Atlas › Modular forms › Weight 2 › Level 882 › 882.2.a

Newspace 882.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(882))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Elliptic curve
882.2.a.a	1	$\mathbb{Q}$	$q - q^{2} + q^{4} - 3q^{5} + O(q^{8})$	+	882a1 rank 1
882.2.a.b	1	$\mathbb{Q}$	$q - q^{2} + q^{4} - 2q^{5} + O(q^{8})$	+	882e1 rank 1
882.2.a.c	1	$\mathbb{Q}$	$q - q^{2} + q^{4} - q^{5} + O(q^{8})$	+	882c1 rank 0
882.2.a.d	1	$\mathbb{Q}$	$q - q^{2} + q^{4} + q^{5} + O(q^{8})$	+	882d1 rank 1
882.2.a.e	1	$\mathbb{Q}$	$q - q^{2} + q^{4} + 3q^{5} + O(q^{8})$	+	882b1 rank 0
882.2.a.f	1	$\mathbb{Q}$	$q + q^{2} + q^{4} - 4q^{5} + O(q^{8})$	−	882l1 rank 0
882.2.a.g	1	$\mathbb{Q}$	$q + q^{2} + q^{4} - 3q^{5} + O(q^{8})$	−	882h1 rank 1
882.2.a.h	1	$\mathbb{Q}$	$q + q^{2} + q^{4} - 3q^{5} + O(q^{8})$	−	882g1 rank 1
882.2.a.i	1	$\mathbb{Q}$	$q + q^{2} + q^{4} + O(q^{8})$	−	882i1 rank 0
882.2.a.j	1	$\mathbb{Q}$	$q + q^{2} + q^{4} + 3q^{5} + O(q^{8})$	−	882f1 rank 0
882.2.a.k	1	$\mathbb{Q}$	$q + q^{2} + q^{4} + 3q^{5} + O(q^{8})$	−	882j1 rank 0
882.2.a.l	1	$\mathbb{Q}$	$q + q^{2} + q^{4} + 4q^{5} + O(q^{8})$	−	882k1 rank 0
882.2.a.m	2	$\mathbb{Q}(\sqrt{2})$	$2q - 2q^{2} + 2q^{4} + O(q^{8})$	+
882.2.a.n	2	$\mathbb{Q}(\sqrt{2})$	$2q - 2q^{2} + 2q^{4} + O(q^{8})$	+
882.2.a.o	2	$\mathbb{Q}(\sqrt{2})$	$2q + 2q^{2} + 2q^{4} + O(q^{8})$	−

Hecke characteristic polynomials

The eigenvalue of $T = T_{5} + 2T_{11} + 3T_{13} + 4T_{17} + 5T_{19} + 6T_{23} + 7T_{29} + 8T_{31} + 9T_{37} + 10T_{41} + 11T_{43} + 12T_{47} + 13T_{53} + 14T_{59} + 15T_{61} + 16T_{67}$ 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 $T$
882.2.a.a	$x + 313$
882.2.a.b	$x + 260$
882.2.a.c	$x - 335$
882.2.a.d	$x + 95$
882.2.a.e	$x - 145$
882.2.a.f	$x - 250$
882.2.a.g	$x + 391$
882.2.a.h	$x + 149$
882.2.a.i	$x + 224$
882.2.a.j	$x + 91$
882.2.a.k	$x + 65$
882.2.a.l	$x - 106$
882.2.a.m	$x^{2} + 644x + 103106$
882.2.a.n	$x^{2} - 688x + 91886$
882.2.a.o	$x^{2} + 156x + 5922$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(882))$	18
Old forms	119
Cusp forms $S_{2}(\Gamma_0(882))$	137
Eisenstein series $E_{2}(\Gamma_0(882))$	63
Modular forms $M_{2}(\Gamma_0(882))$	200

Decomposition of the old subspace

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 3.048 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, 2, 3, 6, 7, 9, 14, 18, 21, 42, 49, 63, 98, 126, 147, 294, 441, 882]: [0, 1, 1, 3, 1, 2, 4, 5, 4, 12, 5, 10, 16, 28, 20, 60, 58, 172] (certified at ell = 2147483647)
T = [(5, 1), (11, 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 18 = 1 x 18 (phi(ord eps) x dim S_k^new); 7 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(882, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 882:2 1000

← 881.2.a · 883.2.a →