Atlas › Modular forms › Weight 4 › Level 143 › 143.4.a

Newspace 143.4.a: $S_{4}^{\mathrm{new}}(\Gamma_0(143))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign
143.4.a.a	4	degree 4	$4q - 4q^{3} + 6q^{4} - 6q^{5} - 13q^{6} - 17q^{7} + O(q^{8})$	+ −	$-1$
143.4.a.b	6	degree 6	$6q - 6q^{2} - 6q^{3} + 26q^{4} - 8q^{5} - 15q^{6} - 53q^{7} + O(q^{8})$	− +	$-1$
143.4.a.c	9	degree 9	$9q + 8q^{3} + 46q^{4} + 30q^{5} + 34q^{6} + 25q^{7} + O(q^{8})$	+ +	$+1$
143.4.a.d	11	degree 11	$11q + 6q^{2} + 6q^{3} + 66q^{4} - 4q^{5} - 14q^{6} + 45q^{7} + O(q^{8})$	− −	$+1$

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 $T$
143.4.a.a	$x^{4} + 4x^{3} - 30x^{2} + 15x + 4$
143.4.a.b	$x^{6} + 12x^{5} - 31x^{4} - 363x^{3} - 750x^{2} - 511x - 106$
143.4.a.c	$x^{9} - 8x^{8} - 228x^{7} + 1469x^{6} + 18148x^{5} - 89189x^{4} - 548824x^{3} + 2275194x^{2} + 5356779x - 20357814$
143.4.a.d	$x^{11} - 12x^{10} - 207x^{9} + 2151x^{8} + 17358x^{7} - 131460x^{6} - 699398x^{5} + 3247241x^{4} + 11800157x^{3} - 35275384x^{2} - 67069355x + 137663052$

Dimensions

Newforms $S_{4}^{\mathrm{new}}(\Gamma_0(143))$	30
Old forms	10
Cusp forms $S_{4}(\Gamma_0(143))$	40
Eisenstein series $E_{4}(\Gamma_0(143))$	4
Modular forms $M_{4}(\Gamma_0(143))$	44

Decomposition of the old subspace

$S_{4}^{\mathrm{old}}(\Gamma_0(143)) =$ $S_{4}^{\mathrm{new}}(\Gamma_0(11))^{\oplus 2}$ $\oplus$ $S_{4}^{\mathrm{new}}(\Gamma_0(13))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.116 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]: [1, 4, 5, 44] (certified at ell = 2147482921)
T = [(2, 1), (3, 1)]; h of degree 30 = 1 x 30 (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(143, 4)

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

cargo run --release -p sagebrush-web --example atlas -- 143:4 1000

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