Atlas › Modular forms › Weight 2 › Level 923 › 923.2.a

Newspace 923.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(923))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	Elliptic curve
923.2.a.a	1	$\mathbb{Q}$	$q + 3q^{3} - 2q^{4} + 2q^{5} + O(q^{8})$	+ −	$+1$	923a1 rank 0
923.2.a.b	10	degree 10	$10q - q^{2} - 4q^{3} + 3q^{4} - 6q^{5} - 3q^{6} - 9q^{7} + O(q^{8})$	− −	$-1$
923.2.a.c	16	degree 16	$16q - 4q^{2} - 4q^{3} + 10q^{4} - 10q^{5} - 5q^{6} - 13q^{7} + O(q^{8})$	+ +	$-1$
923.2.a.d	18	degree 18	$18q + 3q^{2} - q^{3} + 23q^{4} + 6q^{5} + 3q^{6} + 11q^{7} + O(q^{8})$	+ −	$+1$
923.2.a.e	26	degree 26	$26q + 3q^{2} + 6q^{3} + 35q^{4} + 6q^{5} - 7q^{6} + 7q^{7} + O(q^{8})$	− +	$+1$

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 $T$
923.2.a.a	$x - 3$
923.2.a.b	$x^{10} + 5x^{9} - 9x^{8} - 62x^{7} + 7x^{6} + 230x^{5} + 27x^{4} - 349x^{3} + 13x^{2} + 197x - 67$
923.2.a.c	$x^{16} + 8x^{15} - 14x^{14} - 230x^{13} - 96x^{12} + 2444x^{11} + 2301x^{10} - 12583x^{9} - 12982x^{8} + 32937x^{7} + 30667x^{6} - 40584x^{5} - 29767x^{4} + 17897x^{3} + 8468x^{2} + 852x + 8$
923.2.a.d	$x^{18} - 2x^{17} - 65x^{16} + 79x^{15} + 1649x^{14} - 701x^{13} - 20430x^{12} - 6325x^{11} + 125207x^{10} + 117488x^{9} - 320524x^{8} - 480680x^{7} + 159569x^{6} + 460727x^{5} - 3245x^{4} - 177487x^{3} - 2006x^{2} + 24905x - 1701$
923.2.a.e	$x^{26} - 9x^{25} - 52x^{24} + 654x^{23} + 635x^{22} - 19430x^{21} + 12300x^{20} + 305673x^{19} - 444313x^{18} - 2765065x^{17} + 5492212x^{16} + 14751618x^{15} - 35632024x^{14} - 46795977x^{13} + 132809607x^{12} + 90212119x^{11} - 293887222x^{10} - 114827725x^{9} + 388760461x^{8} + 114960573x^{7} - 299714258x^{6} - 95681372x^{5} + 121336227x^{4} + 51487607x^{3} - 17239872x^{2} - 11729116x - 1561960$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(923))$	71
Old forms	12
Cusp forms $S_{2}(\Gamma_0(923))$	83
Eisenstein series $E_{2}(\Gamma_0(923))$	3
Modular forms $M_{2}(\Gamma_0(923))$	86

Decomposition of the old subspace

$S_{2}^{\mathrm{old}}(\Gamma_0(923)) =$ $S_{2}^{\mathrm{new}}(\Gamma_0(71))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.269 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, 13, 71, 923]: [0, 1, 7, 86] (certified at ell = 2147482681)
T = [(2, 1), (3, 1)]; h of degree 71 = 1 x 71 (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(923, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 923:2 1000

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