Atlas › Modular forms › Weight 4 › Level 79 › 79.4.a

Newspace 79.4.a: $S_{4}^{\mathrm{new}}(\Gamma_0(79))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign
79.4.a.a	2	$\mathbb{Q}(\sqrt{17})$	$2q - q^{2} - 2q^{3} - 7q^{4} + q^{6} + 8q^{7} + O(q^{8})$	−	$-1$
79.4.a.b	5	degree 5	$5q - 3q^{2} - 8q^{3} + 23q^{4} - 41q^{5} - 40q^{6} - 20q^{7} + O(q^{8})$	−	$-1$
79.4.a.c	12	degree 12	$12q + 4q^{2} + 8q^{3} + 56q^{4} + 39q^{5} + 21q^{6} + 16q^{7} + O(q^{8})$	+	$+1$

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 $T$
79.4.a.a	$x^{2} + 3x - 2$
79.4.a.b	$x^{5} + 11x^{4} - 14x^{3} - 204x^{2} - 32x + 704$
79.4.a.c	$x^{12} - 12x^{11} - 289x^{10} + 3358x^{9} + 28458x^{8} - 323239x^{7} - 1220466x^{6} + 13292403x^{5} + 23870122x^{4} - 231587208x^{3} - 158130872x^{2} + 1278743984x - 790227904$

Dimensions

Newforms $S_{4}^{\mathrm{new}}(\Gamma_0(79))$	19
Old forms	0
Cusp forms $S_{4}(\Gamma_0(79))$	19
Eisenstein series $E_{4}(\Gamma_0(79))$	2
Modular forms $M_{4}(\Gamma_0(79))$	21

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.099 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, 79]: [1, 21] (certified at ell = 2147483053)
T = [(2, 1), (3, 1)]; h of degree 19 = 1 x 19 (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(79, 4)

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

cargo run --release -p sagebrush-web --example atlas -- 79:4 1000

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