Atlas › Modular forms › Weight 2 › Level 894 › 894.2.a

Newspace 894.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(894))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	Elliptic curve
894.2.a.a	1	$\mathbb{Q}$	$q - q^{2} - q^{3} + q^{4} - 3q^{5} + q^{6} + O(q^{8})$	+ + +	$-1$	894b1 rank 1
894.2.a.b	1	$\mathbb{Q}$	$q - q^{2} - q^{3} + q^{4} + q^{6} + O(q^{8})$	+ + +	$-1$	894a1 rank 1
894.2.a.c	1	$\mathbb{Q}$	$q - q^{2} + q^{3} + q^{4} + q^{5} - q^{6} - 2q^{7} + O(q^{8})$	+ − −	$-1$	894d1 rank 1
894.2.a.d	1	$\mathbb{Q}$	$q - q^{2} + q^{3} + q^{4} + 3q^{5} - q^{6} + 2q^{7} + O(q^{8})$	+ − +	$+1$	894c1 rank 0
894.2.a.e	1	$\mathbb{Q}$	$q + q^{2} - q^{3} + q^{4} - 3q^{5} - q^{6} + 2q^{7} + O(q^{8})$	− + −	$-1$	894f1 rank 1
894.2.a.f	1	$\mathbb{Q}$	$q + q^{2} - q^{3} + q^{4} - q^{6} - 4q^{7} + O(q^{8})$	− + −	$-1$	894e1 rank 1
894.2.a.g	1	$\mathbb{Q}$	$q + q^{2} + q^{3} + q^{4} - 3q^{5} + q^{6} - 4q^{7} + O(q^{8})$	− − +	$-1$	894g1 rank 1
894.2.a.h	2	$\mathbb{Q}(\sqrt{33})$	$2q + 2q^{2} + 2q^{3} + 2q^{4} - q^{5} + 2q^{6} + 8q^{7} + O(q^{8})$	− − −	$+1$
894.2.a.i	3	degree 3	$3q + 3q^{2} + 3q^{3} + 3q^{4} + 3q^{5} + 3q^{6} - 3q^{7} + O(q^{8})$	− − −	$+1$
894.2.a.j	4	degree 4	$4q - 4q^{2} - 4q^{3} + 4q^{4} + 2q^{5} + 4q^{6} - 7q^{7} + O(q^{8})$	+ + −	$+1$
894.2.a.k	4	degree 4	$4q + 4q^{2} - 4q^{3} + 4q^{4} - 4q^{6} + 3q^{7} + O(q^{8})$	− + +	$+1$
894.2.a.l	5	degree 5	$5q - 5q^{2} + 5q^{3} + 5q^{4} - 5q^{5} - 5q^{6} + q^{7} + O(q^{8})$	+ − +	$+1$

Hecke characteristic polynomials

The eigenvalue of $T = T_{5} + 3T_{7}$ 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 $T$
894.2.a.a	$x + 3$
894.2.a.b	$x$
894.2.a.c	$x + 5$
894.2.a.d	$x - 9$
894.2.a.e	$x - 3$
894.2.a.f	$x + 12$
894.2.a.g	$x + 15$
894.2.a.h	$x^{2} - 23x + 124$
894.2.a.i	$x^{3} + 6x^{2} - 9x - 51$
894.2.a.j	$x^{4} + 19x^{3} - 47x^{2} - 1216x + 2705$
894.2.a.k	$x^{4} - 9x^{3} - 163x^{2} + 940x + 1319$
894.2.a.l	$x^{5} + 2x^{4} - 283x^{3} + 907x^{2} + 6462x + 6368$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(894))$	25
Old forms	122
Cusp forms $S_{2}(\Gamma_0(894))$	147
Eisenstein series $E_{2}(\Gamma_0(894))$	7
Modular forms $M_{2}(\Gamma_0(894))$	154

Decomposition of the old subspace

$S_{2}^{\mathrm{old}}(\Gamma_0(894)) =$ $S_{2}^{\mathrm{new}}(\Gamma_0(149))^{\oplus 4}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(298))^{\oplus 2}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(447))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.384 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, 149, 298, 447, 894]: [0, 1, 1, 3, 13, 39, 52, 154] (certified at ell = 2147481629)
T = [(5, 1), (7, 3)]; h of degree 25 = 1 x 25 (phi(ord eps) x dim S_k^new); 4 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(894, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 894:2 1000

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