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Properties

Label 935.2.cd
Level $935$
Weight $2$
Character orbit 935.cd
Rep. character $\chi_{935}(81,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $576$
Newform subspaces $1$
Sturm bound $216$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 935 = 5 \cdot 11 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 935.cd (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 187 \)
Character field: \(\Q(\zeta_{20})\)
Newform subspaces: \( 1 \)
Sturm bound: \(216\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(935, [\chi])\).

Total New Old
Modular forms 896 576 320
Cusp forms 832 576 256
Eisenstein series 64 0 64

Trace form

\( 576 q + 8 q^{3} + 144 q^{4} - 12 q^{6} + O(q^{10}) \) \( 576 q + 8 q^{3} + 144 q^{4} - 12 q^{6} - 16 q^{11} - 24 q^{12} + 40 q^{13} - 24 q^{14} - 144 q^{16} + 24 q^{17} - 56 q^{18} + 8 q^{20} + 32 q^{21} + 100 q^{22} - 32 q^{23} - 36 q^{24} + 8 q^{27} - 48 q^{28} - 16 q^{29} + 16 q^{30} + 16 q^{31} - 88 q^{33} - 88 q^{34} - 32 q^{35} - 40 q^{37} + 104 q^{38} - 72 q^{39} + 100 q^{41} - 60 q^{44} + 40 q^{46} + 8 q^{47} + 120 q^{48} - 8 q^{50} - 32 q^{51} + 112 q^{52} + 16 q^{54} - 16 q^{55} - 48 q^{56} - 20 q^{57} + 80 q^{58} - 88 q^{61} - 64 q^{62} + 36 q^{63} + 72 q^{64} - 8 q^{65} + 32 q^{67} - 72 q^{68} - 96 q^{69} + 16 q^{71} - 280 q^{72} + 88 q^{73} - 60 q^{74} + 12 q^{75} + 184 q^{78} - 84 q^{79} - 16 q^{80} - 88 q^{81} - 44 q^{82} + 96 q^{84} + 32 q^{86} - 48 q^{88} - 16 q^{89} - 76 q^{91} - 112 q^{92} - 144 q^{96} + 88 q^{97} - 256 q^{98} + 80 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(935, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
935.2.cd.a 935.cd 187.p $576$ $7.466$ None \(0\) \(8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{20}]$

Decomposition of \(S_{2}^{\mathrm{old}}(935, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(935, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(187, [\chi])\)\(^{\oplus 2}\)