Atlas › Modular forms › Weight 2 › Level 383 › 383.2.a

Newspace 383.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(383))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign
383.2.a.a	2	$\mathbb{Q}(\sqrt{5})$	$2q - q^{2} - 3q^{3} - q^{4} + q^{5} + 4q^{6} - 4q^{7} + O(q^{8})$	+	$-1$
383.2.a.b	6	degree 6	$6q - 3q^{2} + q^{3} + 3q^{4} - 4q^{5} - 7q^{6} - 7q^{7} + O(q^{8})$	+	$-1$
383.2.a.c	24	degree 24	$24q + 5q^{2} + 2q^{3} + 29q^{4} + 3q^{5} + q^{6} + 17q^{7} + O(q^{8})$	−	$+1$

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 $T$
383.2.a.a	$x^{2} + 4x - 1$
383.2.a.b	$x^{6} + 2x^{5} - 5x^{4} - 5x^{3} + 6x^{2} + x - 1$
383.2.a.c	$x^{24} - 7x^{23} - 68x^{22} + 547x^{21} + 1699x^{20} - 17354x^{19} - 18019x^{18} + 295509x^{17} + 27978x^{16} - 2989084x^{15} + 1171334x^{14} + 18749018x^{13} - 11850892x^{12} - 74160017x^{11} + 52592868x^{10} + 185125453x^{9} - 123483693x^{8} - 283928163x^{7} + 152509261x^{6} + 247140619x^{5} - 86979981x^{4} - 99950623x^{3} + 15551343x^{2} + 9163522x - 1592767$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(383))$	32
Old forms	0
Cusp forms $S_{2}(\Gamma_0(383))$	32
Eisenstein series $E_{2}(\Gamma_0(383))$	1
Modular forms $M_{2}(\Gamma_0(383))$	33

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.183 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, 383]: [0, 33] (certified at ell = 2147476031)
T = [(2, 1), (3, 1)]; h of degree 32 = 1 x 32 (phi(ord eps) x dim S_k^new); 4 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(383, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 383:2 1000

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