Properties

Label 64.4.e
Level $64$
Weight $4$
Character orbit 64.e
Rep. character $\chi_{64}(17,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $10$
Newform subspaces $1$
Sturm bound $32$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 64 = 2^{6} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 64.e (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(32\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 56 14 42
Cusp forms 40 10 30
Eisenstein series 16 4 12

Trace form

\( 10 q + 2 q^{3} - 2 q^{5} + O(q^{10}) \) \( 10 q + 2 q^{3} - 2 q^{5} - 18 q^{11} - 2 q^{13} + 124 q^{15} - 4 q^{17} + 26 q^{19} + 52 q^{21} - 184 q^{27} - 202 q^{29} - 368 q^{31} - 4 q^{33} - 476 q^{35} - 10 q^{37} + 838 q^{43} + 194 q^{45} + 944 q^{47} + 94 q^{49} + 1500 q^{51} - 378 q^{53} - 1706 q^{59} + 910 q^{61} - 2628 q^{63} - 492 q^{65} - 1942 q^{67} + 580 q^{69} + 2954 q^{75} - 268 q^{77} + 4416 q^{79} + 482 q^{81} + 2562 q^{83} - 12 q^{85} - 3332 q^{91} - 2192 q^{93} - 6900 q^{95} - 4 q^{97} - 4958 q^{99} + O(q^{100}) \)

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.e.a 64.e 16.e $10$ $3.776$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(2\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{5}q^{3}+\beta _{3}q^{5}+(3\beta _{1}-\beta _{4})q^{7}+(5\beta _{1}+\cdots)q^{9}+\cdots\)

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

\( S_{4}^{\mathrm{old}}(64, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 3}\)