Atlas › Modular forms › Weight 2 › Level 889 › 889.2.a

Newspace 889.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(889))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign
889.2.a.a	12	degree 12	$12q - 7q^{2} - 4q^{3} + 9q^{4} - 7q^{5} - 2q^{6} + 12q^{7} + O(q^{8})$	− −	$-1$
889.2.a.b	15	degree 15	$15q + 4q^{3} + 14q^{4} + 7q^{5} + 8q^{6} - 15q^{7} + O(q^{8})$	+ −	$+1$
889.2.a.c	16	degree 16	$16q - 2q^{2} - 4q^{3} + 12q^{4} - 9q^{5} - 12q^{6} - 16q^{7} + O(q^{8})$	+ +	$-1$
889.2.a.d	20	degree 20	$20q + 8q^{2} + 24q^{4} + 3q^{5} + 6q^{6} + 20q^{7} + O(q^{8})$	− +	$+1$

Hecke characteristic polynomials

The eigenvalue of $T = T_{2} + T_{3}$ 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 $T$
889.2.a.a	$x^{12} + 11x^{11} + 29x^{10} - 64x^{9} - 373x^{8} - 298x^{7} + 611x^{6} + 898x^{5} + 58x^{4} - 342x^{3} - 146x^{2} - 21x - 1$
889.2.a.b	$x^{15} - 4x^{14} - 49x^{13} + 183x^{12} + 795x^{11} - 2534x^{10} - 5816x^{9} + 12232x^{8} + 23195x^{7} - 18713x^{6} - 41176x^{5} + 1205x^{4} + 25916x^{3} + 10258x^{2} - 854x - 691$
889.2.a.c	$x^{16} + 6x^{15} - 23x^{14} - 165x^{13} + 218x^{12} + 1835x^{11} - 1263x^{10} - 10574x^{9} + 5684x^{8} + 32989x^{7} - 18945x^{6} - 51413x^{5} + 35124x^{4} + 29146x^{3} - 23456x^{2} - 300x + 1681$
889.2.a.d	$x^{20} - 8x^{19} - 51x^{18} + 541x^{17} + 547x^{16} - 13299x^{15} + 7394x^{14} + 158777x^{13} - 196010x^{12} - 1010024x^{11} + 1579950x^{10} + 3487473x^{9} - 5931582x^{8} - 6432909x^{7} + 10767695x^{6} + 6439893x^{5} - 9049055x^{4} - 3575206x^{3} + 3089232x^{2} + 794926x - 302981$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(889))$	63
Old forms	20
Cusp forms $S_{2}(\Gamma_0(889))$	83
Eisenstein series $E_{2}(\Gamma_0(889))$	3
Modular forms $M_{2}(\Gamma_0(889))$	86

Decomposition of the old subspace

$S_{2}^{\mathrm{old}}(\Gamma_0(889)) =$ $S_{2}^{\mathrm{new}}(\Gamma_0(127))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.258 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, 7, 127, 889]: [0, 1, 11, 86] (certified at ell = 2147483647)
T = [(2, 1), (3, 1)]; h of degree 63 = 1 x 63 (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(889, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 889:2 1000

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