Space of modular forms of level 752, weight 1, and Character 752.g

• Label: 752.1.g
• Level: $752$
• Weight: $1$
• Character orbit: 752.g
• Rep. character: $\chi_{752}(657,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $96$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 752 = 2^{4} \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	752.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 47 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(96\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(752, [\chi])\).

	Total	New	Old
Modular forms	18	3	15
Cusp forms	12	2	10
Eisenstein series	6	1	5

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	2	0	0	0

Trace form

\( 2 q + q^{3} + q^{7} + q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(752, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
752.1.g.a	$752$	$1$	752.g	47.b	$2$	$2$	$2$	$0.375$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-47}) \)	None	✓	$2$	$0$	\(0\)	\(1\)	\(0\)	\(1\)	$1$		\(q+(1-\beta )q^{3}+\beta q^{7}+(1-\beta )q^{9}+(-1+\cdots)q^{17}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(752, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(752, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(47, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(94, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(188, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(376, [\chi])\)\(^{\oplus 2}\)