Atlas › Modular forms › Weight 2 › Level 890 › 890.2.a

Newspace 890.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(890))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	Elliptic curve
890.2.a.a	1	$\mathbb{Q}$	$q - q^{2} - 2q^{3} + q^{4} - q^{5} + 2q^{6} - 2q^{7} + O(q^{8})$	+ + +	$-1$	890b1 rank 1
890.2.a.b	1	$\mathbb{Q}$	$q - q^{2} - 2q^{3} + q^{4} + q^{5} + 2q^{6} + 2q^{7} + O(q^{8})$	+ − −	$-1$	890e1 rank 1
890.2.a.c	1	$\mathbb{Q}$	$q - q^{2} + q^{4} - q^{5} + 2q^{7} + O(q^{8})$	+ + +	$-1$	890a1 rank 1
890.2.a.d	1	$\mathbb{Q}$	$q - q^{2} + q^{3} + q^{4} + q^{5} - q^{6} - 4q^{7} + O(q^{8})$	+ − −	$-1$	890d1 rank 1
890.2.a.e	1	$\mathbb{Q}$	$q - q^{2} + 2q^{3} + q^{4} - q^{5} - 2q^{6} + 4q^{7} + O(q^{8})$	+ + −	$+1$	890c1 rank 0
890.2.a.f	1	$\mathbb{Q}$	$q + q^{2} - 3q^{3} + q^{4} - q^{5} - 3q^{6} + O(q^{8})$	− + −	$-1$	890f1 rank 1
890.2.a.g	1	$\mathbb{Q}$	$q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} - 2q^{7} + O(q^{8})$	− − +	$-1$	890g1 rank 1
890.2.a.h	1	$\mathbb{Q}$	$q + q^{2} + q^{4} + q^{5} + 4q^{7} + O(q^{8})$	− − −	$+1$	890h1 rank 0
890.2.a.i	2	$\mathbb{Q}(\sqrt{33})$	$2q - 2q^{2} - q^{3} + 2q^{4} - 2q^{5} + q^{6} - 4q^{7} + O(q^{8})$	+ + +	$-1$
890.2.a.j	2	$\mathbb{Q}(\sqrt{3})$	$2q + 2q^{2} + 2q^{4} - 2q^{5} - 6q^{7} + O(q^{8})$	− + −	$-1$
890.2.a.k	3	degree 3	$3q - 3q^{2} + q^{3} + 3q^{4} - 3q^{5} - q^{6} + O(q^{8})$	+ + −	$+1$
890.2.a.l	5	degree 5	$5q + 5q^{2} + q^{3} + 5q^{4} - 5q^{5} + q^{6} + 8q^{7} + O(q^{8})$	− + +	$+1$
890.2.a.m	5	degree 5	$5q + 5q^{2} + q^{3} + 5q^{4} + 5q^{5} + q^{6} + O(q^{8})$	− − −	$+1$
890.2.a.n	6	degree 6	$6q - 6q^{2} + 3q^{3} + 6q^{4} + 6q^{5} - 3q^{6} + 6q^{7} + O(q^{8})$	+ − +	$+1$

Hecke characteristic polynomials

The eigenvalue of $T = T_{3} + 2T_{7} + 3T_{17} + 4T_{19} + 5T_{23} + 6T_{11} + 7T_{13} + 8T_{29}$ 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 $T$
890.2.a.a	$x - 54$
890.2.a.b	$x + 48$
890.2.a.c	$x + 10$
890.2.a.d	$x + 45$
890.2.a.e	$x - 52$
890.2.a.f	$x + 21$
890.2.a.g	$x + 131$
890.2.a.h	$x - 36$
890.2.a.i	$x^{2} - 3x - 402$
890.2.a.j	$x^{2} + 108x + 216$
890.2.a.k	$x^{3} - 49x^{2} - 1249x - 2517$
890.2.a.l	$x^{5} - 111x^{4} - 1855x^{3} + 534543x^{2} - 18812200x + 199389900$
890.2.a.m	$x^{5} - 69x^{4} - 12565x^{3} + 681043x^{2} + 17559576x + 6534984$
890.2.a.n	$x^{6} - 97x^{5} - 1521x^{4} + 263913x^{3} + 1440846x^{2} - 199484612x - 2300296392$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(890))$	31
Old forms	100
Cusp forms $S_{2}(\Gamma_0(890))$	131
Eisenstein series $E_{2}(\Gamma_0(890))$	7
Modular forms $M_{2}(\Gamma_0(890))$	138

Decomposition of the old subspace

$S_{2}^{\mathrm{old}}(\Gamma_0(890)) =$ $S_{2}^{\mathrm{new}}(\Gamma_0(89))^{\oplus 4}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(178))^{\oplus 2}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(445))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.956 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, 89, 178, 445, 890]: [0, 1, 1, 3, 8, 24, 46, 138] (certified at ell = 2147482921)
T = [(3, 1), (7, 2), (17, 3), (19, 4), (23, 5), (11, 6), (13, 7), (29, 8)]; h of degree 31 = 1 x 31 (phi(ord eps) x dim S_k^new); 9 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(890, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 890:2 1000

← 889.2.a · 891.2.a →