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

• Label: 352.2.g
• Level: $352$
• Weight: $2$
• Character orbit: 352.g
• Rep. character: $\chi_{352}(175,\cdot)$
• Character field: $\Q$
• Dimension: $10$
• Newform subspaces: $2$
• Sturm bound: $96$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 352 = 2^{5} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	352.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 88 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(96\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	56	14	42
Cusp forms	40	10	30
Eisenstein series	16	4	12

Trace form

\( 10 q + 4 q^{3} + 2 q^{9} + O(q^{10}) \)

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.g.a	$352$	$2$	352.g	88.g	$2$	$2$	$2$	$2.811$	\(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{-2}) \)					88.2.g.a	$4$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-2q^{3}+q^{9}+(3+\beta )q^{11}+4\beta q^{17}+\cdots\)
352.2.g.b	$352$	$2$	352.g	88.g	$2$	$8$	$8$	$2.811$	8.0.\(\cdots\).6	None			✓		88.2.g.b	$4$	$0$	\(0\)	\(8\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+\beta _{1})q^{3}+\beta _{6}q^{5}-\beta _{7}q^{7}+2\beta _{1}q^{9}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(352, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(88, [\chi])\)\(^{\oplus 3}\)