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Properties

Label 64.6.e
Level $64$
Weight $6$
Character orbit 64.e
Rep. character $\chi_{64}(17,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $18$
Newform subspaces $1$
Sturm bound $48$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 64 = 2^{6} \)
Weight: \( k \) \(=\) \( 6 \)
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: \(48\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(64, [\chi])\).

Total New Old
Modular forms 88 22 66
Cusp forms 72 18 54
Eisenstein series 16 4 12

Trace form

\( 18 q + 2 q^{3} - 2 q^{5} + O(q^{10}) \) \( 18 q + 2 q^{3} - 2 q^{5} + 606 q^{11} - 2 q^{13} - 1796 q^{15} - 4 q^{17} + 2362 q^{19} + 484 q^{21} - 4216 q^{27} + 4070 q^{29} + 11536 q^{31} - 4 q^{33} - 8636 q^{35} - 10650 q^{37} + 15382 q^{43} + 5762 q^{45} - 44176 q^{47} - 14410 q^{49} + 2748 q^{51} + 24726 q^{53} + 29734 q^{59} - 48082 q^{61} + 12156 q^{63} + 27684 q^{65} + 75210 q^{67} + 22804 q^{69} - 154726 q^{75} + 41060 q^{77} + 52864 q^{79} - 13126 q^{81} - 227838 q^{83} - 138652 q^{85} + 231164 q^{91} + 180688 q^{93} + 250380 q^{95} - 4 q^{97} + 296770 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(64, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
64.6.e.a 64.e 16.e $18$ $10.265$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(0\) \(2\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{6}q^{3}-\beta _{5}q^{5}+(-11\beta _{1}+\beta _{4})q^{7}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(64, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(64, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 2}\)