Properties

Label 80.4.d
Level $80$
Weight $4$
Character orbit 80.d
Rep. character $\chi_{80}(41,\cdot)$
Character field $\Q$
Dimension $0$
Newform subspaces $0$
Sturm bound $48$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 80 = 2^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 80.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 0 \)
Sturm bound: \(48\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(80, [\chi])\).

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

Decomposition of \(S_{4}^{\mathrm{old}}(80, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(80, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 2}\)