Space of modular forms of level 2232, weight 1, and Character 2232.i

• Label: 2232.1.i
• Level: $2232$
• Weight: $1$
• Character orbit: 2232.i
• Rep. character: $\chi_{2232}(1549,\cdot)$
• Character field: $\Q$
• Dimension: $11$
• Newform subspaces: $5$
• Sturm bound: $384$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 2232 = 2^{3} \cdot 3^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2232.i (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 248 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(384\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2232, [\chi])\).

	Total	New	Old
Modular forms	34	13	21
Cusp forms	26	11	15
Eisenstein series	8	2	6

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	11	0	0	0

Trace form

\( 11 q + 2 q^{2} + 2 q^{4} - q^{8} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2232, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2232.1.i.a	$2232$	$1$	2232.i	248.g	$2$	$1$	$1$	$1.114$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-31}) \), \(\Q(\sqrt{-62}) \)	\(\Q(\sqrt{2}) \)	✓				248.1.g.a	$4$	$0$	\(-1\)	\(0\)	\(0\)	\(-2\)	$1$		\(q-q^{2}+q^{4}-2q^{7}-q^{8}+2q^{14}+q^{16}+\cdots\)
2232.1.i.b	$2232$	$1$	2232.i	248.g	$2$	$2$	$2$	$1.114$	\(\Q(\sqrt{-1}) \)	$D_{2}$	\(\Q(\sqrt{-6}) \), \(\Q(\sqrt{-31}) \)	\(\Q(\sqrt{186}) \)		✓			2232.1.i.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$1$		\(q-iq^{2}-q^{4}-iq^{5}-q^{7}+iq^{8}-2q^{10}+\cdots\)
2232.1.i.c	$2232$	$1$	2232.i	248.g	$2$	$2$	$2$	$1.114$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-31}) \)	None					248.1.g.c	$4$	$0$	\(1\)	\(0\)	\(0\)	\(2\)	$1$		\(q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+(\zeta_{6}+\zeta_{6}^{2})q^{5}+\cdots\)
2232.1.i.d	$2232$	$1$	2232.i	248.g	$2$	$2$	$2$	$1.114$	\(\Q(\sqrt{2}) \)	$D_{4}$	\(\Q(\sqrt{-62}) \)	None	✓				248.1.g.b	$4$	$0$	\(2\)	\(0\)	\(0\)	\(0\)	$1$		\(q+q^{2}+q^{4}+q^{8}-\beta q^{11}+\beta q^{13}+\cdots\)
2232.1.i.e	$2232$	$1$	2232.i	248.g	$2$	$4$	$4$	$1.114$	\(\Q(\zeta_{12})\)	$D_{6}$	\(\Q(\sqrt{-31}) \)	None		✓	✓		2232.1.i.e	$8$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$1$		\(q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{3}q^{5}+q^{7}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(2232, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(2232, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(248, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(744, [\chi])\)\(^{\oplus 2}\)