Properties

Label 975.2.cq
Level 975975
Weight 22
Character orbit 975.cq
Rep. character χ975(28,)\chi_{975}(28,\cdot)
Character field Q(ζ60)\Q(\zeta_{60})
Dimension 11201120
Newform subspaces 11
Sturm bound 280280
Trace bound 00

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Defining parameters

Level: N N == 975=35213 975 = 3 \cdot 5^{2} \cdot 13
Weight: k k == 2 2
Character orbit: [χ][\chi] == 975.cq (of order 6060 and degree 1616)
Character conductor: cond(χ)\operatorname{cond}(\chi) == 325 325
Character field: Q(ζ60)\Q(\zeta_{60})
Newform subspaces: 1 1
Sturm bound: 280280
Trace bound: 00

Dimensions

The following table gives the dimensions of various subspaces of M2(975,[χ])M_{2}(975, [\chi]).

Total New Old
Modular forms 2304 1120 1184
Cusp forms 2176 1120 1056
Eisenstein series 128 0 128

Trace form

1120q140q4+8q516q12+4q15+140q16+20q1732q18+20q19+100q20+28q22+8q23+20q2540q29+60q32+8q3340q34+60q37++56q98+O(q100) 1120 q - 140 q^{4} + 8 q^{5} - 16 q^{12} + 4 q^{15} + 140 q^{16} + 20 q^{17} - 32 q^{18} + 20 q^{19} + 100 q^{20} + 28 q^{22} + 8 q^{23} + 20 q^{25} - 40 q^{29} + 60 q^{32} + 8 q^{33} - 40 q^{34} + 60 q^{37}+ \cdots + 56 q^{98}+O(q^{100}) Copy content Toggle raw display

Decomposition of S2new(975,[χ])S_{2}^{\mathrm{new}}(975, [\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}
975.2.cq.a 975.cq 325.ai 11201120 7.7857.785 None 975.2.cq.a 00 00 88 00 SU(2)[C60]\mathrm{SU}(2)[C_{60}]

Decomposition of S2old(975,[χ])S_{2}^{\mathrm{old}}(975, [\chi]) into lower level spaces

S2old(975,[χ]) S_{2}^{\mathrm{old}}(975, [\chi]) \simeq S2new(325,[χ])S_{2}^{\mathrm{new}}(325, [\chi])2^{\oplus 2}