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Properties

Label 64.3.f
Level $64$
Weight $3$
Character orbit 64.f
Rep. character $\chi_{64}(15,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $6$
Newform subspaces $1$
Sturm bound $24$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 64 = 2^{6} \)
Weight: \( k \) \(=\) \( 3 \)
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: \(24\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(64, [\chi])\).

Total New Old
Modular forms 40 10 30
Cusp forms 24 6 18
Eisenstein series 16 4 12

Trace form

\( 6 q + 2 q^{3} - 2 q^{5} + 4 q^{7} + O(q^{10}) \) \( 6 q + 2 q^{3} - 2 q^{5} + 4 q^{7} + 18 q^{11} - 2 q^{13} - 4 q^{17} - 30 q^{19} - 20 q^{21} - 60 q^{23} - 64 q^{27} - 18 q^{29} - 4 q^{33} + 100 q^{35} + 46 q^{37} + 196 q^{39} + 114 q^{43} + 66 q^{45} - 46 q^{49} - 156 q^{51} + 78 q^{53} - 252 q^{55} - 206 q^{59} + 30 q^{61} + 12 q^{65} + 226 q^{67} - 116 q^{69} + 260 q^{71} + 238 q^{75} - 212 q^{77} + 86 q^{81} - 318 q^{83} - 212 q^{85} - 444 q^{87} - 188 q^{91} - 32 q^{93} - 4 q^{97} + 226 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(64, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
64.3.f.a 64.f 16.f $6$ $1.744$ 6.0.399424.1 None \(0\) \(2\) \(-2\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{5}q^{3}+(-1-\beta _{1}-\beta _{3}-\beta _{5})q^{5}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(64, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(64, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 2}\)