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Properties

Label 935.2.bz
Level $935$
Weight $2$
Character orbit 935.bz
Rep. character $\chi_{935}(18,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $768$
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.bz (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 55 \)
Character field: \(\Q(\zeta_{20})\)
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 896 768 128
Cusp forms 832 768 64
Eisenstein series 64 0 64

Trace form

\( 768 q - 4 q^{3} + O(q^{10}) \) \( 768 q - 4 q^{3} + 8 q^{11} - 96 q^{12} - 40 q^{15} + 192 q^{16} - 76 q^{20} - 28 q^{22} - 16 q^{23} + 12 q^{25} - 48 q^{26} - 4 q^{27} - 120 q^{28} - 80 q^{30} - 132 q^{33} + 96 q^{36} + 36 q^{37} - 72 q^{38} - 120 q^{41} - 40 q^{42} - 16 q^{45} - 240 q^{46} + 52 q^{47} + 136 q^{48} + 80 q^{50} + 36 q^{53} + 52 q^{55} - 32 q^{56} - 160 q^{57} + 48 q^{58} + 32 q^{60} + 80 q^{62} + 80 q^{66} + 80 q^{67} - 48 q^{70} - 40 q^{71} - 120 q^{73} - 80 q^{75} - 124 q^{77} - 160 q^{78} + 216 q^{81} - 16 q^{82} - 200 q^{83} - 80 q^{86} - 304 q^{88} - 160 q^{90} - 56 q^{91} + 44 q^{92} + 172 q^{93} + 80 q^{95} - 40 q^{96} - 28 q^{97} + O(q^{100}) \)

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.bz.a 935.bz 55.l $768$ $7.466$ None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{20}]$

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

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