Atlas › Modular forms › Weight 2 › Level 874 › 874.2.a

Newspace 874.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(874))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	Elliptic curve
874.2.a.a	1	$\mathbb{Q}$	$q - q^{2} - 3q^{3} + q^{4} + q^{5} + 3q^{6} + 2q^{7} + O(q^{8})$	+ + −	$+1$	874b1 rank 0
874.2.a.b	1	$\mathbb{Q}$	$q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} - 2q^{7} + O(q^{8})$	+ − −	$-1$	874c1 rank 1
874.2.a.c	1	$\mathbb{Q}$	$q - q^{2} + 3q^{3} + q^{4} + q^{5} - 3q^{6} + 2q^{7} + O(q^{8})$	+ + −	$+1$	874a1 rank 0
874.2.a.d	1	$\mathbb{Q}$	$q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} - 2q^{7} + O(q^{8})$	− + −	$-1$	874e1 rank 1
874.2.a.e	1	$\mathbb{Q}$	$q + q^{2} + q^{3} + q^{4} - 3q^{5} + q^{6} - 2q^{7} + O(q^{8})$	− + −	$-1$	874d1 rank 1
874.2.a.f	1	$\mathbb{Q}$	$q + q^{2} + q^{3} + q^{4} + 3q^{5} + q^{6} + 2q^{7} + O(q^{8})$	− − −	$+1$	874f1 rank 0
874.2.a.g	2	$\mathbb{Q}(\sqrt{5})$	$2q - 2q^{2} + 2q^{4} - q^{5} + q^{7} + O(q^{8})$	+ + −	$+1$
874.2.a.h	2	$\mathbb{Q}(\sqrt{2})$	$2q + 2q^{2} - 2q^{3} + 2q^{4} - 2q^{5} - 2q^{6} - 4q^{7} + O(q^{8})$	− − +	$-1$
874.2.a.i	3	degree 3	$3q - 3q^{2} - 2q^{3} + 3q^{4} - 3q^{5} + 2q^{6} + 5q^{7} + O(q^{8})$	+ − −	$-1$
874.2.a.j	4	degree 4	$4q - 4q^{2} - q^{3} + 4q^{4} - 4q^{5} + q^{6} + q^{7} + O(q^{8})$	+ + +	$-1$
874.2.a.k	4	degree 4	$4q - 4q^{2} + 2q^{3} + 4q^{4} - q^{5} - 2q^{6} - 5q^{7} + O(q^{8})$	+ − +	$+1$
874.2.a.l	5	degree 5	$5q + 5q^{2} - 2q^{3} + 5q^{4} - 2q^{6} + 2q^{7} + O(q^{8})$	− − −	$+1$
874.2.a.m	7	degree 7	$7q + 7q^{2} + q^{3} + 7q^{4} + 7q^{5} + q^{6} + O(q^{8})$	− + +	$+1$

Hecke characteristic polynomials

The eigenvalue of $T = T_{3} + 3T_{5}$ 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 $T$
874.2.a.a	$x$
874.2.a.b	$x + 4$
874.2.a.c	$x - 6$
874.2.a.d	$x - 2$
874.2.a.e	$x + 8$
874.2.a.f	$x - 10$
874.2.a.g	$x^{2} + 3x - 99$
874.2.a.h	$x^{2} + 8x + 14$
874.2.a.i	$x^{3} + 11x^{2} - 39x - 512$
874.2.a.j	$x^{4} + 13x^{3} - 51x^{2} - 404x + 1138$
874.2.a.k	$x^{4} + x^{3} - 93x^{2} - 234x + 478$
874.2.a.l	$x^{5} + 2x^{4} - 103x^{3} + 46x^{2} + 1669x - 506$
874.2.a.m	$x^{7} - 22x^{6} - 27x^{5} + 3406x^{4} - 20925x^{3} + 3812x^{2} + 143434x - 186692$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(874))$	33
Old forms	84
Cusp forms $S_{2}(\Gamma_0(874))$	117
Eisenstein series $E_{2}(\Gamma_0(874))$	7
Modular forms $M_{2}(\Gamma_0(874))$	124

Decomposition of the old subspace

$S_{2}^{\mathrm{old}}(\Gamma_0(874)) =$ $S_{2}^{\mathrm{new}}(\Gamma_0(19))^{\oplus 4}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(23))^{\oplus 4}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(38))^{\oplus 2}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(46))^{\oplus 2}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(437))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.323 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, 19, 23, 38, 46, 437, 874]: [0, 1, 2, 3, 7, 8, 42, 124] (certified at ell = 2147483647)
T = [(3, 1), (5, 3)]; h of degree 33 = 1 x 33 (phi(ord eps) x dim S_k^new); 5 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(874, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 874:2 1000

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