Atlas › Modular forms › Weight 2 › Level 792 › 792.2.a › 792.2.a.j

Newform orbit 792.2.a.j

Trace form

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

$2q + 4q^{7} + 2q^{11} + 4q^{13} - 4q^{17} + 4q^{19} + O(q^{25})$

Coefficient field

The coefficients $a_n$ generate $\mathbb{Q}(\sqrt{2})$ . It is generated by the eigenvalue $\alpha$ of $T = T_{5} + 2T_{7} + 3T_{13} + 4T_{19} + 5T_{23} + 6T_{29} + 7T_{17} + 8T_{31} + 9T_{37} + 10T_{41} + 11T_{43} + 12T_{47} + 13T_{53} + 14T_{59} + 15T_{61} + 16T_{67}$ , whose minimal polynomial is

$x^{2} - 380x - 33092$

Atkin–Lehner signs

$p$	$w_p$
2	— ( $2^2 \mid 792$ )
3	— ( $3^2 \mid 792$ )
11	$-1$

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	0	0	4	2	4	−4	4	0	−4	8	4	−12	12	8	−8	8	12	0	8	−4	4	8	−32	−12

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

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 2.739 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 label, dimension and $\operatorname{tr} a_p$ for every $p < 1000$ equal LMFDB's.

The engine's checks

dim M^+ at levels [1, 2, 3, 4, 6, 8, 9, 11, 12, 18, 22, 24, 33, 36, 44, 66, 72, 88, 99, 132, 198, 264, 396, 792]: [0, 1, 1, 2, 3, 3, 2, 2, 5, 5, 5, 8, 6, 9, 9, 16, 16, 16, 14, 30, 40, 56, 78, 152] (certified at ell = 2147482951)
T = [(5, 1), (7, 2), (13, 3), (19, 4), (23, 5), (29, 6), (17, 7), (31, 8), (37, 9), (41, 10), (43, 11), (47, 12), (53, 13), (59, 14), (61, 15), (67, 16)]; h of degree 13 = 1 x 13 (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(792, 2)[9]   # 792.2.a.j

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

cargo run --release -p sagebrush-web --example atlas -- 792:2 1000