Properties

Label 936.2.ds
Level 936936
Weight 22
Character orbit 936.ds
Rep. character χ936(353,)\chi_{936}(353,\cdot)
Character field Q(ζ12)\Q(\zeta_{12})
Dimension 168168
Newform subspaces 11
Sturm bound 336336
Trace bound 00

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Defining parameters

Level: N N == 936=233213 936 = 2^{3} \cdot 3^{2} \cdot 13
Weight: k k == 2 2
Character orbit: [χ][\chi] == 936.ds (of order 1212 and degree 44)
Character conductor: cond(χ)\operatorname{cond}(\chi) == 117 117
Character field: Q(ζ12)\Q(\zeta_{12})
Newform subspaces: 1 1
Sturm bound: 336336
Trace bound: 00

Dimensions

The following table gives the dimensions of various subspaces of M2(936,[χ])M_{2}(936, [\chi]).

Total New Old
Modular forms 704 168 536
Cusp forms 640 168 472
Eisenstein series 64 0 64

Trace form

168q8q15+16q2112q27+24q31+4q33+36q35+40q39+36q43+12q45+36q5736q63+36q65+36q69+72q7172q77+48q81+60q83+28q99+O(q100) 168 q - 8 q^{15} + 16 q^{21} - 12 q^{27} + 24 q^{31} + 4 q^{33} + 36 q^{35} + 40 q^{39} + 36 q^{43} + 12 q^{45} + 36 q^{57} - 36 q^{63} + 36 q^{65} + 36 q^{69} + 72 q^{71} - 72 q^{77} + 48 q^{81} + 60 q^{83}+ \cdots - 28 q^{99}+O(q^{100}) Copy content Toggle raw display

Decomposition of S2new(936,[χ])S_{2}^{\mathrm{new}}(936, [\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}
936.2.ds.a 936.ds 117.x 168168 7.4747.474 None 936.2.ds.a 00 00 00 00 SU(2)[C12]\mathrm{SU}(2)[C_{12}]

Decomposition of S2old(936,[χ])S_{2}^{\mathrm{old}}(936, [\chi]) into lower level spaces

S2old(936,[χ]) S_{2}^{\mathrm{old}}(936, [\chi]) \simeq S2new(117,[χ])S_{2}^{\mathrm{new}}(117, [\chi])4^{\oplus 4}\oplusS2new(234,[χ])S_{2}^{\mathrm{new}}(234, [\chi])3^{\oplus 3}\oplusS2new(468,[χ])S_{2}^{\mathrm{new}}(468, [\chi])2^{\oplus 2}