Atlas › Modular forms › Weight 2 › Level 467 › 467.2.a › 467.2.a.c

Newform orbit 467.2.a.c

Trace form

The 26 newforms in this orbit are conjugate over $\mathbb{Q}$ ; the sum of their $q$ -expansions is

$26q + 5q^{2} + 4q^{3} + 33q^{4} + 3q^{5} - 3q^{6} + 11q^{7} + 12q^{8} + 30q^{9} + 7q^{10} + 8q^{12} + 47q^{13} - 3q^{14} - 3q^{15} + 47q^{16} + 14q^{17} + 20q^{18} + 4q^{19} - 12q^{20} + 18q^{21} + 17q^{22} + 4q^{23} - 16q^{24} + O(q^{25})$

Coefficient field

The coefficients $a_n$ generate a number field of degree 26. It is generated by the eigenvalue $\alpha$ of $T = T_{2} + T_{3}$ , whose minimal polynomial is

$x^{26} - 9x^{25} - 53x^{24} + 649x^{23} + 814x^{22} - 19447x^{21} + 3358x^{20} + 319374x^{19} - 240958x^{18} - 3208940x^{17} + 3035847x^{16} + 20867128x^{15} - 18433838x^{14} - 89962822x^{13} + 56243433x^{12} + 254111628x^{11} - 58544501x^{10} - 436261101x^{9} - 96791485x^{8} + 359299537x^{7} + 243818373x^{6} - 27636107x^{5} - 70591471x^{4} - 19580337x^{3} + 94825x^{2} + 517075x + 17021$

Atkin–Lehner signs

$p$	$w_p$
467	$-1$

For $p \parallel N$ every form in the orbit has $a_p = -p^{k/2-1} w_p$ . The Fricke sign is $w_N = -1$ , so the sign of the functional equation is $(-1)^{k/2} w_N = +1$ : each L-function in the orbit has even analytic rank.

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
$\operatorname{tr} a_p$	5	4	3	11	0	47	14	4	4	17	7	71	2	46	−5	33	−8	34	20	−17	29	19	−16	−29	9

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

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.193 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, 467]: [0, 40] (certified at ell = 2147483179)
T = [(2, 1), (3, 1)]; h of degree 39 = 1 x 39 (phi(ord eps) x dim S_k^new); 4 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(467, 2)[2]   # 467.2.a.c

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

cargo run --release -p sagebrush-web --example atlas -- 467:2 1000