Space of modular forms of level 812, weight 1, and Character 812.g

• Label: 812.1.g
• Level: $812$
• Weight: $1$
• Character orbit: 812.g
• Rep. character: $\chi_{812}(405,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $3$
• Sturm bound: $120$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 812 = 2^{2} \cdot 7 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	812.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 203 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(120\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(812, [\chi])\).

	Total	New	Old
Modular forms	13	4	9
Cusp forms	7	4	3
Eisenstein series	6	0	6

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	4	0	0	0

Trace form

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

Decomposition of \(S_{1}^{\mathrm{new}}(812, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
812.1.g.a	$812$	$1$	812.g	203.c	$2$	$1$	$1$	$0.405$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-203}) \)	None	✓	$2$	$0$	\(0\)	\(-1\)	\(0\)	\(1\)	$1$		\(q-q^{3}+q^{7}+2q^{17}-q^{19}-q^{21}+\cdots\)
812.1.g.b	$812$	$1$	812.g	203.c	$2$	$1$	$1$	$0.405$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-203}) \)	None	✓	$2$	$0$	\(0\)	\(1\)	\(0\)	\(1\)	$1$		\(q+q^{3}+q^{7}-2q^{17}+q^{19}+q^{21}+\cdots\)
812.1.g.c	$812$	$1$	812.g	203.c	$2$	$2$	$2$	$0.405$	\(\Q(\sqrt{3}) \)	$D_{6}$	\(\Q(\sqrt{-203}) \)	None	✓	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$		\(q-\beta q^{3}-q^{7}+2q^{9}+\beta q^{19}+\beta q^{21}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(812, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(812, [\chi]) \cong \)