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Properties

Label 64.8.e
Level $64$
Weight $8$
Character orbit 64.e
Rep. character $\chi_{64}(17,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $26$
Newform subspaces $1$
Sturm bound $64$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 64 = 2^{6} \)
Weight: \( k \) \(=\) \( 8 \)
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: \(64\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(64, [\chi])\).

Total New Old
Modular forms 120 30 90
Cusp forms 104 26 78
Eisenstein series 16 4 12

Trace form

\( 26 q + 2 q^{3} - 2 q^{5} + O(q^{10}) \) \( 26 q + 2 q^{3} - 2 q^{5} - 1202 q^{11} - 2 q^{13} + 27004 q^{15} - 4 q^{17} - 60582 q^{19} + 4372 q^{21} + 233672 q^{27} - 51690 q^{29} - 357488 q^{31} - 4 q^{33} + 252004 q^{35} + 415574 q^{37} - 569754 q^{43} + 151874 q^{45} + 2076464 q^{47} - 1647090 q^{49} - 2609508 q^{51} + 907814 q^{53} + 4865142 q^{59} + 2279886 q^{61} - 8295108 q^{63} - 1426892 q^{65} + 5564458 q^{67} - 4786076 q^{69} - 6212566 q^{75} + 7604308 q^{77} + 9598912 q^{79} - 5314414 q^{81} - 4531198 q^{83} + 7377748 q^{85} - 2587652 q^{91} - 14504144 q^{93} + 4900620 q^{95} - 4 q^{97} - 18815006 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(64, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
64.8.e.a 64.e 16.e $26$ $19.993$ None 16.8.e.a \(0\) \(2\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{8}^{\mathrm{old}}(64, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(64, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 2}\)