Space of modular forms of level 416, weight 3, and Character 416.o

• Label: 416.3.o
• Level: $416$
• Weight: $3$
• Character orbit: 416.o
• Rep. character: $\chi_{416}(103,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $0$
• Newform subspaces: $0$
• Sturm bound: $168$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 416 = 2^{5} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	416.o (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 208 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 0 \)
Sturm bound:			\(168\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(416, [\chi])\).

	Total	New	Old
Modular forms	232	0	232
Cusp forms	216	0	216
Eisenstein series	16	0	16

Decomposition of \(S_{3}^{\mathrm{old}}(416, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(416, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(208, [\chi])\)\(^{\oplus 2}\)