Atlas › Modular forms › Weight 2 › Level 483 › 483.2.a

Newspace 483.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(483))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	Elliptic curve
483.2.a.a	1	$\mathbb{Q}$	$q + 2q^{2} + q^{3} + 2q^{4} + 2q^{6} + q^{7} + O(q^{8})$	− − −	$+1$	483b1 rank 0
483.2.a.b	1	$\mathbb{Q}$	$q + 2q^{2} + q^{3} + 2q^{4} + 4q^{5} + 2q^{6} - q^{7} + O(q^{8})$	− + +	$+1$	483a1 rank 0
483.2.a.c	2	$\mathbb{Q}(\sqrt{5})$	$2q - 3q^{2} + 2q^{3} + 3q^{4} - 5q^{5} - 3q^{6} + 2q^{7} + O(q^{8})$	− − +	$-1$
483.2.a.d	2	$\mathbb{Q}(\sqrt{5})$	$2q - q^{2} - 2q^{3} - q^{4} + q^{5} + q^{6} - 2q^{7} + O(q^{8})$	+ + +	$-1$
483.2.a.e	2	$\mathbb{Q}(\sqrt{5})$	$2q - q^{2} + 2q^{3} - q^{4} + 5q^{5} - q^{6} + 2q^{7} + O(q^{8})$	− − −	$+1$
483.2.a.f	2	$\mathbb{Q}(\sqrt{13})$	$2q - q^{2} + 2q^{3} + 3q^{4} - 5q^{5} - q^{6} - 2q^{7} + O(q^{8})$	− + −	$-1$
483.2.a.g	2	$\mathbb{Q}(\sqrt{5})$	$2q + q^{2} - 2q^{3} - q^{4} - 3q^{5} - q^{6} + 2q^{7} + O(q^{8})$	+ − −	$-1$
483.2.a.h	3	degree 3	$3q + 3q^{3} + 6q^{4} + 3q^{5} - 3q^{7} + O(q^{8})$	− + +	$+1$
483.2.a.i	4	degree 4	$4q - 4q^{3} + 4q^{4} + 5q^{5} + 4q^{7} + O(q^{8})$	+ − +	$+1$
483.2.a.j	4	degree 4	$4q + 2q^{2} - 4q^{3} + 4q^{4} + 5q^{5} - 2q^{6} - 4q^{7} + O(q^{8})$	+ + −	$+1$

Hecke characteristic polynomials

The eigenvalue of $T = T_{2} + 3T_{5}$ 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 $T$
483.2.a.a	$x - 2$
483.2.a.b	$x - 14$
483.2.a.c	$x^{2} + 18x + 61$
483.2.a.d	$x^{2} - 2x - 19$
483.2.a.e	$x^{2} - 14x + 29$
483.2.a.f	$x^{2} + 16x + 51$
483.2.a.g	$x^{2} + 8x + 11$
483.2.a.h	$x^{3} - 9x^{2} + 3x + 53$
483.2.a.i	$x^{4} - 15x^{3} - 27x^{2} + 595x + 1478$
483.2.a.j	$x^{4} - 17x^{3} - 7x^{2} + 1241x - 4786$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(483))$	23
Old forms	38
Cusp forms $S_{2}(\Gamma_0(483))$	61
Eisenstein series $E_{2}(\Gamma_0(483))$	7
Modular forms $M_{2}(\Gamma_0(483))$	68

Decomposition of the old subspace

$S_{2}^{\mathrm{old}}(\Gamma_0(483)) =$ $S_{2}^{\mathrm{new}}(\Gamma_0(21))^{\oplus 2}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(23))^{\oplus 4}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(69))^{\oplus 2}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(161))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.228 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, 3, 7, 21, 23, 69, 161, 483]: [0, 1, 1, 4, 3, 10, 18, 68] (certified at ell = 2147483647)
T = [(2, 1), (5, 3)]; h of degree 23 = 1 x 23 (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(483, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 483:2 1000

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