Properties

Label 64.3.d
Level $64$
Weight $3$
Character orbit 64.d
Rep. character $\chi_{64}(31,\cdot)$
Character field $\Q$
Dimension $4$
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.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
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 22 4 18
Cusp forms 10 4 6
Eisenstein series 12 0 12

Trace form

\( 4 q + 12 q^{9} + O(q^{10}) \) \( 4 q + 12 q^{9} - 24 q^{17} - 92 q^{25} + 48 q^{33} + 264 q^{41} - 60 q^{49} - 336 q^{57} + 192 q^{65} + 232 q^{73} - 396 q^{81} - 408 q^{89} + 104 q^{97} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
64.3.d.a $4$ $1.744$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{3}-\zeta_{12}^{2}q^{5}-\zeta_{12}^{3}q^{7}+3q^{9}+\cdots\)

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

\( S_{3}^{\mathrm{old}}(64, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 2}\)