Atlas › Modular forms › Weight 10 › Level 7 › 7.10.a

Newspace 7.10.a: $S_{10}^{\mathrm{new}}(\Gamma_0(7))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
7.10.a.a	2	$\mathbb{Q}(\sqrt{193})$	$2q - 6q^{2} - 86q^{3} - 620q^{4} - 2238q^{5} - 3988q^{6} - 4802q^{7} + O(q^{8})$	+	$-1$
7.10.a.b	3	degree 3	$3q + 21q^{2} + 84q^{3} + 1557q^{4} + 1554q^{5} + 4914q^{6} + 7203q^{7} + O(q^{8})$	−	$+1$

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 $T$
7.10.a.a	$x^{2} + 92x - 17184$
7.10.a.b	$x^{3} - 105x^{2} - 17472x + 845676$

Dimensions

Newforms $S_{10}^{\mathrm{new}}(\Gamma_0(7))$	5
Old forms	0
Cusp forms $S_{10}(\Gamma_0(7))$	5
Eisenstein series $E_{10}(\Gamma_0(7))$	2
Modular forms $M_{10}(\Gamma_0(7))$	7

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.273 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, 7]: [1, 7] (certified at ell = 2147483647)
T = [(2, 1), (3, 1)]; h of degree 5 = 1 x 5 (phi(ord eps) x dim S_k^new); 2 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(7, 10)

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

cargo run --release -p sagebrush-web --example atlas -- 7:10 1000

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