Properties

Label 64.2.b
Level $64$
Weight $2$
Character orbit 64.b
Rep. character $\chi_{64}(33,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $1$
Sturm bound $16$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 64 = 2^{6} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 64.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(16\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(64, [\chi])\).

Total New Old
Modular forms 14 2 12
Cusp forms 2 2 0
Eisenstein series 12 0 12

Trace form

\( 2q - 2q^{9} + O(q^{10}) \) \( 2q - 2q^{9} - 12q^{17} + 10q^{25} + 24q^{33} - 12q^{41} - 14q^{49} - 8q^{57} + 4q^{73} - 22q^{81} + 36q^{89} + 20q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(64, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
64.2.b.a \(2\) \(0.511\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-2}) \) \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}-q^{9}-3iq^{11}-6q^{17}+iq^{19}+\cdots\)