Atlas › Modular forms › Weight 6 › Level 67 › 67.6.a

Newspace 67.6.a: $S_{6}^{\mathrm{new}}(\Gamma_0(67))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
67.6.a.a	13	degree 13	$13q - 16q^{2} - 27q^{3} + 202q^{4} - 222q^{5} - 141q^{6} - 293q^{7} + O(q^{8})$	+	$-1$
67.6.a.b	15	degree 15	$15q + 12q^{2} + 27q^{3} + 282q^{4} + 228q^{5} + 147q^{6} + 99q^{7} + O(q^{8})$	−	$+1$

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 $T$
67.6.a.a	$x^{13} + 43x^{12} - 1283x^{11} - 51929x^{10} + 794183x^{9} + 21130939x^{8} - 262463638x^{7} - 3127147533x^{6} + 33994956891x^{5} + 197973067973x^{4} - 1714241302815x^{3} - 5259059192055x^{2} + 26073066653685x + 48504043340550$
67.6.a.b	$x^{15} - 39x^{14} - 2455x^{13} + 91451x^{12} + 2586183x^{11} - 84207393x^{10} - 1545307782x^{9} + 38652414207x^{8} + 565050235631x^{7} - 9221170524861x^{6} - 124335483896261x^{5} + 1046255872022023x^{4} + 14936043406349895x^{3} - 33860482772343282x^{2} - 743628283091088750x - 1560515808302001900$

Dimensions

Newforms $S_{6}^{\mathrm{new}}(\Gamma_0(67))$	28
Old forms	0
Cusp forms $S_{6}(\Gamma_0(67))$	28
Eisenstein series $E_{6}(\Gamma_0(67))$	2
Modular forms $M_{6}(\Gamma_0(67))$	30

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.238 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, 30] (certified at ell = 2147483647)
T = [(2, 1), (3, 1)]; h of degree 28 = 1 x 28 (phi(ord eps) x dim S_k^new); 5 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, 6)

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

cargo run --release -p sagebrush-web --example atlas -- 67:6 1000

← 66.6.a · 68.6.a →