Properties

Label 64.8.b
Level $64$
Weight $8$
Character orbit 64.b
Rep. character $\chi_{64}(33,\cdot)$
Character field $\Q$
Dimension $14$
Newform subspaces $3$
Sturm bound $64$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 64 = 2^{6} \)
Weight: \( k \) \(=\) \( 8 \)
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: \(64\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 62 14 48
Cusp forms 50 14 36
Eisenstein series 12 0 12

Trace form

\( 14 q - 10206 q^{9} + O(q^{10}) \) \( 14 q - 10206 q^{9} - 8724 q^{17} - 170378 q^{25} - 297048 q^{33} - 3127476 q^{41} + 2669182 q^{49} + 5161224 q^{57} + 999936 q^{65} - 1493828 q^{73} + 5427462 q^{81} + 15671772 q^{89} - 23867380 q^{97} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
64.8.b.a 64.b 8.b $2$ $19.993$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-2}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+43iq^{3}-5209q^{9}+4407iq^{11}+\cdots\)
64.8.b.b 64.b 8.b $4$ $19.993$ \(\Q(i, \sqrt{435})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+15\beta _{1}q^{3}+\beta _{3}q^{5}+\beta _{2}q^{7}+1287q^{9}+\cdots\)
64.8.b.c 64.b 8.b $8$ $19.993$ 8.0.\(\cdots\).10 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{4}+\beta _{6})q^{3}+\beta _{1}q^{5}-\beta _{7}q^{7}+(-617+\cdots)q^{9}+\cdots\)

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

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