Properties

Label 4.8.a
Level $4$
Weight $8$
Character orbit 4.a
Rep. character $\chi_{4}(1,\cdot)$
Character field $\Q$
Dimension $0$
Newform subspaces $0$
Sturm bound $4$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 4 = 2^{2} \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 4.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 0 \)
Sturm bound: \(4\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_0(4))\).

Total New Old
Modular forms 5 0 5
Cusp forms 2 0 2
Eisenstein series 3 0 3

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_0(4))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_0(4)) \simeq \) \(S_{8}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 2}\)