Atlas › Modular forms › Weight 2 › Level 891 › 891.2.a

Newspace 891.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(891))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Elliptic curve
891.2.a.a	1	$\mathbb{Q}$	$q - 2q^{2} + 2q^{4} - 2q^{5} + 4q^{7} + O(q^{8})$	−	891e1 rank 0
891.2.a.b	1	$\mathbb{Q}$	$q - q^{2} - q^{4} - q^{5} - 2q^{7} + O(q^{8})$	+	891a1 rank 1
891.2.a.c	1	$\mathbb{Q}$	$q - q^{2} - q^{4} - q^{5} + 4q^{7} + O(q^{8})$	+	891g1 rank 0
891.2.a.d	1	$\mathbb{Q}$	$q - 2q^{4} - 3q^{5} - 4q^{7} + O(q^{8})$	−	891b1 rank 0
891.2.a.e	1	$\mathbb{Q}$	$q - 2q^{4} + 3q^{5} - 4q^{7} + O(q^{8})$	+	891f1 rank 0
891.2.a.f	1	$\mathbb{Q}$	$q + q^{2} - q^{4} + q^{5} - 2q^{7} + O(q^{8})$	−	891c1 rank 0
891.2.a.g	1	$\mathbb{Q}$	$q + q^{2} - q^{4} + q^{5} + 4q^{7} + O(q^{8})$	−	891d1 rank 0
891.2.a.h	1	$\mathbb{Q}$	$q + 2q^{2} + 2q^{4} + 2q^{5} + 4q^{7} + O(q^{8})$	+	891h1 rank 0
891.2.a.i	2	$\mathbb{Q}(\sqrt{13})$	$2q - q^{2} + 3q^{4} - q^{5} + O(q^{8})$	+
891.2.a.j	2	$\mathbb{Q}(\sqrt{13})$	$2q + q^{2} + 3q^{4} + q^{5} + O(q^{8})$	−
891.2.a.k	3	degree 3	$3q - 3q^{5} - 3q^{7} + O(q^{8})$	−
891.2.a.l	3	degree 3	$3q + 3q^{5} - 3q^{7} + O(q^{8})$	+
891.2.a.m	3	degree 3	$3q + 6q^{4} - 6q^{5} + O(q^{8})$	+
891.2.a.n	3	degree 3	$3q + 6q^{4} + 6q^{5} + O(q^{8})$	−
891.2.a.o	4	degree 4	$4q - 2q^{2} + 2q^{4} - 8q^{5} - 2q^{7} + O(q^{8})$	−
891.2.a.p	4	degree 4	$4q - q^{2} + 11q^{4} - 4q^{5} + q^{7} + O(q^{8})$	+
891.2.a.q	4	degree 4	$4q + q^{2} + 11q^{4} + 4q^{5} + q^{7} + O(q^{8})$	−
891.2.a.r	4	degree 4	$4q + 2q^{2} + 2q^{4} + 8q^{5} - 2q^{7} + O(q^{8})$	+

Hecke characteristic polynomials

The eigenvalue of $T = T_{2} + 3T_{5} + 5T_{7} + 7T_{13}$ generates each orbit's coefficient field; on the newspace its characteristic polynomial factors over $\mathbb{Q}$ as one irreducible factor per orbit:

Orbit	Characteristic polynomial of $T$
891.2.a.a	$x - 40$
891.2.a.b	$x - 35$
891.2.a.c	$x - 2$
891.2.a.d	$x + 15$
891.2.a.e	$x - 3$
891.2.a.f	$x - 43$
891.2.a.g	$x - 10$
891.2.a.h	$x - 56$
891.2.a.i	$x^{2} + 67x + 1119$
891.2.a.j	$x^{2} + 59x + 711$
891.2.a.k	$x^{3} + 87x^{2} + 1920x + 12563$
891.2.a.l	$x^{3} + 69x^{2} + 1260x + 6859$
891.2.a.m	$x^{3} + 18x^{2} - 1158x + 9421$
891.2.a.n	$x^{3} - 18x^{2} - 642x + 11909$
891.2.a.o	$x^{4} + 8x^{3} - 675x^{2} + 4958x - 7523$
891.2.a.p	$x^{4} - 41x^{3} - 1650x^{2} + 43309x + 867826$
891.2.a.q	$x^{4} - 67x^{3} - 1122x^{2} + 112385x - 979670$
891.2.a.r	$x^{4} - 44x^{3} - 1215x^{2} + 83434x - 1032443$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(891))$	40
Old forms	57
Cusp forms $S_{2}(\Gamma_0(891))$	97
Eisenstein series $E_{2}(\Gamma_0(891))$	23
Modular forms $M_{2}(\Gamma_0(891))$	120

Decomposition of the old subspace

$S_{2}^{\mathrm{old}}(\Gamma_0(891)) =$ $S_{2}^{\mathrm{new}}(\Gamma_0(11))^{\oplus 5}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(27))^{\oplus 4}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(33))^{\oplus 4}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(81))^{\oplus 2}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(99))^{\oplus 3}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(297))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.406 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, 3, 9, 11, 27, 33, 81, 99, 297, 891]: [0, 1, 2, 2, 4, 6, 10, 14, 38, 110] (certified at ell = 2147482801)
T = [(2, 1), (5, 3), (7, 5), (13, 7)]; h of degree 40 = 1 x 40 (phi(ord eps) x dim S_k^new); 9 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(891, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 891:2 1000

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