Properties

Label 1728.1.o
Level $1728$
Weight $1$
Character orbit 1728.o
Rep. character $\chi_{1728}(127,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $4$
Newform subspaces $1$
Sturm bound $288$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 1728 = 2^{6} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1728.o (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 36 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(288\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 108 8 100
Cusp forms 36 4 32
Eisenstein series 72 4 68

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 0 4 0 0

Trace form

\( 4q + 2q^{5} + O(q^{10}) \) \( 4q + 2q^{5} + 2q^{13} - 2q^{29} + 2q^{41} + 2q^{61} - 2q^{65} - 2q^{77} - 2q^{97} + O(q^{100}) \)

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.o.a \(4\) \(0.862\) \(\Q(\zeta_{12})\) \(A_{4}\) None None \(0\) \(0\) \(2\) \(0\) \(q-\zeta_{12}^{4}q^{5}+\zeta_{12}^{5}q^{7}-\zeta_{12}^{5}q^{11}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(1728, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(864, [\chi])\)\(^{\oplus 2}\)