Atlas › Modular forms › Weight 2 › Level 954 › 954.2.a › 954.2.a.p

Newform orbit 954.2.a.p

Trace form

The 3 newforms in this orbit are conjugate over $\mathbb{Q}$ ; the sum of their $q$ -expansions is

$3q - 3q^{2} + 3q^{4} - 3q^{7} - 3q^{8} - 3q^{11} + 6q^{13} + 3q^{14} + 3q^{16} - 6q^{17} + 15q^{19} + 3q^{22} - 3q^{23} + O(q^{25})$

Coefficient field

The coefficients $a_n$ generate a number field of degree 3. It is generated by the eigenvalue $\alpha$ of $T = T_{5} + 3T_{7} + 5T_{11} + 7T_{13} + 9T_{17}$ , whose minimal polynomial is

$x^{3} + 36x^{2} - 2079x + 18130$

Atkin–Lehner signs

$p$	$w_p$
2	$+1$
3	— ( $3^2 \mid 954$ )
53	$-1$

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
$\operatorname{tr} a_p$	−3	0	0	−3	−3	6	−6	15	−3	−9	18	−6	3	−6	0	3	12	−15	9	15	−12	18	24	12	3

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

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.761 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, 6, 9, 18, 53, 106, 159, 318, 477, 954]: [0, 1, 1, 3, 2, 5, 5, 15, 20, 58, 56, 166] (certified at ell = 2147483053)
T = [(5, 1), (7, 3), (11, 5), (13, 7), (17, 9)]; h of degree 23 = 1 x 23 (phi(ord eps) x dim S_k^new); 6 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(954, 2)[15]   # 954.2.a.p

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

cargo run --release -p sagebrush-web --example atlas -- 954:2 1000