Properties

Label 1568.1.h
Level $1568$
Weight $1$
Character orbit 1568.h
Rep. character $\chi_{1568}(881,\cdot)$
Character field $\Q$
Dimension $0$
Newform subspaces $0$
Sturm bound $224$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1568 = 2^{5} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1568.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 56 \)
Character field: \(\Q\)
Newform subspaces: \( 0 \)
Sturm bound: \(224\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1568, [\chi])\).

Total New Old
Modular forms 40 4 36
Cusp forms 8 0 8
Eisenstein series 32 4 28

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 \(S_{1}^{\mathrm{old}}(1568, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1568, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 2}\)