Space of modular forms of level 1816, weight 1, and Character 1816.g

• Label: 1816.1.g
• Level: $1816$
• Weight: $1$
• Character orbit: 1816.g
• Rep. character: $\chi_{1816}(1361,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $228$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1816 = 2^{3} \cdot 227 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1816.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 227 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(228\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1816, [\chi])\).

	Total	New	Old
Modular forms	24	2	22
Cusp forms	20	2	18
Eisenstein series	4	0	4

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

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

Trace form

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

Decomposition of \(S_{1}^{\mathrm{new}}(1816, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1816.1.g.a	$1816$	$1$	1816.g	227.b	$2$	$2$	$2$	$0.906$	\(\Q(\sqrt{-2}) \)	$S_{4}$	None	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$1$		\(q-\beta q^{5}+q^{7}-q^{9}-q^{11}-\beta q^{17}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1816, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1816, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(227, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(454, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(908, [\chi])\)\(^{\oplus 2}\)