↑

Properties

Label 935.2.m
Level $935$
Weight $2$
Character orbit 935.m
Rep. character $\chi_{935}(307,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $192$
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.m (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 55 \)
Character field: \(\Q(i)\)
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 224 192 32
Cusp forms 208 192 16
Eisenstein series 16 0 16

Trace form

\( 192 q + 4 q^{3} + O(q^{10}) \) \( 192 q + 4 q^{3} - 8 q^{11} + 16 q^{12} - 192 q^{16} - 24 q^{20} + 28 q^{22} - 4 q^{23} - 12 q^{25} + 48 q^{26} + 4 q^{27} + 32 q^{33} - 256 q^{36} - 36 q^{37} - 48 q^{38} + 80 q^{42} + 76 q^{45} + 8 q^{47} + 24 q^{48} + 24 q^{53} - 52 q^{55} + 32 q^{56} + 112 q^{58} + 48 q^{60} - 80 q^{66} - 20 q^{67} - 32 q^{70} + 40 q^{71} - 80 q^{75} - 36 q^{77} - 80 q^{78} - 216 q^{81} - 64 q^{82} + 80 q^{86} - 16 q^{88} + 96 q^{91} + 56 q^{92} - 52 q^{93} + 148 q^{97} + O(q^{100}) \)

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.m.a 935.m 55.e $192$ $7.466$ None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$

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

\( S_{2}^{\mathrm{old}}(935, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 2}\)