Properties

Label 155.2.q
Level 155155
Weight 22
Character orbit 155.q
Rep. character χ155(41,)\chi_{155}(41,\cdot)
Character field Q(ζ15)\Q(\zeta_{15})
Dimension 8080
Newform subspaces 22
Sturm bound 3232
Trace bound 22

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Defining parameters

Level: N N == 155=531 155 = 5 \cdot 31
Weight: k k == 2 2
Character orbit: [χ][\chi] == 155.q (of order 1515 and degree 88)
Character conductor: cond(χ)\operatorname{cond}(\chi) == 31 31
Character field: Q(ζ15)\Q(\zeta_{15})
Newform subspaces: 2 2
Sturm bound: 3232
Trace bound: 22
Distinguishing TpT_p: 22

Dimensions

The following table gives the dimensions of various subspaces of M2(155,[χ])M_{2}(155, [\chi]).

Total New Old
Modular forms 144 80 64
Cusp forms 112 80 32
Eisenstein series 32 0 32

Trace form

80q+2q312q48q6+2q718q8+8q92q1012q1114q124q1316q148q158q166q17+10q1822q194q2032q21++70q99+O(q100) 80 q + 2 q^{3} - 12 q^{4} - 8 q^{6} + 2 q^{7} - 18 q^{8} + 8 q^{9} - 2 q^{10} - 12 q^{11} - 14 q^{12} - 4 q^{13} - 16 q^{14} - 8 q^{15} - 8 q^{16} - 6 q^{17} + 10 q^{18} - 22 q^{19} - 4 q^{20} - 32 q^{21}+ \cdots + 70 q^{99}+O(q^{100}) Copy content Toggle raw display

Decomposition of S2new(155,[χ])S_{2}^{\mathrm{new}}(155, [\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}
155.2.q.a 155.q 31.g 4040 1.2381.238 None 155.2.q.a 2-2 1-1 2020 44 SU(2)[C15]\mathrm{SU}(2)[C_{15}]
155.2.q.b 155.q 31.g 4040 1.2381.238 None 155.2.q.b 22 33 20-20 2-2 SU(2)[C15]\mathrm{SU}(2)[C_{15}]

Decomposition of S2old(155,[χ])S_{2}^{\mathrm{old}}(155, [\chi]) into lower level spaces

S2old(155,[χ]) S_{2}^{\mathrm{old}}(155, [\chi]) \simeq S2new(31,[χ])S_{2}^{\mathrm{new}}(31, [\chi])2^{\oplus 2}