Properties

Label 165.4.w
Level 165165
Weight 44
Character orbit 165.w
Rep. character χ165(7,)\chi_{165}(7,\cdot)
Character field Q(ζ20)\Q(\zeta_{20})
Dimension 288288
Newform subspaces 11
Sturm bound 9696
Trace bound 00

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Defining parameters

Level: N N == 165=3511 165 = 3 \cdot 5 \cdot 11
Weight: k k == 4 4
Character orbit: [χ][\chi] == 165.w (of order 2020 and degree 88)
Character conductor: cond(χ)\operatorname{cond}(\chi) == 55 55
Character field: Q(ζ20)\Q(\zeta_{20})
Newform subspaces: 1 1
Sturm bound: 9696
Trace bound: 00

Dimensions

The following table gives the dimensions of various subspaces of M4(165,[χ])M_{4}(165, [\chi]).

Total New Old
Modular forms 608 288 320
Cusp forms 544 288 256
Eisenstein series 64 0 64

Trace form

288q+32q540q756q11+48q12252q15+1264q16640q17+1140q20+356q22224q23232q25+240q26+720q282040q30432q31228q33++9744q97+O(q100) 288 q + 32 q^{5} - 40 q^{7} - 56 q^{11} + 48 q^{12} - 252 q^{15} + 1264 q^{16} - 640 q^{17} + 1140 q^{20} + 356 q^{22} - 224 q^{23} - 232 q^{25} + 240 q^{26} + 720 q^{28} - 2040 q^{30} - 432 q^{31} - 228 q^{33}+ \cdots + 9744 q^{97}+O(q^{100}) Copy content Toggle raw display

Decomposition of S4new(165,[χ])S_{4}^{\mathrm{new}}(165, [\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}
165.4.w.a 165.w 55.l 288288 9.7359.735 None 165.4.w.a 00 00 3232 40-40 SU(2)[C20]\mathrm{SU}(2)[C_{20}]

Decomposition of S4old(165,[χ])S_{4}^{\mathrm{old}}(165, [\chi]) into lower level spaces

S4old(165,[χ]) S_{4}^{\mathrm{old}}(165, [\chi]) \simeq S4new(55,[χ])S_{4}^{\mathrm{new}}(55, [\chi])2^{\oplus 2}