Atlas › Modular forms › Weight 2 › Level 833 › 833.2.a › 833.2.a.k

Newform orbit 833.2.a.k

Trace form

The 8 newforms in this orbit are conjugate over $\mathbb{Q}$ ; the sum of their $q$ -expansions is

$8q - 2q^{2} + 8q^{3} + 6q^{4} + 4q^{5} - 6q^{6} - 6q^{8} + 8q^{9} + 12q^{10} + 4q^{11} + 20q^{12} + 12q^{13} - 4q^{15} - 6q^{16} + 8q^{17} - 6q^{18} + 16q^{19} - 18q^{20} + 8q^{22} - 4q^{23} - 8q^{24} + O(q^{25})$

Coefficient field

The coefficients $a_n$ generate a number field of degree 8. It is generated by the eigenvalue $\alpha$ of $T = T_{2} + 3T_{3} + 5T_{11} + 7T_{13} + 9T_{19}$ , whose minimal polynomial is

$x^{8} - 270x^{7} + 28577x^{6} - 1494688x^{5} + 38684789x^{4} - 357532408x^{3} - 3235951687x^{2} + 75178110990x - 297026166263$

Atkin–Lehner signs

$p$	$w_p$
7	— ( $7^2 \mid 833$ )
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
$\operatorname{tr} a_p$	−2	8	4	0	4	12	8	16	−4	0	28	8	4	−8	28	−8	−8	8	−20	40	8	4	−4	−4	40

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

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.385 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, 7, 17, 49, 119, 833]: [0, 1, 2, 5, 14, 86] (certified at ell = 2147480161)
T = [(2, 1), (3, 3), (11, 5), (13, 7), (19, 9)]; h of degree 54 = 1 x 54 (phi(ord eps) x dim S_k^new); 14 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(833, 2)[10]   # 833.2.a.k

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

cargo run --release -p sagebrush-web --example atlas -- 833:2 1000