Atlas › Modular forms › Weight 2 › Level 918 › 918.2.a

Newspace 918.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(918))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Elliptic curve
918.2.a.a	1	$\mathbb{Q}$	$q - q^{2} + q^{4} - 3q^{5} + 2q^{7} + O(q^{8})$	+ −	918f1 rank 1
918.2.a.b	1	$\mathbb{Q}$	$q - q^{2} + q^{4} - q^{5} - 2q^{7} + O(q^{8})$	+ +	918a1 rank 1
918.2.a.c	1	$\mathbb{Q}$	$q - q^{2} + q^{4} - q^{5} + 3q^{7} + O(q^{8})$	+ +	918b1 rank 1
918.2.a.d	1	$\mathbb{Q}$	$q - q^{2} + q^{4} - 4q^{7} + O(q^{8})$	+ −	918e1 rank 1
918.2.a.e	1	$\mathbb{Q}$	$q - q^{2} + q^{4} + 2q^{5} - 2q^{7} + O(q^{8})$	+ +	918c1 rank 1
918.2.a.f	1	$\mathbb{Q}$	$q - q^{2} + q^{4} + 3q^{5} - q^{7} + O(q^{8})$	+ −	918d1 rank 0
918.2.a.g	1	$\mathbb{Q}$	$q + q^{2} + q^{4} - 3q^{5} - q^{7} + O(q^{8})$	− +	918j1 rank 1
918.2.a.h	1	$\mathbb{Q}$	$q + q^{2} + q^{4} - 2q^{5} - 2q^{7} + O(q^{8})$	− −	918h1 rank 1
918.2.a.i	1	$\mathbb{Q}$	$q + q^{2} + q^{4} - 4q^{7} + O(q^{8})$	− +	918i1 rank 1
918.2.a.j	1	$\mathbb{Q}$	$q + q^{2} + q^{4} + q^{5} - 2q^{7} + O(q^{8})$	− −	918k1 rank 0
918.2.a.k	1	$\mathbb{Q}$	$q + q^{2} + q^{4} + q^{5} + 3q^{7} + O(q^{8})$	− −	918l1 rank 0
918.2.a.l	1	$\mathbb{Q}$	$q + q^{2} + q^{4} + 3q^{5} + 2q^{7} + O(q^{8})$	− +	918g1 rank 0
918.2.a.m	2	$\mathbb{Q}(\sqrt{6})$	$2q - 2q^{2} + 2q^{4} + 4q^{7} + O(q^{8})$	+ −
918.2.a.n	2	$\mathbb{Q}(\sqrt{7})$	$2q - 2q^{2} + 2q^{4} + 2q^{5} + 2q^{7} + O(q^{8})$	+ +
918.2.a.o	2	$\mathbb{Q}(\sqrt{7})$	$2q + 2q^{2} + 2q^{4} - 2q^{5} + 2q^{7} + O(q^{8})$	− −
918.2.a.p	2	$\mathbb{Q}(\sqrt{6})$	$2q + 2q^{2} + 2q^{4} + 4q^{7} + O(q^{8})$	− +

Hecke characteristic polynomials

The eigenvalue of $T = 3208T_{5} + 171T_{7} + 940T_{11} + 6115T_{13} + 4440T_{19} + 6039T_{23} + 7794T_{29} + 3537T_{31}$ 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 $T$
918.2.a.a	$x + 28720$
918.2.a.b	$x + 63034$
918.2.a.c	$x + 16814$
918.2.a.d	$x + 64111$
918.2.a.e	$x + 104737$
918.2.a.f	$x - 64982$
918.2.a.g	$x + 125902$
918.2.a.h	$x - 2077$
918.2.a.i	$x + 39157$
918.2.a.j	$x - 161200$
918.2.a.k	$x + 42290$
918.2.a.l	$x + 20002$
918.2.a.m	$x^{2} - 20818x - 1047246023$
918.2.a.n	$x^{2} - 103002x + 2487151853$
918.2.a.o	$x^{2} - 52638x - 1079206939$
918.2.a.p	$x^{2} - 93286x + 323340049$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(918))$	20
Old forms	131
Cusp forms $S_{2}(\Gamma_0(918))$	151
Eisenstein series $E_{2}(\Gamma_0(918))$	23
Modular forms $M_{2}(\Gamma_0(918))$	174

Decomposition of the old subspace

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 1.915 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, 6, 9, 17, 18, 27, 34, 51, 54, 102, 153, 306, 459, 918]: [0, 1, 1, 3, 2, 2, 5, 4, 6, 8, 11, 22, 20, 58, 56, 166] (certified at ell = 2147482801)
T = [(5, 3208), (7, 171), (11, 940), (13, 6115), (19, 4440), (23, 6039), (29, 7794), (31, 3537)]; h of degree 20 = 1 x 20 (phi(ord eps) x dim S_k^new); 12 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(918, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 918:2 1000

← 917.2.a · 919.2.a →