Properties

Label 576.1.b
Level $576$
Weight $1$
Character orbit 576.b
Rep. character $\chi_{576}(415,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $1$
Sturm bound $96$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 576.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(96\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(576, [\chi])\).

Total New Old
Modular forms 26 2 24
Cusp forms 2 2 0
Eisenstein series 24 0 24

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 2 0 0 0

Trace form

\( 2 q + O(q^{10}) \) \( 2 q + 2 q^{25} - 6 q^{49} - 4 q^{73} + 4 q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(576, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
576.1.b.a $2$ $0.287$ \(\Q(\sqrt{-1}) \) $D_{2}$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-6}) \) \(\Q(\sqrt{2}) \) \(0\) \(0\) \(0\) \(0\) \(q-iq^{7}+q^{25}+iq^{31}-3q^{49}-q^{73}+\cdots\)