Properties

Label 64.24.b
Level $64$
Weight $24$
Character orbit 64.b
Rep. character $\chi_{64}(33,\cdot)$
Character field $\Q$
Dimension $46$
Newform subspaces $3$
Sturm bound $192$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 64 = 2^{6} \)
Weight: \( k \) \(=\) \( 24 \)
Character orbit: \([\chi]\) \(=\) 64.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(192\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{24}(64, [\chi])\).

Total New Old
Modular forms 190 46 144
Cusp forms 178 46 132
Eisenstein series 12 0 12

Trace form

\( 46 q - 1443528742014 q^{9} + O(q^{10}) \) \( 46 q - 1443528742014 q^{9} + 337815163347756 q^{17} - 87651015775149418 q^{25} + 782292390906536232 q^{33} + 5242077893811964812 q^{41} + 117408011885940940958 q^{49} - 29988080933688397176 q^{57} + 2256743822070655120896 q^{65} - 80464020574566173188 q^{73} + 8368877271278797171878 q^{81} - 18375869889201376094436 q^{89} + 408558106283620724461900 q^{97} + O(q^{100}) \)

Decomposition of \(S_{24}^{\mathrm{new}}(64, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
64.24.b.a 64.b 8.b $2$ $214.531$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-2}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+306773iq^{3}-282295515289q^{9}+\cdots\)
64.24.b.b 64.b 8.b $12$ $214.531$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(91\beta _{2}-\beta _{5})q^{3}+\beta _{1}q^{5}+\beta _{9}q^{7}+\cdots\)
64.24.b.c 64.b 8.b $32$ $214.531$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{24}^{\mathrm{old}}(64, [\chi])\) into lower level spaces

\( S_{24}^{\mathrm{old}}(64, [\chi]) \cong \) \(S_{24}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 2}\)