Atlas › Modular forms › Weight 2 › Level 943 › 943.2.a

Newspace 943.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(943))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	Elliptic curve
943.2.a.a	1	$\mathbb{Q}$	$q + q^{2} - q^{4} - 2q^{5} + 2q^{7} + O(q^{8})$	+ −	$+1$	943a1 rank 0
943.2.a.b	13	degree 13	$13q - 6q^{2} - 5q^{3} + 10q^{4} - 6q^{5} + 2q^{6} - 7q^{7} + O(q^{8})$	− −	$-1$
943.2.a.c	16	degree 16	$16q - 7q^{2} - q^{3} + 15q^{4} - 12q^{5} - 7q^{7} + O(q^{8})$	+ +	$-1$
943.2.a.d	19	degree 19	$19q + 6q^{2} + 3q^{3} + 20q^{4} + 14q^{5} + 2q^{6} + 3q^{7} + O(q^{8})$	+ −	$+1$
943.2.a.e	24	degree 24	$24q + 9q^{2} + 3q^{3} + 31q^{4} + 12q^{5} + 4q^{6} - 3q^{7} + O(q^{8})$	− +	$+1$

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 $T$
943.2.a.a	$x - 1$
943.2.a.b	$x^{13} + 11x^{12} + 22x^{11} - 124x^{10} - 413x^{9} + 444x^{8} + 1943x^{7} - 1139x^{6} - 3526x^{5} + 2669x^{4} + 1725x^{3} - 2253x^{2} + 721x - 73$
943.2.a.c	$x^{16} + 8x^{15} - 18x^{14} - 252x^{13} - 44x^{12} + 2897x^{11} + 2512x^{10} - 15693x^{9} - 18286x^{8} + 41909x^{7} + 56009x^{6} - 50293x^{5} - 74634x^{4} + 18452x^{3} + 32333x^{2} - 840x - 1807$
943.2.a.d	$x^{19} - 9x^{18} - 37x^{17} + 531x^{16} - 128x^{15} - 10731x^{14} + 17487x^{13} + 91134x^{12} - 215276x^{11} - 322498x^{10} + 981673x^{9} + 397383x^{8} - 1744971x^{7} - 196916x^{6} + 1204106x^{5} + 153175x^{4} - 289094x^{3} - 73538x^{2} + 4815x + 1597$
943.2.a.e	$x^{24} - 12x^{23} - 26x^{22} + 788x^{21} - 1030x^{20} - 20411x^{19} + 53328x^{18} + 269443x^{17} - 938833x^{16} - 1999161x^{15} + 8637467x^{14} + 9014073x^{13} - 46745018x^{12} - 27391005x^{11} + 154506755x^{10} + 65750525x^{9} - 306155081x^{8} - 133506119x^{7} + 330323615x^{6} + 186667767x^{5} - 141875132x^{4} - 121940356x^{3} - 9903763x^{2} + 10565556x + 2179933$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(943))$	73
Old forms	10
Cusp forms $S_{2}(\Gamma_0(943))$	83
Eisenstein series $E_{2}(\Gamma_0(943))$	3
Modular forms $M_{2}(\Gamma_0(943))$	86

Decomposition of the old subspace

$S_{2}^{\mathrm{old}}(\Gamma_0(943)) =$ $S_{2}^{\mathrm{new}}(\Gamma_0(23))^{\oplus 2}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(41))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.283 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, 23, 41, 943]: [0, 3, 4, 86] (certified at ell = 2147482921)
T = [(2, 1), (3, 1)]; h of degree 73 = 1 x 73 (phi(ord eps) x dim S_k^new); 8 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(943, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 943:2 1000

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