Properties

Label 64.2.e
Level $64$
Weight $2$
Character orbit 64.e
Rep. character $\chi_{64}(17,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $2$
Newform subspaces $1$
Sturm bound $16$
Trace bound $0$

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Defining parameters

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

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(64, [\chi])\).

Total New Old
Modular forms 24 6 18
Cusp forms 8 2 6
Eisenstein series 16 4 12

Trace form

\( 2 q + 2 q^{3} - 2 q^{5} + O(q^{10}) \) \( 2 q + 2 q^{3} - 2 q^{5} - 2 q^{11} - 2 q^{13} - 4 q^{15} - 4 q^{17} - 6 q^{19} + 4 q^{21} + 8 q^{27} + 6 q^{29} + 16 q^{31} - 4 q^{33} + 4 q^{35} + 6 q^{37} - 10 q^{43} + 2 q^{45} - 16 q^{47} + 6 q^{49} - 4 q^{51} - 10 q^{53} + 6 q^{59} - 18 q^{61} - 4 q^{63} + 4 q^{65} + 10 q^{67} - 12 q^{69} - 6 q^{75} + 4 q^{77} + 10 q^{81} + 2 q^{83} + 4 q^{85} - 4 q^{91} + 16 q^{93} + 12 q^{95} - 4 q^{97} + 2 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(64, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
64.2.e.a 64.e 16.e $2$ $0.511$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1-i)q^{3}+(-1-i)q^{5}+2iq^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(64, [\chi])\) into lower level spaces

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