Space of modular forms of level 3552, weight 2, and Character 3552.o

• Label: 3552.2.o
• Level: $3552$
• Weight: $2$
• Character orbit: 3552.o
• Rep. character: $\chi_{3552}(2737,\cdot)$
• Character field: $\Q$
• Dimension: $76$
• Newform subspaces: $1$
• Sturm bound: $1216$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 3552 = 2^{5} \cdot 3 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3552.o (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 296 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(1216\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3552, [\chi])\).

	Total	New	Old
Modular forms	624	76	548
Cusp forms	592	76	516
Eisenstein series	32	0	32

Trace form

\( 76 q - 8 q^{7} - 76 q^{9} + 84 q^{25} - 8 q^{41} + 60 q^{49} + 8 q^{63} + 48 q^{65} + 16 q^{71} + 24 q^{73} + 76 q^{81}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3552, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3552.2.o.a	$3552$	$2$	3552.o	296.e	$2$	$76$	$76$	$28.363$		None			✓	✓	888.2.o.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(3552, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3552, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(296, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(888, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1184, [\chi])\)\(^{\oplus 2}\)