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Properties

Label 935.2.bg
Level $935$
Weight $2$
Character orbit 935.bg
Rep. character $\chi_{935}(169,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $416$
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.bg (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 935 \)
Character field: \(\Q(\zeta_{10})\)
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 448 448 0
Cusp forms 416 416 0
Eisenstein series 32 32 0

Trace form

\( 416 q + 88 q^{4} - 120 q^{9} + O(q^{10}) \) \( 416 q + 88 q^{4} - 120 q^{9} + 10 q^{15} - 128 q^{16} - 36 q^{19} + 48 q^{21} + 16 q^{25} - 20 q^{26} - 68 q^{30} - 16 q^{34} - 6 q^{35} + 20 q^{36} - 168 q^{49} + 28 q^{50} + 22 q^{51} + 62 q^{55} + 76 q^{59} - 16 q^{60} + 172 q^{64} - 164 q^{66} - 44 q^{69} - 88 q^{70} - 168 q^{76} - 48 q^{81} - 208 q^{84} + 26 q^{85} + 140 q^{86} - 40 q^{89} - 96 q^{94} + O(q^{100}) \)

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.bg.a 935.bg 935.ag $416$ $7.466$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$