Atlas › Modular forms › Weight 2 › Level 952 › 952.2.a › 952.2.a.g

Newform orbit 952.2.a.g

Trace form

The 4 newforms in this orbit are conjugate over $\mathbb{Q}$ ; the sum of their $q$ -expansions is

$4q + 3q^{3} - q^{5} - 4q^{7} + 7q^{9} + 4q^{11} - 8q^{13} + 12q^{15} + 4q^{17} + 14q^{19} - 3q^{21} + 8q^{23} + O(q^{25})$

Coefficient field

The coefficients $a_n$ generate a number field of degree 4. It is generated by the eigenvalue $\alpha$ of $T = T_{3} + 3T_{5}$ , whose minimal polynomial is

$x^{4} - 185x^{2} - 400x + 100$

Atkin–Lehner signs

$p$	$w_p$
2	— ( $2^2 \mid 952$ )
7	$+1$
17	$-1$

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	3	−1	−4	4	−8	4	14	8	4	5	−4	−7	19	8	5	0	−23	15	2	−5	−24	10	−16	−15

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

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.588 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, 4, 7, 8, 14, 17, 28, 34, 56, 68, 119, 136, 238, 476, 952]: [0, 1, 2, 1, 3, 4, 2, 7, 6, 12, 12, 14, 22, 40, 78, 152] (certified at ell = 2147483137)
T = [(3, 1), (5, 3)]; h of degree 24 = 1 x 24 (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(952, 2)[6]   # 952.2.a.g

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

cargo run --release -p sagebrush-web --example atlas -- 952:2 1000