Properties

Label 768.1.h
Level $768$
Weight $1$
Character orbit 768.h
Rep. character $\chi_{768}(641,\cdot)$
Character field $\Q$
Dimension $0$
Newform subspaces $0$
Sturm bound $128$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 768 = 2^{8} \cdot 3 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 768.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 24 \)
Character field: \(\Q\)
Newform subspaces: \( 0 \)
Sturm bound: \(128\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(768, [\chi])\).

Total New Old
Modular forms 34 4 30
Cusp forms 10 0 10
Eisenstein series 24 4 20

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

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

Decomposition of \(S_{1}^{\mathrm{old}}(768, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(768, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(384, [\chi])\)\(^{\oplus 2}\)