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

Newform orbit 467.2.a.b

Trace form

The 12 newforms in this orbit are conjugate over $\mathbb{Q}$ ; the sum of their $q$ -expansions is

$12q - 5q^{2} - 3q^{3} + 7q^{4} - 7q^{5} - 3q^{6} - 12q^{7} - 12q^{8} - 5q^{9} - 9q^{10} - 6q^{11} - 12q^{12} - 29q^{13} + 7q^{14} - 5q^{15} - 3q^{16} - q^{17} - 6q^{18} - 8q^{19} + 6q^{20} - 11q^{21} - 19q^{22} + 5q^{23} + 8q^{24} + O(q^{25})$

Coefficient field

The coefficients $a_n$ generate a number field of degree 12. It is generated by the eigenvalue $\alpha$ of $T = T_{2} + T_{3}$ , whose minimal polynomial is

$x^{12} + 8x^{11} + 4x^{10} - 82x^{9} - 83x^{8} + 315x^{7} + 183x^{6} - 549x^{5} + 88x^{4} + 159x^{3} - 41x^{2} - 3x + 1$

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 odd 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	−3	−7	−12	−6	−29	−1	−8	5	−15	−11	−51	6	−32	5	−24	25	−28	−6	33	−35	−3	7	15	−22

$\operatorname{tr} a_n$ 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)[1]   # 467.2.a.b

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

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