Atlas › Modular forms › Weight 4 › Level 61 › 61.4.a

Newspace 61.4.a: $S_{4}^{\mathrm{new}}(\Gamma_0(61))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
61.4.a.a	6	degree 6	$6q - 7q^{2} - 13q^{3} + 17q^{4} - 16q^{5} - 29q^{6} - 27q^{7} + O(q^{8})$	−	$-1$
61.4.a.b	9	degree 9	$9q + 3q^{2} + 11q^{3} + 53q^{4} + 24q^{5} + 7q^{6} + q^{7} + O(q^{8})$	+	$+1$

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 $T$
61.4.a.a	$x^{6} + 20x^{5} + 123x^{4} + 117x^{3} - 1046x^{2} - 2229x - 1088$
61.4.a.b	$x^{9} - 14x^{8} - 153x^{7} + 3069x^{6} - 3700x^{5} - 144155x^{4} + 772756x^{3} - 945860x^{2} - 772044x + 95616$

Dimensions

Newforms $S_{4}^{\mathrm{new}}(\Gamma_0(61))$	15
Old forms	0
Cusp forms $S_{4}(\Gamma_0(61))$	15
Eisenstein series $E_{4}(\Gamma_0(61))$	2
Modular forms $M_{4}(\Gamma_0(61))$	17

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.095 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, 61]: [1, 17] (certified at ell = 2147482921)
T = [(2, 1), (3, 1)]; h of degree 15 = 1 x 15 (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(61, 4)

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

cargo run --release -p sagebrush-web --example atlas -- 61:4 1000

← 60.4.a · 62.4.a →