Properties

Label 672.2.cj
Level 672672
Weight 22
Character orbit 672.cj
Rep. character χ672(37,)\chi_{672}(37,\cdot)
Character field Q(ζ24)\Q(\zeta_{24})
Dimension 512512
Newform subspaces 11
Sturm bound 256256
Trace bound 00

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Defining parameters

Level: N N == 672=2537 672 = 2^{5} \cdot 3 \cdot 7
Weight: k k == 2 2
Character orbit: [χ][\chi] == 672.cj (of order 2424 and degree 88)
Character conductor: cond(χ)\operatorname{cond}(\chi) == 224 224
Character field: Q(ζ24)\Q(\zeta_{24})
Newform subspaces: 1 1
Sturm bound: 256256
Trace bound: 00

Dimensions

The following table gives the dimensions of various subspaces of M2(672,[χ])M_{2}(672, [\chi]).

Total New Old
Modular forms 1056 512 544
Cusp forms 992 512 480
Eisenstein series 64 0 64

Trace form

512q64q14+8q16+8q18+64q20+16q22+16q2340q28+96q31+48q3580q38+64q4032q438q4448q50+24q52+32q5332q58+88q98+O(q100) 512 q - 64 q^{14} + 8 q^{16} + 8 q^{18} + 64 q^{20} + 16 q^{22} + 16 q^{23} - 40 q^{28} + 96 q^{31} + 48 q^{35} - 80 q^{38} + 64 q^{40} - 32 q^{43} - 8 q^{44} - 48 q^{50} + 24 q^{52} + 32 q^{53} - 32 q^{58}+ \cdots - 88 q^{98}+O(q^{100}) Copy content Toggle raw display

Decomposition of S2new(672,[χ])S_{2}^{\mathrm{new}}(672, [\chi]) into newform subspaces

Label Char Prim Dim AA Field CM Minimal twist Traces Sato-Tate qq-expansion
a2a_{2} a3a_{3} a5a_{5} a7a_{7}
672.2.cj.a 672.cj 224.ad 512512 5.3665.366 None 672.2.cj.a 00 00 00 00 SU(2)[C24]\mathrm{SU}(2)[C_{24}]

Decomposition of S2old(672,[χ])S_{2}^{\mathrm{old}}(672, [\chi]) into lower level spaces

S2old(672,[χ]) S_{2}^{\mathrm{old}}(672, [\chi]) \simeq S2new(224,[χ])S_{2}^{\mathrm{new}}(224, [\chi])2^{\oplus 2}