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

• Label: 352.2.e
• Level: $352$
• Weight: $2$
• Character orbit: 352.e
• Rep. character: $\chi_{352}(351,\cdot)$
• Character field: $\Q$
• Dimension: $12$
• Newform subspaces: $1$
• Sturm bound: $96$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 352 = 2^{5} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	352.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 44 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
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	56	12	44
Cusp forms	40	12	28
Eisenstein series	16	0	16

Trace form

\( 12 q - 4 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(352, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
352.2.e.a	$352$	$2$	352.e	44.c	$2$	$12$	$12$	$2.811$	12.0.\(\cdots\).1	None		✓	✓	✓	352.2.e.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{15}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{3}-\beta _{5}q^{5}+\beta _{8}q^{7}+\beta _{3}q^{9}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(352, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(44, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(176, [\chi])\)\(^{\oplus 2}\)