Atlas › Modular forms › Weight 2 › Level 893 › 893.2.a

Newspace 893.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(893))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign
893.2.a.a	12	degree 12	$12q - q^{2} - 9q^{3} + 7q^{4} - 7q^{5} - 13q^{7} + O(q^{8})$	− −	$-1$
893.2.a.b	16	degree 16	$16q - 4q^{2} - 13q^{3} + 10q^{4} - q^{5} - 9q^{7} + O(q^{8})$	+ +	$-1$
893.2.a.c	18	degree 18	$18q + q^{2} + 13q^{3} + 21q^{4} + 5q^{5} + 6q^{6} + 3q^{7} + O(q^{8})$	+ −	$+1$
893.2.a.d	23	degree 23	$23q + q^{2} + 13q^{3} + 31q^{4} + q^{5} + 2q^{6} + 15q^{7} + O(q^{8})$	− +	$+1$

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 $T$
893.2.a.a	$x^{12} + 10x^{11} + 11x^{10} - 155x^{9} - 367x^{8} + 677x^{7} + 1892x^{6} - 973x^{5} - 2235x^{4} + 632x^{3} + 588x^{2} - 117x - 27$
893.2.a.b	$x^{16} + 17x^{15} + 93x^{14} + 54x^{13} - 1197x^{12} - 3306x^{11} + 3030x^{10} + 20928x^{9} + 6975x^{8} - 54304x^{7} - 34874x^{6} + 75090x^{5} + 40735x^{4} - 61657x^{3} - 10104x^{2} + 23117x - 5165$
893.2.a.c	$x^{18} - 14x^{17} + 27x^{16} + 449x^{15} - 2194x^{14} - 2501x^{13} + 31566x^{12} - 20376x^{11} - 187457x^{10} + 236402x^{9} + 568307x^{8} - 838197x^{7} - 1011786x^{6} + 1362149x^{5} + 1123987x^{4} - 1004995x^{3} - 703855x^{2} + 249097x + 163363$
893.2.a.d	$x^{23} - 14x^{22} + 6x^{21} + 727x^{20} - 2542x^{19} - 12617x^{18} + 74421x^{17} + 58617x^{16} - 908986x^{15} + 605273x^{14} + 5330573x^{13} - 7848145x^{12} - 14786238x^{11} + 33791207x^{10} + 14100828x^{9} - 67103658x^{8} + 12374221x^{7} + 60779511x^{6} - 29647482x^{5} - 21466791x^{4} + 14359283x^{3} + 2035950x^{2} - 1556484x - 174139$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(893))$	69
Old forms	10
Cusp forms $S_{2}(\Gamma_0(893))$	79
Eisenstein series $E_{2}(\Gamma_0(893))$	3
Modular forms $M_{2}(\Gamma_0(893))$	82

Decomposition of the old subspace

$S_{2}^{\mathrm{old}}(\Gamma_0(893)) =$ $S_{2}^{\mathrm{new}}(\Gamma_0(19))^{\oplus 2}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(47))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.27 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, 19, 47, 893]: [0, 2, 5, 82] (certified at ell = 2147479273)
T = [(2, 1), (3, 1)]; h of degree 69 = 1 x 69 (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(893, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 893:2 1000

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