Space of modular forms of level 352, weight 2, and Character 352.i

• Label: 352.2.i
• Level: $352$
• Weight: $2$
• Character orbit: 352.i
• Rep. character: $\chi_{352}(87,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $0$
• Newform subspaces: $0$
• Sturm bound: $96$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 352 = 2^{5} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	352.i (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 176 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 0 \)
Sturm bound:			\(96\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(352, [\chi])\).

	Total	New	Old
Modular forms	104	0	104
Cusp forms	88	0	88
Eisenstein series	16	0	16

Decomposition of \(S_{2}^{\mathrm{old}}(352, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(352, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(176, [\chi])\)\(^{\oplus 2}\)