Space of modular forms of level 380, weight 1, and Character 380.g

• Label: 380.1.g
• Level: $380$
• Weight: $1$
• Character orbit: 380.g
• Rep. character: $\chi_{380}(189,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $60$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	380.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 95 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(60\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(380, [\chi])\).

	Total	New	Old
Modular forms	17	2	15
Cusp forms	11	2	9
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	2	0	0	0

Trace form

\( 2 q - q^{5} - 2 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(380, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
380.1.g.a	$380$	$1$	380.g	95.d	$2$	$2$	$2$	$0.190$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-19}) \)	None		$4$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)	$1$		\(q+\zeta_{6}^{2}q^{5}+(\zeta_{6}+\zeta_{6}^{2})q^{7}-q^{9}+q^{11}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(380, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(380, [\chi]) \cong \)