Atlas › Modular forms › Weight 2 › Level 143 › 143.2.a

Newspace 143.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(143))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	Elliptic curve
143.2.a.a	1	$\mathbb{Q}$	$q - q^{3} - 2q^{4} - q^{5} - 2q^{7} + O(q^{8})$	+ +	$-1$	143a1 rank 1
143.2.a.b	4	degree 4	$4q + 3q^{2} + 3q^{4} - q^{6} + 6q^{7} + O(q^{8})$	− +	$+1$
143.2.a.c	6	degree 6	$6q + 3q^{3} + 8q^{4} + q^{5} - 3q^{6} + 4q^{7} + O(q^{8})$	+ −	$+1$

Hecke characteristic polynomials

The eigenvalue of $T = T_{2} + T_{3}$ 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 $T$
143.2.a.a	$x + 1$
143.2.a.b	$x^{4} - 3x^{3} - 7x^{2} + 29x - 21$
143.2.a.c	$x^{6} - 3x^{5} - 18x^{4} + 50x^{3} - 2x^{2} - 45x + 5$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(143))$	11
Old forms	2
Cusp forms $S_{2}(\Gamma_0(143))$	13
Eisenstein series $E_{2}(\Gamma_0(143))$	3
Modular forms $M_{2}(\Gamma_0(143))$	16

Decomposition of the old subspace

$S_{2}^{\mathrm{old}}(\Gamma_0(143)) =$ $S_{2}^{\mathrm{new}}(\Gamma_0(11))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.172 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, 11, 13, 143]: [0, 2, 1, 16] (certified at ell = 2147482921)
T = [(2, 1), (3, 1)]; h of degree 11 = 1 x 11 (phi(ord eps) x dim S_k^new); 2 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(143, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 143:2 1000

← 142.2.a · 144.2.a →