Atlas › Modular forms › Weight 2 › Level 960 › 960.2.a

Newspace 960.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(960))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Elliptic curve
960.2.a.a	1	$\mathbb{Q}$	$q - q^{3} - q^{5} + O(q^{8})$	+ +	960i1 rank 0
960.2.a.b	1	$\mathbb{Q}$	$q - q^{3} - q^{5} + O(q^{8})$	+ +	960a1 rank 1
960.2.a.c	1	$\mathbb{Q}$	$q - q^{3} - q^{5} + O(q^{8})$	+ +	960b1 rank 1
960.2.a.d	1	$\mathbb{Q}$	$q - q^{3} - q^{5} + 4q^{7} + O(q^{8})$	+ +	960j1 rank 0
960.2.a.e	1	$\mathbb{Q}$	$q - q^{3} + q^{5} - 4q^{7} + O(q^{8})$	+ −	960e1 rank 0
960.2.a.f	1	$\mathbb{Q}$	$q - q^{3} + q^{5} + O(q^{8})$	+ −	960k1 rank 1
960.2.a.g	1	$\mathbb{Q}$	$q - q^{3} + q^{5} + 4q^{7} + O(q^{8})$	+ −	960c1 rank 0
960.2.a.h	1	$\mathbb{Q}$	$q - q^{3} + q^{5} + 4q^{7} + O(q^{8})$	+ −	960d1 rank 0
960.2.a.i	1	$\mathbb{Q}$	$q + q^{3} - q^{5} - 4q^{7} + O(q^{8})$	− +	960m1 rank 1
960.2.a.j	1	$\mathbb{Q}$	$q + q^{3} - q^{5} + O(q^{8})$	− +	960l1 rank 1
960.2.a.k	1	$\mathbb{Q}$	$q + q^{3} - q^{5} + O(q^{8})$	− +	960f1 rank 0
960.2.a.l	1	$\mathbb{Q}$	$q + q^{3} - q^{5} + O(q^{8})$	− +	960g1 rank 0
960.2.a.m	1	$\mathbb{Q}$	$q + q^{3} + q^{5} - 4q^{7} + O(q^{8})$	− −	960h1 rank 1
960.2.a.n	1	$\mathbb{Q}$	$q + q^{3} + q^{5} - 4q^{7} + O(q^{8})$	− −	960p1 rank 0
960.2.a.o	1	$\mathbb{Q}$	$q + q^{3} + q^{5} + O(q^{8})$	− −	960n1 rank 0
960.2.a.p	1	$\mathbb{Q}$	$q + q^{3} + q^{5} + 4q^{7} + O(q^{8})$	− −	960o1 rank 0

Hecke characteristic polynomials

The eigenvalue of $T = 3171T_{7} + 4390T_{11} + 6706T_{13} + 9950T_{17} + 7802T_{19} + 8602T_{23} + 4058T_{29} + 9130T_{31}$ 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 $T$
960.2.a.a	$x - 55076$
960.2.a.b	$x + 82140$
960.2.a.c	$x + 116092$
960.2.a.d	$x - 81960$
960.2.a.e	$x - 162200$
960.2.a.f	$x + 54532$
960.2.a.g	$x + 42656$
960.2.a.h	$x - 37056$
960.2.a.i	$x + 158304$
960.2.a.j	$x + 67548$
960.2.a.k	$x - 190948$
960.2.a.l	$x - 27780$
960.2.a.m	$x + 158888$
960.2.a.n	$x - 132024$
960.2.a.o	$x - 36604$
960.2.a.p	$x + 20928$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(960))$	16
Old forms	153
Cusp forms $S_{2}(\Gamma_0(960))$	169
Eisenstein series $E_{2}(\Gamma_0(960))$	47
Modular forms $M_{2}(\Gamma_0(960))$	216

Decomposition of the old subspace

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 3.651 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, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480, 960]: [0, 1, 1, 2, 1, 3, 3, 3, 5, 4, 4, 6, 8, 10, 6, 10, 12, 18, 10, 16, 20, 32, 28, 36, 56, 52, 104, 200] (certified at ell = 2147483489)
T = [(7, 3171), (11, 4390), (13, 6706), (17, 9950), (19, 7802), (23, 8602), (29, 4058), (31, 9130)]; h of degree 16 = 1 x 16 (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(960, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 960:2 1000

← 959.2.a · 961.2.a →