Properties

Label 3762.2.d
Level 37623762
Weight 22
Character orbit 3762.d
Rep. character χ3762(683,)\chi_{3762}(683,\cdot)
Character field Q\Q
Dimension 7272
Newform subspaces 22
Sturm bound 14401440
Trace bound 22

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Defining parameters

Level: N N == 3762=2321119 3762 = 2 \cdot 3^{2} \cdot 11 \cdot 19
Weight: k k == 2 2
Character orbit: [χ][\chi] == 3762.d (of order 22 and degree 11)
Character conductor: cond(χ)\operatorname{cond}(\chi) == 57 57
Character field: Q\Q
Newform subspaces: 2 2
Sturm bound: 14401440
Trace bound: 22

Dimensions

The following table gives the dimensions of various subspaces of M2(3762,[χ])M_{2}(3762, [\chi]).

Total New Old
Modular forms 736 72 664
Cusp forms 704 72 632
Eisenstein series 32 0 32

Trace form

72q+72q416q7+72q1624q19104q2516q28+48q43+136q49+16q5848q61+72q64+80q7324q76+48q8264q85+O(q100) 72 q + 72 q^{4} - 16 q^{7} + 72 q^{16} - 24 q^{19} - 104 q^{25} - 16 q^{28} + 48 q^{43} + 136 q^{49} + 16 q^{58} - 48 q^{61} + 72 q^{64} + 80 q^{73} - 24 q^{76} + 48 q^{82} - 64 q^{85}+O(q^{100}) Copy content Toggle raw display

Decomposition of S2new(3762,[χ])S_{2}^{\mathrm{new}}(3762, [\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}
3762.2.d.a 3762.d 57.d 3636 30.04030.040 None 3762.2.d.a 36-36 00 00 8-8 SU(2)[C2]\mathrm{SU}(2)[C_{2}]
3762.2.d.b 3762.d 57.d 3636 30.04030.040 None 3762.2.d.a 3636 00 00 8-8 SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Decomposition of S2old(3762,[χ])S_{2}^{\mathrm{old}}(3762, [\chi]) into lower level spaces