↑

Properties

Label 935.2.z
Level $935$
Weight $2$
Character orbit 935.z
Rep. character $\chi_{935}(144,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $368$
Newform subspaces $1$
Sturm bound $216$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 935 = 5 \cdot 11 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 935.z (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 85 \)
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 448 368 80
Cusp forms 416 368 48
Eisenstein series 32 0 32

Trace form

\( 368 q - 16 q^{6} + O(q^{10}) \) \( 368 q - 16 q^{6} + 24 q^{10} + 16 q^{14} + 24 q^{15} - 416 q^{16} + 32 q^{19} + 40 q^{20} - 16 q^{24} - 48 q^{25} - 32 q^{26} - 64 q^{29} - 64 q^{34} - 32 q^{35} + 64 q^{36} + 32 q^{39} - 64 q^{40} + 80 q^{41} - 16 q^{44} - 104 q^{45} - 48 q^{46} - 48 q^{50} + 64 q^{54} - 16 q^{59} - 8 q^{60} - 64 q^{61} - 64 q^{65} - 128 q^{69} + 32 q^{70} - 16 q^{71} + 112 q^{74} - 40 q^{75} + 64 q^{76} + 96 q^{79} - 32 q^{85} - 32 q^{86} + 40 q^{90} - 96 q^{91} + 144 q^{94} + 80 q^{95} + 64 q^{96} + O(q^{100}) \)

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.z.a 935.z 85.m $368$ $7.466$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{8}]$

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

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