Properties

Label 1728.1.j
Level $1728$
Weight $1$
Character orbit 1728.j
Rep. character $\chi_{1728}(593,\cdot)$
Character field $\Q(\zeta_{4})$
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.j (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 48 \)
Character field: \(\Q(i)\)
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 64 4 60
Cusp forms 16 4 12
Eisenstein series 48 0 48

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

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

Trace form

\( 4 q + O(q^{10}) \) \( 4 q - 4 q^{13} - 4 q^{31} + 4 q^{43} - 4 q^{67} - 4 q^{85} + 4 q^{91} + 4 q^{97} + O(q^{100}) \)

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.j.a \(4\) \(0.862\) \(\Q(\zeta_{8})\) \(S_{4}\) None None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{5}+\zeta_{8}^{2}q^{7}-\zeta_{8}q^{11}+(-1+\cdots)q^{13}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(1728, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(432, [\chi])\)\(^{\oplus 3}\)