Space of modular forms of level 80, weight 4, and Character 80.o

• Label: 80.4.o
• Level: $80$
• Weight: $4$
• Character orbit: 80.o
• Rep. character: $\chi_{80}(7,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $0$
• Newform subspaces: $0$
• Sturm bound: $48$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
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:			\(48\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	80	0	80
Cusp forms	64	0	64
Eisenstein series	16	0	16

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

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