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Properties

Label 935.2.bw
Level $935$
Weight $2$
Character orbit 935.bw
Rep. character $\chi_{935}(118,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $832$
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.bw (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 935 \)
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 896 896 0
Cusp forms 832 832 0
Eisenstein series 64 64 0

Trace form

\( 832 q - 20 q^{2} - 20 q^{8} + O(q^{10}) \) \( 832 q - 20 q^{2} - 20 q^{8} - 20 q^{13} - 12 q^{15} + 144 q^{16} - 20 q^{17} - 20 q^{18} - 52 q^{25} - 8 q^{26} - 20 q^{30} - 24 q^{33} - 20 q^{35} - 320 q^{36} + 60 q^{38} + 84 q^{42} - 20 q^{47} - 20 q^{50} + 100 q^{51} - 100 q^{52} - 12 q^{53} + 12 q^{55} - 188 q^{60} - 72 q^{66} - 256 q^{67} + 50 q^{68} + 92 q^{70} - 200 q^{72} + 64 q^{77} + 192 q^{81} - 20 q^{83} + 30 q^{85} - 168 q^{86} + 108 q^{93} + O(q^{100}) \)

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.bw.a 935.bw 935.aw $832$ $7.466$ None \(-20\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{20}]$