Space of modular forms of level 2205, weight 1, and Character 2205.q

• Label: 2205.1.q
• Level: $2205$
• Weight: $1$
• Character orbit: 2205.q
• Rep. character: $\chi_{2205}(619,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $4$
• Newform subspaces: $2$
• Sturm bound: $336$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 2205 = 3^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2205.q (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 315 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(336\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2205, [\chi])\).

	Total	New	Old
Modular forms	36	20	16
Cusp forms	4	4	0
Eisenstein series	32	16	16

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

\( 4 q + 4 q^{4} - 2 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2205, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2205.1.q.a	$2205$	$1$	2205.q	315.q	$6$	$2$	$1$	$1.100$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-35}) \)	None		$4$	$0$	\(0\)	\(-1\)	\(-1\)	\(0\)	$1$		\(q+\zeta_{6}^{2}q^{3}+q^{4}+\zeta_{6}^{2}q^{5}-\zeta_{6}q^{9}+\cdots\)
2205.1.q.b	$2205$	$1$	2205.q	315.q	$6$	$2$	$1$	$1.100$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-35}) \)	None		$4$	$0$	\(0\)	\(1\)	\(1\)	\(0\)	$1$		\(q-\zeta_{6}^{2}q^{3}+q^{4}-\zeta_{6}^{2}q^{5}-\zeta_{6}q^{9}+\cdots\)