 1180x^{5} + 383x^{4} + 499x^{3} - 130x^{2} - 37x + 1$
379.2.a.b	$x^{18} - 4x^{17} - 64x^{16} + 278x^{15} + 1448x^{14} - 7045x^{13} - 14011x^{12} + 82429x^{11} + 58010x^{10} - 494437x^{9} - 49143x^{8} + 1529365x^{7} - 295872x^{6} - 2184929x^{5} + 631519x^{4} + 990787x^{3} - 103546x^{2} - 144136x - 12488$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(379))$	31
Old forms	0
Cusp forms $S_{2}(\Gamma_0(379))$	31
Eisenstein series $E_{2}(\Gamma_0(379))$	1
Modular forms $M_{2}(\Gamma_0(379))$	32

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.181 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, 379]: [0, 32] (certified at ell = 2147481883)
T = [(2, 1), (3, 1)]; h of degree 31 = 1 x 31 (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(379, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 379:2 1000

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