Properties

Label 32.3.c
Level $32$
Weight $3$
Character orbit 32.c
Rep. character $\chi_{32}(31,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $1$
Sturm bound $12$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 32 = 2^{5} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 32.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 4 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(12\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(32, [\chi])\).

Total New Old
Modular forms 12 2 10
Cusp forms 4 2 2
Eisenstein series 8 0 8

Trace form

\( 2q + 4q^{5} - 14q^{9} + O(q^{10}) \) \( 2q + 4q^{5} - 14q^{9} - 28q^{13} + 36q^{17} + 64q^{21} - 42q^{25} - 28q^{29} + 32q^{33} - 60q^{37} - 28q^{41} - 28q^{45} - 30q^{49} + 132q^{53} + 96q^{57} + 164q^{61} - 56q^{65} - 320q^{69} + 132q^{73} - 64q^{77} - 190q^{81} + 72q^{85} - 60q^{89} + 256q^{93} - 28q^{97} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(32, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
32.3.c.a \(2\) \(0.872\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) \(q+iq^{3}+2q^{5}-2iq^{7}-7q^{9}-iq^{11}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(32, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(32, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 2}\)