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Properties

Label 935.2.s
Level $935$
Weight $2$
Character orbit 935.s
Rep. character $\chi_{935}(89,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $176$
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.s (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 85 \)
Character field: \(\Q(i)\)
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 224 176 48
Cusp forms 208 176 32
Eisenstein series 16 0 16

Trace form

\( 176 q + 168 q^{4} + 4 q^{5} + 8 q^{6} + O(q^{10}) \) \( 176 q + 168 q^{4} + 4 q^{5} + 8 q^{6} - 8 q^{10} - 8 q^{14} + 136 q^{16} + 8 q^{20} - 48 q^{21} + 8 q^{24} - 104 q^{30} - 24 q^{31} - 24 q^{34} - 64 q^{35} - 16 q^{39} - 56 q^{40} - 16 q^{41} - 8 q^{44} + 12 q^{45} + 40 q^{46} + 24 q^{50} - 136 q^{54} - 24 q^{56} + 72 q^{61} + 88 q^{64} - 16 q^{65} + 160 q^{69} + 32 q^{71} + 32 q^{74} - 120 q^{75} + 32 q^{79} - 4 q^{80} - 112 q^{81} - 192 q^{84} + 84 q^{85} - 144 q^{86} - 48 q^{89} + 108 q^{90} + 16 q^{91} + 100 q^{95} - 72 q^{96} + O(q^{100}) \)

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.s.a 935.s 85.j $176$ $7.466$ None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{4}]$

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

\( S_{2}^{\mathrm{old}}(935, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(85, [\chi])\)\(^{\oplus 2}\)