Properties

Label 576.1.g
Level $576$
Weight $1$
Character orbit 576.g
Rep. character $\chi_{576}(127,\cdot)$
Character field $\Q$
Dimension $1$
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.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 4 \)
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 28 2 26
Cusp forms 4 1 3
Eisenstein series 24 1 23

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 1 0 0 0

Trace form

\( q + O(q^{10}) \) \( q + 2 q^{13} - q^{25} - 2 q^{37} + q^{49} - 2 q^{61} - 2 q^{73} - 2 q^{97} + O(q^{100}) \)

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.g.a $1$ $0.287$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{3}) \) \(0\) \(0\) \(0\) \(0\) \(q+2q^{13}-q^{25}-2q^{37}+q^{49}-2q^{61}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(576, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(576, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 3}\)