Atlas › Modular forms › Weight 10 › Level 24 › 24.10.a › 24.10.a.d

Newform orbit 24.10.a.d

Trace form

The 2 newforms in this orbit are conjugate over $\mathbb{Q}$ ; the sum of their $q$ -expansions is

$2q - 162q^{3} - 772q^{5} - 2880q^{7} + 13122q^{9} + 42248q^{11} + 277436q^{13} + 62532q^{15} + 731524q^{17} + 656632q^{19} + 233280q^{21} + 1253744q^{23} + O(q^{25})$

Coefficient field

The coefficients $a_n$ generate $\mathbb{Q}(\sqrt{109})$ . It is generated by the eigenvalue $\alpha$ of $T = T_{5} + T_{7}$ , whose minimal polynomial is

$x^{2} + 3652x - 60956540$

Atkin–Lehner signs

$p$	$w_p$
2	— ( $2^2 \mid 24$ )
3	$+1$

For $p \parallel N$ every form in the orbit has $a_p = -p^{k/2-1} w_p$ .

Traces of Hecke eigenvalues

$p$	2	3	5	7	11	13	17	19	23	29	31	37	41	43	47	53	59	61	67	71	73	79	83	89	97
$\operatorname{tr} a_p$	0	−162	−772	−2880	42248	277436	731524	656632	1253744	979212	−7609904	15860172	−829452	−5383672	−6514560	−42168964	74106248	233394236	237129592	129456016	−66510700	−372667216	561880312	−192447372	1487834884

$\operatorname{tr} a_n$ for every $n \le 1000$ is in the JSON.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.325 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, 2, 3, 4, 6, 8, 12, 24]: [1, 3, 4, 6, 11, 11, 21, 40] (certified at ell = 2147483647)
T = [(5, 1), (7, 1)]; h of degree 5 = 1 x 5 (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(24, 10)[3]   # 24.10.a.d

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

cargo run --release -p sagebrush-web --example atlas -- 24:10 1000