Space of modular forms of level 3552, weight 1, and Character 3552.i

• Label: 3552.1.i
• Level: $3552$
• Weight: $1$
• Character orbit: 3552.i
• Rep. character: $\chi_{3552}(1553,\cdot)$
• Character field: $\Q$
• Dimension: $12$
• Newform subspaces: $5$
• Sturm bound: $608$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 3552 = 2^{5} \cdot 3 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3552.i (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 888 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(608\)
Trace bound:			\(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3552, [\chi])\).

	Total	New	Old
Modular forms	64	16	48
Cusp forms	48	12	36
Eisenstein series	16	4	12

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	12	0	0	0

Trace form

\( 12 q + 4 q^{7} - 4 q^{9} - 4 q^{25} - 4 q^{33} + 8 q^{49} + 4 q^{63} - 4 q^{73} + 12 q^{81}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3552, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3552.1.i.a	$3552$	$1$	3552.i	888.i	$2$	$1$	$1$	$1.773$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-222}) \)	None	✓				888.1.i.a	$2$	$0$	\(0\)	\(-1\)	\(0\)	\(1\)	$1$		\(q-q^{3}+q^{7}+q^{9}+q^{11}-q^{13}-q^{17}+\cdots\)
3552.1.i.b	$3552$	$1$	3552.i	888.i	$2$	$1$	$1$	$1.773$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-222}) \)	None	✓				888.1.i.a	$2$	$0$	\(0\)	\(-1\)	\(0\)	\(1\)	$1$		\(q-q^{3}+q^{7}+q^{9}+q^{11}+q^{13}+q^{17}+\cdots\)
3552.1.i.c	$3552$	$1$	3552.i	888.i	$2$	$1$	$1$	$1.773$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-222}) \)	None	✓				888.1.i.a	$2$	$0$	\(0\)	\(1\)	\(0\)	\(1\)	$1$		\(q+q^{3}+q^{7}+q^{9}-q^{11}-q^{13}+q^{17}+\cdots\)
3552.1.i.d	$3552$	$1$	3552.i	888.i	$2$	$1$	$1$	$1.773$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-222}) \)	None	✓				888.1.i.a	$2$	$0$	\(0\)	\(1\)	\(0\)	\(1\)	$1$		\(q+q^{3}+q^{7}+q^{9}-q^{11}+q^{13}-q^{17}+\cdots\)
3552.1.i.e	$3552$	$1$	3552.i	888.i	$2$	$8$	$8$	$1.773$	\(\Q(\zeta_{16})\)	$D_{8}$	\(\Q(\sqrt{-111}) \)	None			✓		888.1.i.e	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$		\(q-\zeta_{16}^{4}q^{3}+(-\zeta_{16}^{3}-\zeta_{16}^{5})q^{5}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3552, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3552, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(888, [\chi])\)\(^{\oplus 3}\)