Properties

Label 935.2.bc
Level $935$
Weight $2$
Character orbit 935.bc
Rep. character $\chi_{935}(32,\cdot)$
Character field $\Q(\zeta_{8})$
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.bc (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 935 \)
Character field: \(\Q(\zeta_{8})\)
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

\( 416 q - 8 q^{3} + 400 q^{4} + O(q^{10}) \) \( 416 q - 8 q^{3} + 400 q^{4} - 8 q^{11} - 48 q^{12} - 32 q^{14} - 8 q^{15} + 336 q^{16} - 24 q^{20} - 28 q^{22} - 40 q^{23} - 16 q^{25} - 32 q^{26} + 16 q^{27} + 16 q^{31} - 16 q^{34} - 80 q^{36} + 24 q^{37} - 32 q^{38} - 48 q^{42} - 16 q^{44} + 8 q^{45} - 128 q^{48} - 32 q^{49} - 16 q^{53} + 8 q^{55} - 80 q^{56} + 32 q^{58} + 96 q^{59} - 56 q^{60} + 144 q^{64} + 8 q^{66} - 80 q^{67} + 64 q^{70} - 48 q^{71} + 48 q^{75} + 40 q^{77} - 48 q^{78} - 80 q^{80} + 48 q^{82} + 32 q^{86} - 64 q^{88} - 32 q^{89} + 32 q^{91} - 328 q^{92} + 24 q^{97} - 24 q^{99} + O(q^{100}) \)

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.bc.a 935.bc 935.ac $416$ $7.466$ None \(0\) \(-8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{8}]$