Properties

Label 4.8.a
Level 4
Weight 8
Character orbit a
Rep. character \(\chi_{4}(1,\cdot)\)
Character field \(\Q\)
Dimension 0
Newforms 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: \(\Q\)
Newforms: \( 0 \)
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

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