Properties

Label 64.4.b
Level $64$
Weight $4$
Character orbit 64.b
Rep. character $\chi_{64}(33,\cdot)$
Character field $\Q$
Dimension $6$
Newform subspaces $2$
Sturm bound $32$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 64 = 2^{6} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 64.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(32\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(64, [\chi])\).

Total New Old
Modular forms 30 6 24
Cusp forms 18 6 12
Eisenstein series 12 0 12

Trace form

\( 6 q - 54 q^{9} + O(q^{10}) \) \( 6 q - 54 q^{9} + 156 q^{17} - 18 q^{25} - 696 q^{33} + 828 q^{41} + 1014 q^{49} - 1368 q^{57} - 2304 q^{65} + 876 q^{73} + 6942 q^{81} - 2676 q^{89} - 8772 q^{97} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(64, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
64.4.b.a 64.b 8.b $2$ $3.776$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-2}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+5iq^{3}-73q^{9}+9iq^{11}+90q^{17}+\cdots\)
64.4.b.b 64.b 8.b $4$ $3.776$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{12}q^{3}-\zeta_{12}^{2}q^{5}+\zeta_{12}^{3}q^{7}+23q^{9}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(64, [\chi])\) into lower level spaces

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