Atlas › Modular forms › Weight 2 › Level 950 › 950.2.a › 950.2.a.k

Newform orbit 950.2.a.k

Trace form

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

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

Coefficient field

The coefficients $a_n$ generate a number field of degree 3. It is generated by the eigenvalue $\alpha$ of $T = T_{3} + 2T_{7} + 3T_{11} + 4T_{13} + 5T_{17} + 6T_{23} + 7T_{29} + 8T_{31} + 9T_{37} + 10T_{41} + 11T_{43} + 12T_{47}$ , whose minimal polynomial is

$x^{3} + 95x^{2} - 1192x - 63015$

Atkin–Lehner signs

$p$	$w_p$
2	$+1$
5	— ( $5^2 \mid 950$ )
19	$+1$

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	−2	0	−2	2	2	4	−3	−14	14	−4	17	−8	−2	−13	10	−6	22	0	−2	12	24	−12	−30	0

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

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 1.806 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, 5, 10, 19, 25, 38, 50, 95, 190, 475, 950]: [0, 1, 1, 3, 2, 3, 7, 9, 12, 34, 52, 154] (certified at ell = 2147482801)
T = [(3, 1), (7, 2), (11, 3), (13, 4), (17, 5), (23, 6), (29, 7), (31, 8), (37, 9), (41, 10), (43, 11), (47, 12)]; h of degree 29 = 1 x 29 (phi(ord eps) x dim S_k^new); 10 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(950, 2)[10]   # 950.2.a.k

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

cargo run --release -p sagebrush-web --example atlas -- 950:2 1000