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Properties

Label 64.9.f
Level $64$
Weight $9$
Character orbit 64.f
Rep. character $\chi_{64}(15,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $30$
Newform subspaces $1$
Sturm bound $72$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 64 = 2^{6} \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 64.f (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(72\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(64, [\chi])\).

Total New Old
Modular forms 136 34 102
Cusp forms 120 30 90
Eisenstein series 16 4 12

Trace form

\( 30 q + 2 q^{3} - 2 q^{5} + 4 q^{7} + 19778 q^{11} - 2 q^{13} - 4 q^{17} - 167550 q^{19} - 13124 q^{21} + 845572 q^{23} - 38656 q^{27} + 1066174 q^{29} - 4 q^{33} - 426620 q^{35} + 2360254 q^{37} + 7650052 q^{39}+ \cdots - 184838270 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{9}^{\mathrm{new}}(64, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
64.9.f.a 64.f 16.f $30$ $26.072$ None 16.9.f.a \(0\) \(2\) \(-2\) \(4\) $\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{9}^{\mathrm{old}}(64, [\chi])\) into lower level spaces

\( S_{9}^{\mathrm{old}}(64, [\chi]) \simeq \) \(S_{9}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 3}\)