Atlas › Modular forms › Weight 2 › Level 950 › 950.2.a

Newspace 950.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(950))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Elliptic curve
950.2.a.a	1	$\mathbb{Q}$	$q - q^{2} - q^{3} + q^{4} + q^{6} + q^{7} + O(q^{8})$	+ −	950b1 rank 0
950.2.a.b	1	$\mathbb{Q}$	$q - q^{2} + q^{3} + q^{4} - q^{6} - 3q^{7} + O(q^{8})$	+ +	950a1 rank 1
950.2.a.c	1	$\mathbb{Q}$	$q - q^{2} + 3q^{3} + q^{4} - 3q^{6} + 5q^{7} + O(q^{8})$	+ −	950c1 rank 0
950.2.a.d	1	$\mathbb{Q}$	$q + q^{2} - q^{3} + q^{4} - q^{6} + q^{7} + O(q^{8})$	− −	950e1 rank 1
950.2.a.e	1	$\mathbb{Q}$	$q + q^{2} + q^{3} + q^{4} + q^{6} + q^{7} + O(q^{8})$	− +	950d1 rank 0
950.2.a.f	2	$\mathbb{Q}(\sqrt{2})$	$2q - 2q^{2} + 2q^{3} + 2q^{4} - 2q^{6} + 6q^{7} + O(q^{8})$	+ +
950.2.a.g	2	$\mathbb{Q}(\sqrt{2})$	$2q + 2q^{2} - 2q^{3} + 2q^{4} - 2q^{6} - 6q^{7} + O(q^{8})$	− +
950.2.a.h	2	$\mathbb{Q}(\sqrt{17})$	$2q + 2q^{2} + q^{3} + 2q^{4} + q^{6} + q^{7} + O(q^{8})$	− +
950.2.a.i	3	degree 3	$3q - 3q^{2} - 2q^{3} + 3q^{4} + 2q^{6} - 4q^{7} + O(q^{8})$	+ −
950.2.a.j	3	degree 3	$3q - 3q^{2} - 2q^{3} + 3q^{4} + 2q^{6} - 2q^{7} + O(q^{8})$	+ −
950.2.a.k	3	degree 3	$3q - 3q^{2} - 2q^{3} + 3q^{4} + 2q^{6} - 2q^{7} + O(q^{8})$	+ +
950.2.a.l	3	degree 3	$3q + 3q^{2} + 2q^{3} + 3q^{4} + 2q^{6} + 2q^{7} + O(q^{8})$	− −
950.2.a.m	3	degree 3	$3q + 3q^{2} + 2q^{3} + 3q^{4} + 2q^{6} + 2q^{7} + O(q^{8})$	− +
950.2.a.n	3	degree 3	$3q + 3q^{2} + 2q^{3} + 3q^{4} + 2q^{6} + 4q^{7} + O(q^{8})$	− −

Hecke characteristic polynomials

The eigenvalue of $T = T_{3} + 2T_{7} + 3T_{11} + 4T_{13} + 5T_{17} + 6T_{23} + 7T_{29} + 8T_{31} + 9T_{37} + 10T_{41} + 11T_{43} + 12T_{47}$ 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 $T$
950.2.a.a	$x - 125$
950.2.a.b	$x + 305$
950.2.a.c	$x + 167$
950.2.a.d	$x + 145$
950.2.a.e	$x - 61$
950.2.a.f	$x^{2} - 230x - 3337$
950.2.a.g	$x^{2} + 250x - 4777$
950.2.a.h	$x^{2} - 339x - 4934$
950.2.a.i	$x^{3} + 192x^{2} + 10503x + 140670$
950.2.a.j	$x^{3} - 209x^{2} + 11636x - 188263$
950.2.a.k	$x^{3} + 95x^{2} - 1192x - 63015$
950.2.a.l	$x^{3} - 15x^{2} - 11658x + 408735$
950.2.a.m	$x^{3} - 79x^{2} - 70802x - 689497$
950.2.a.n	$x^{3} - 184x^{2} - 9313x + 538862$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(950))$	29
Old forms	110
Cusp forms $S_{2}(\Gamma_0(950))$	139
Eisenstein series $E_{2}(\Gamma_0(950))$	23
Modular forms $M_{2}(\Gamma_0(950))$	162

Decomposition of the old subspace

$S_{2}^{\mathrm{old}}(\Gamma_0(950)) =$ $S_{2}^{\mathrm{new}}(\Gamma_0(19))^{\oplus 6}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(38))^{\oplus 3}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(50))^{\oplus 2}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(95))^{\oplus 4}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(190))^{\oplus 2}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(475))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 1.806 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, 5, 10, 19, 25, 38, 50, 95, 190, 475, 950]: [0, 1, 1, 3, 2, 3, 7, 9, 12, 34, 52, 154] (certified at ell = 2147482801)
T = [(3, 1), (7, 2), (11, 3), (13, 4), (17, 5), (23, 6), (29, 7), (31, 8), (37, 9), (41, 10), (43, 11), (47, 12)]; h of degree 29 = 1 x 29 (phi(ord eps) x dim S_k^new); 10 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(950, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 950:2 1000

← 949.2.a · 951.2.a →