Properties

Label 432.1.g
Level $432$
Weight $1$
Character orbit 432.g
Rep. character $\chi_{432}(271,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $1$
Sturm bound $72$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 432.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 4 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(72\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(432, [\chi])\).

Total New Old
Modular forms 22 2 20
Cusp forms 4 2 2
Eisenstein series 18 0 18

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

\( 2 q + O(q^{10}) \) \( 2 q + 2 q^{13} - 2 q^{25} - 2 q^{37} - 4 q^{49} - 2 q^{61} + 2 q^{73} + 2 q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(432, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
432.1.g.a $2$ $0.216$ \(\Q(\sqrt{-3}) \) $D_{6}$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{6}+\zeta_{6}^{2})q^{7}+q^{13}+(-\zeta_{6}-\zeta_{6}^{2}+\cdots)q^{19}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(432, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(432, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)