Atlas › Modular forms › Weight 4 › Level 83 › 83.4.a

Newspace 83.4.a: $S_{4}^{\mathrm{new}}(\Gamma_0(83))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
83.4.a.a	7	degree 7	$7q - 5q^{2} - 11q^{3} + 13q^{4} - 17q^{5} - 27q^{6} - 46q^{7} + O(q^{8})$	−	$-1$
83.4.a.b	13	degree 13	$13q + 5q^{2} + 7q^{3} + 73q^{4} + 33q^{5} - 3q^{6} + 52q^{7} + O(q^{8})$	+	$+1$

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 $T$
83.4.a.a	$x^{7} + 16x^{6} + 18x^{5} - 406x^{4} - 1175x^{3} + 1778x^{2} + 9644x + 8964$
83.4.a.b	$x^{13} - 12x^{12} - 278x^{11} + 3262x^{10} + 27544x^{9} - 320612x^{8} - 1210811x^{7} + 14512388x^{6} + 21941285x^{5} - 308390534x^{4} - 49861687x^{3} + 2605953954x^{2} - 1837881750x - 3474959174$

Dimensions

Newforms $S_{4}^{\mathrm{new}}(\Gamma_0(83))$	20
Old forms	0
Cusp forms $S_{4}(\Gamma_0(83))$	20
Eisenstein series $E_{4}(\Gamma_0(83))$	2
Modular forms $M_{4}(\Gamma_0(83))$	22

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.1 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, 83]: [1, 22] (certified at ell = 2147483323)
T = [(2, 1), (3, 1)]; h of degree 20 = 1 x 20 (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(83, 4)

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

cargo run --release -p sagebrush-web --example atlas -- 83:4 1000

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