Atlas › Modular forms › Weight 2 › Level 880 › 880.2.a › 880.2.a.l

Newform orbit 880.2.a.l

Trace form

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

$2q - q^{3} - 2q^{5} - 3q^{7} + 3q^{9} - 2q^{11} + 2q^{13} + q^{15} + 7q^{17} - 9q^{19} - 7q^{21} - 6q^{23} + O(q^{25})$

Coefficient field

The coefficients $a_n$ generate $\mathbb{Q}(\sqrt{17})$ . It is generated by the eigenvalue $\alpha$ of $T = T_{3} + 2T_{7} + 3T_{13} + 4T_{17} + 5T_{19} + 6T_{23} + 7T_{29} + 8T_{31} + 9T_{37} + 10T_{41} + 11T_{43} + 12T_{47} + 13T_{53} + 14T_{59} + 15T_{61} + 16T_{67}$ , whose minimal polynomial is

$x^{2} + 474x + 11952$

Atkin–Lehner signs

$p$	$w_p$
2	— ( $2^2 \mid 880$ )
5	$+1$
11	$+1$

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	−1	−2	−3	−2	2	7	−9	−6	−5	−5	−1	−20	−2	6	−13	2	−3	0	9	18	−10	−20	−1	26

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

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 3.261 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, 5, 8, 10, 11, 16, 20, 22, 40, 44, 55, 80, 88, 110, 176, 220, 440, 880]: [0, 1, 2, 1, 3, 3, 2, 4, 6, 5, 10, 9, 8, 16, 16, 22, 28, 42, 80, 152] (certified at ell = 2147482921)
T = [(3, 1), (7, 2), (13, 3), (17, 4), (19, 5), (23, 6), (29, 7), (31, 8), (37, 9), (41, 10), (43, 11), (47, 12), (53, 13), (59, 14), (61, 15), (67, 16)]; h of degree 20 = 1 x 20 (phi(ord eps) x dim S_k^new); 8 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(880, 2)[11]   # 880.2.a.l

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

cargo run --release -p sagebrush-web --example atlas -- 880:2 1000