Space of modular forms of level 2005, weight 1, and Character 2005.g

• Label: 2005.1.g
• Level: $2005$
• Weight: $1$
• Character orbit: 2005.g
• Rep. character: $\chi_{2005}(1202,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $10$
• Newform subspaces: $2$
• Sturm bound: $201$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 2005 = 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2005.g (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 2005 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(201\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2005, [\chi])\).

	Total	New	Old
Modular forms	14	14	0
Cusp forms	10	10	0
Eisenstein series	4	4	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	10	0	0	0

Trace form

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

Decomposition of \(S_{1}^{\mathrm{new}}(2005, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2005.1.g.a	$2005$	$1$	2005.g	2005.g	$4$	$2$	$1$	$1.001$	\(\Q(\sqrt{-1}) \)	$D_{4}$	None	\(\Q(\sqrt{401}) \)		$4$	$0$	\(2\)	\(0\)	\(2\)	\(-2\)	$1$		\(q+(1-i)q^{2}-iq^{4}+q^{5}+(-1+i+\cdots)q^{7}+\cdots\)
2005.1.g.b	$2005$	$1$	2005.g	2005.g	$4$	$8$	$4$	$1.001$	\(\Q(\zeta_{20})\)	$D_{20}$	None	\(\Q(\sqrt{401}) \)		$4$	$0$	\(-2\)	\(0\)	\(-2\)	\(2\)	$1$		\(q+(-\zeta_{20}+\zeta_{20}^{4})q^{2}+(\zeta_{20}^{2}-\zeta_{20}^{5}+\cdots)q^{4}+\cdots\)