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

Newform orbit 25.10.a.d

Trace form

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

$3q + 33q^{2} + 89q^{3} + 341q^{4} + 3421q^{6} + 5258q^{7} - 105q^{8} + 58234q^{9} - 54699q^{11} + 141853q^{12} + 215884q^{13} + 272922q^{14} - 699247q^{16} + 334983q^{17} + 2571854q^{18} + 818845q^{19} - 2375394q^{21} + 72761q^{22} + 3526854q^{23} + 2805735q^{24} + O(q^{25})$

Coefficient field

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

$x^{3} - 122x^{2} - 55559x + 584448$

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
$\operatorname{tr} a_p$	33	89	0	5258	−54699	215884	334983	818845	3526854	2175480	4274066	−10305042	5926311	−24429956	66858708	132620514	5670960	125306926	88829483	297550596	181321729	−310025170	−731088801	−1103860035	−332236842

$\operatorname{tr} a_n$ 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)[3]   # 25.10.a.d

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

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