Properties

Label 1536.1.e
Level $1536$
Weight $1$
Character orbit 1536.e
Rep. character $\chi_{1536}(1025,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $2$
Sturm bound $256$
Trace bound $9$

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Defining parameters

Level: \( N \) \(=\) \( 1536 = 2^{9} \cdot 3 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1536.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(256\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1536, [\chi])\).

Total New Old
Modular forms 48 8 40
Cusp forms 16 8 8
Eisenstein series 32 0 32

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 8 0 0 0

Trace form

\( 8q - 4q^{9} + O(q^{10}) \) \( 8q - 4q^{9} + 4q^{33} + 4q^{57} - 8q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1536, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1536.1.e.a \(4\) \(0.767\) \(\Q(\zeta_{8})\) \(D_{4}\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{2}q^{3}+(-\zeta_{8}-\zeta_{8}^{3})q^{5}+(-\zeta_{8}+\cdots)q^{7}+\cdots\)
1536.1.e.b \(4\) \(0.767\) \(\Q(\zeta_{8})\) \(D_{4}\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{3}+\zeta_{8}^{2}q^{9}+(\zeta_{8}+\zeta_{8}^{3})q^{11}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1536, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1536, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(768, [\chi])\)\(^{\oplus 2}\)