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Properties

Label 64.7.f
Level $64$
Weight $7$
Character orbit 64.f
Rep. character $\chi_{64}(15,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $22$
Newform subspaces $1$
Sturm bound $56$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 64 = 2^{6} \)
Weight: \( k \) \(=\) \( 7 \)
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: \(56\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(64, [\chi])\).

Total New Old
Modular forms 104 26 78
Cusp forms 88 22 66
Eisenstein series 16 4 12

Trace form

\( 22 q + 2 q^{3} - 2 q^{5} + 4 q^{7} + O(q^{10}) \) \( 22 q + 2 q^{3} - 2 q^{5} + 4 q^{7} - 1358 q^{11} - 2 q^{13} - 4 q^{17} - 3934 q^{19} - 1460 q^{21} + 13124 q^{23} - 35776 q^{27} - 33202 q^{29} - 4 q^{33} + 112420 q^{35} + 3598 q^{37} - 254396 q^{39} + 267986 q^{43} + 32706 q^{45} + 168066 q^{49} - 301788 q^{51} - 221842 q^{53} + 232708 q^{55} - 39150 q^{59} + 326494 q^{61} + 186412 q^{65} + 122786 q^{67} - 543188 q^{69} + 267012 q^{71} + 275278 q^{75} + 231180 q^{77} - 354298 q^{81} + 288322 q^{83} + 340748 q^{85} - 2029884 q^{87} - 302396 q^{91} - 1173344 q^{93} - 4 q^{97} + 271522 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{7}^{\mathrm{new}}(64, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
64.7.f.a 64.f 16.f $22$ $14.723$ None 16.7.f.a \(0\) \(2\) \(-2\) \(4\) $\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{7}^{\mathrm{old}}(64, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(64, [\chi]) \simeq \) \(S_{7}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 2}\)