Properties

Label 935.2.e
Level $935$
Weight $2$
Character orbit 935.e
Rep. character $\chi_{935}(254,\cdot)$
Character field $\Q$
Dimension $88$
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.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 85 \)
Character field: \(\Q\)
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 112 88 24
Cusp forms 104 88 16
Eisenstein series 8 0 8

Trace form

\( 88 q - 76 q^{4} + 80 q^{9} + O(q^{10}) \) \( 88 q - 76 q^{4} + 80 q^{9} + 12 q^{15} + 60 q^{16} - 16 q^{19} - 24 q^{21} + 4 q^{25} + 48 q^{26} - 36 q^{30} - 48 q^{34} + 4 q^{35} + 12 q^{36} + 80 q^{49} + 80 q^{50} + 28 q^{51} - 72 q^{59} - 120 q^{60} + 4 q^{64} + 16 q^{66} - 72 q^{69} + 24 q^{70} - 8 q^{76} + 40 q^{81} + 32 q^{84} + 18 q^{85} - 48 q^{86} + 48 q^{89} + 144 q^{94} + O(q^{100}) \)

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.e.a 935.e 85.c $88$ $7.466$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$

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

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