Atlas › Modular forms › Weight 12 › Level 24 › 24.12.a › 24.12.a.d

Newform orbit 24.12.a.d

Trace form

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

$2q + 486q^{3} + 1564q^{5} + 37776q^{7} + 118098q^{9} + 570568q^{11} - 272596q^{13} + 380052q^{15} + 1055780q^{17} + 18953656q^{19} + 9179568q^{21} + 72749968q^{23} + O(q^{25})$

Coefficient field

The coefficients $a_n$ generate $\mathbb{Q}(\sqrt{3061})$ . It is generated by the eigenvalue $\alpha$ of $T = T_{5} + 3T_{7}$ , whose minimal polynomial is

$x^{2} - 114892x + 2848680100$

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	486	1564	37776	570568	−272596	1055780	18953656	72749968	261426924	−55418528	330603516	708690996	−2041855480	−3992785824	1322567548	164296744	4411708556	−5445151208	11130361904	−16981651276	−26863947904	67369585976	−9278078316	−250392711740

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

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.383 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]: [2, 4, 5, 7, 13, 13, 25, 48] (certified at ell = 2147483647)
T = [(5, 1), (7, 3)]; 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, 12)[3]   # 24.12.a.d

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

cargo run --release -p sagebrush-web --example atlas -- 24:12 1000