Properties

Label 80.2.o
Level $80$
Weight $2$
Character orbit 80.o
Rep. character $\chi_{80}(7,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $0$
Newform subspaces $0$
Sturm bound $24$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 80 = 2^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 80.o (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 40 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 0 \)
Sturm bound: \(24\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(80, [\chi])\).

Total New Old
Modular forms 32 0 32
Cusp forms 16 0 16
Eisenstein series 16 0 16

Decomposition of \(S_{2}^{\mathrm{old}}(80, [\chi])\) into lower level spaces

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