Properties

Label 1728.1.e
Level $1728$
Weight $1$
Character orbit 1728.e
Rep. character $\chi_{1728}(1025,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $2$
Sturm bound $288$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 1728 = 2^{6} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1728.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(288\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1728, [\chi])\).

Total New Old
Modular forms 58 2 56
Cusp forms 22 2 20
Eisenstein series 36 0 36

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

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

Decomposition of \(S_{1}^{\mathrm{new}}(1728, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1728.1.e.a \(1\) \(0.862\) \(\Q\) \(D_{3}\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-1\) \(q-q^{7}+q^{13}+q^{19}+q^{25}+2q^{31}+\cdots\)
1728.1.e.b \(1\) \(0.862\) \(\Q\) \(D_{3}\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(1\) \(q+q^{7}+q^{13}-q^{19}+q^{25}-2q^{31}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1728, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1728, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(432, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 2}\)