Properties

Label 432.1.e
Level $432$
Weight $1$
Character orbit 432.e
Rep. character $\chi_{432}(161,\cdot)$
Character field $\Q$
Dimension $1$
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.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
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 1 21
Cusp forms 4 1 3
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 1 0 0 0

Trace form

\( q + q^{7} + O(q^{10}) \) \( q + q^{7} - q^{13} + q^{19} + q^{25} - 2 q^{31} - q^{37} - 2 q^{43} - q^{61} + q^{67} - q^{73} + q^{79} - q^{91} - q^{97} + O(q^{100}) \)

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.e.a \(1\) \(0.216\) \(\Q\) \(D_{3}\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(1\) \(q+q^{7}-q^{13}+q^{19}+q^{25}-2q^{31}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(432, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 3}\)