Properties

Label 64.9.d
Level $64$
Weight $9$
Character orbit 64.d
Rep. character $\chi_{64}(31,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $2$
Sturm bound $72$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 64 = 2^{6} \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 64.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(72\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(64, [\chi])\).

Total New Old
Modular forms 70 16 54
Cusp forms 58 16 42
Eisenstein series 12 0 12

Trace form

\( 16 q + 34992 q^{9} + O(q^{10}) \) \( 16 q + 34992 q^{9} + 231840 q^{17} - 2312432 q^{25} - 4958016 q^{33} + 1691424 q^{41} - 1042416 q^{49} - 24274752 q^{57} - 67850496 q^{65} + 51448480 q^{73} + 392846544 q^{81} + 85417632 q^{89} - 269794912 q^{97} + O(q^{100}) \)

Decomposition of \(S_{9}^{\mathrm{new}}(64, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
64.9.d.a 64.d 8.d $4$ $26.072$ \(\Q(i, \sqrt{1731})\) None 64.9.d.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}+\beta _{3}q^{5}-7\beta _{2}q^{7}+363q^{9}+\cdots\)
64.9.d.b 64.d 8.d $12$ $26.072$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None 64.9.d.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+\beta _{4}q^{5}+\beta _{10}q^{7}+(2795+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{9}^{\mathrm{old}}(64, [\chi])\) into lower level spaces

\( S_{9}^{\mathrm{old}}(64, [\chi]) \simeq \) \(S_{9}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 2}\)