Atlas › Modular forms › Weight 4 › Level 67 › 67.4.a

Newspace 67.4.a: $S_{4}^{\mathrm{new}}(\Gamma_0(67))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
67.4.a.a	7	degree 7	$7q - 6q^{2} - 9q^{3} + 14q^{4} - 45q^{5} - 39q^{6} - 32q^{7} + O(q^{8})$	−	$-1$
67.4.a.b	9	degree 9	$9q + 8q^{2} + 9q^{3} + 34q^{4} + 45q^{5} + 9q^{6} + 24q^{7} + O(q^{8})$	+	$+1$

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 $T$
67.4.a.a	$x^{7} + 15x^{6} + 21x^{5} - 403x^{4} - 1666x^{3} - 2425x^{2} - 1452x - 303$
67.4.a.b	$x^{9} - 17x^{8} - 85x^{7} + 2825x^{6} - 8544x^{5} - 99181x^{4} + 712884x^{3} - 1560903x^{2} + 1340766x - 383670$

Dimensions

Newforms $S_{4}^{\mathrm{new}}(\Gamma_0(67))$	16
Old forms	0
Cusp forms $S_{4}(\Gamma_0(67))$	16
Eisenstein series $E_{4}(\Gamma_0(67))$	2
Modular forms $M_{4}(\Gamma_0(67))$	18

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.096 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, 67]: [1, 18] (certified at ell = 2147483647)
T = [(2, 1), (3, 1)]; h of degree 16 = 1 x 16 (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(67, 4)

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

cargo run --release -p sagebrush-web --example atlas -- 67:4 1000

← 66.4.a · 68.4.a →