๐ŸŒฟ Sagebrush Atlas
Atlas โ€บ Modular forms โ€บ Weight 2 โ€บ Level 952 โ€บ 952.2.a

Newspace 952.2.a: S2new(ฮ“0(952))S_{2}^{\mathrm{new}}(\Gamma_0(952))

Newforms

LabelDimCoefficient fieldTrace formAL signsSignCMElliptic curve
952.2.a.a2Q(5)\mathbb{Q}(\sqrt{5}) 2qโˆ’q3โˆ’3q5+2q7+O(q8)2q - q^{3} - 3q^{5} + 2q^{7} + O(q^{8})โˆ’ โˆ’
952.2.a.b2Q(13)\mathbb{Q}(\sqrt{13}) 2q+q3โˆ’3q5โˆ’2q7+O(q8)2q + q^{3} - 3q^{5} - 2q^{7} + O(q^{8})+ โˆ’
952.2.a.c3degree 3 3qโˆ’3q3โˆ’5q5+3q7+O(q8)3q - 3q^{3} - 5q^{5} + 3q^{7} + O(q^{8})โˆ’ +
952.2.a.d3degree 3 3qโˆ’3q3+q5โˆ’3q7+O(q8)3q - 3q^{3} + q^{5} - 3q^{7} + O(q^{8})+ +
952.2.a.e3degree 3 3qโˆ’q3+3q5โˆ’3q7+O(q8)3q - q^{3} + 3q^{5} - 3q^{7} + O(q^{8})+ +
952.2.a.f3degree 3 3q+q3+3q5+3q7+O(q8)3q + q^{3} + 3q^{5} + 3q^{7} + O(q^{8})โˆ’ +
952.2.a.g4degree 4 4q+3q3โˆ’q5โˆ’4q7+O(q8)4q + 3q^{3} - q^{5} - 4q^{7} + O(q^{8})+ โˆ’
952.2.a.h4degree 4 4q+3q3+5q5+4q7+O(q8)4q + 3q^{3} + 5q^{5} + 4q^{7} + O(q^{8})โˆ’ โˆ’

Hecke characteristic polynomials

The eigenvalue of T=T3+3T5T = T_{3} + 3T_{5} generates each orbit's coefficient field; on the newspace its characteristic polynomial factors over Q\mathbb{Q} as one irreducible factor per orbit:

OrbitCharacteristic polynomial of TT
952.2.a.ax2+10x+5x^{2} + 10x + 5
952.2.a.bx2+8x+3x^{2} + 8x + 3
952.2.a.cx3+18x2+47xโˆ’182x^{3} + 18x^{2} + 47x - 182
952.2.a.dx3โˆ’43xโˆ’106x^{3} - 43x - 106
952.2.a.ex3โˆ’8x2โˆ’115x+918x^{3} - 8x^{2} - 115x + 918
952.2.a.fx3โˆ’10x2โˆ’17x+262x^{3} - 10x^{2} - 17x + 262
952.2.a.gx4โˆ’185x2โˆ’400x+100x^{4} - 185x^{2} - 400x + 100
952.2.a.hx4โˆ’18x3+49x2+124xโˆ’236x^{4} - 18x^{3} + 49x^{2} + 124x - 236

Dimensions

Newforms S2new(ฮ“0(952))S_{2}^{\mathrm{new}}(\Gamma_0(952))24
Old forms113
Cusp forms S2(ฮ“0(952))S_{2}(\Gamma_0(952))137
Eisenstein series E2(ฮ“0(952))E_{2}(\Gamma_0(952))15
Modular forms M2(ฮ“0(952))M_{2}(\Gamma_0(952))152

Decomposition of the old subspace

S2old(ฮ“0(952))=S_{2}^{\mathrm{old}}(\Gamma_0(952)) = S2new(ฮ“0(14))โŠ•6S_{2}^{\mathrm{new}}(\Gamma_0(14))^{\oplus 6} โŠ•\oplus S2new(ฮ“0(17))โŠ•8S_{2}^{\mathrm{new}}(\Gamma_0(17))^{\oplus 8} โŠ•\oplus S2new(ฮ“0(34))โŠ•6S_{2}^{\mathrm{new}}(\Gamma_0(34))^{\oplus 6} โŠ•\oplus S2new(ฮ“0(56))โŠ•2S_{2}^{\mathrm{new}}(\Gamma_0(56))^{\oplus 2} โŠ•\oplus S2new(ฮ“0(68))โŠ•4S_{2}^{\mathrm{new}}(\Gamma_0(68))^{\oplus 4} โŠ•\oplus S2new(ฮ“0(119))โŠ•4S_{2}^{\mathrm{new}}(\Gamma_0(119))^{\oplus 4} โŠ•\oplus S2new(ฮ“0(136))โŠ•2S_{2}^{\mathrm{new}}(\Gamma_0(136))^{\oplus 2} โŠ•\oplus S2new(ฮ“0(238))โŠ•3S_{2}^{\mathrm{new}}(\Gamma_0(238))^{\oplus 3} โŠ•\oplus S2new(ฮ“0(476))โŠ•2S_{2}^{\mathrm{new}}(\Gamma_0(476))^{\oplus 2}

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.588 s (one thread) and proven: the dimensions are certified, and the characteristic polynomial of TT over Z\mathbb{Z} is reconstructed by CRT past a rigorous coefficient bound.

The engine's checks
  • dim M^+ at levels [1, 2, 4, 7, 8, 14, 17, 28, 34, 56, 68, 119, 136, 238, 476, 952]: [0, 1, 2, 1, 3, 4, 2, 7, 6, 12, 12, 14, 22, 40, 78, 152] (certified at ell = 2147483137)
  • T = [(3, 1), (5, 3)]; h of degree 24 = 1 x 24 (phi(ord eps) x dim S_k^new); 4 primes, 0 rejected
Open in the notebook ยท JSON ยท stored data
Recompute it yourself

In Sage mode at sagebrush.space (or npx sagebrush --sage):

newform_orbits(952, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 952:2 1000

โ† 951.2.a ยท 953.2.a โ†’