Atlas › Modular forms › Weight 10 › Level 25 › 25.10.a › 25.10.a.b

Newform orbit 25.10.a.b

Trace form

The 2 newforms in this orbit are conjugate over $\mathbb{Q}$ ; the sum of their $q$ -expansions is

$2q + 10q^{2} - 260q^{3} + 1044q^{4} - 5336q^{6} - 1700q^{7} + 20280q^{8} + 2506q^{9} + 23984q^{11} - 176080q^{12} - 115020q^{13} - 440352q^{14} - 312048q^{16} - 412820q^{17} + 1061890q^{18} - 296520q^{19} + 1084704q^{21} - 3714280q^{22} + 1049220q^{23} - 2878560q^{24} + O(q^{25})$

Coefficient field

The coefficients $a_n$ generate $\mathbb{Q}(\sqrt{1009})$ . It is generated by the eigenvalue $\alpha$ of $T = T_{2} + T_{3}$ , whose minimal polynomial is

$x^{2} + 250x + 14616$

Atkin–Lehner signs

$p$	$w_p$
5	— ( $5^2 \mid 25$ )

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
$\operatorname{tr} a_p$	10	−260	0	−1700	23984	−115020	−412820	−296520	1049220	−3666980	1613144	21121940	−26957276	−52889700	−58412180	39035140	−54995560	−274579716	318580	−7130936	−120858180	6877520	−1402348740	830088660	−638394580

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

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.304 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 engine's checks

dim M^+ at levels [1, 5, 25]: [1, 5, 23] (certified at ell = 2147482921)
T = [(2, 1), (3, 1)]; h of degree 13 = 1 x 13 (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(25, 10)[1]   # 25.10.a.b

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

cargo run --release -p sagebrush-web --example atlas -- 25:10 1000