Space of modular forms of level 3675, weight 1, and Character 3675.cg

• Label: 3675.1.cg
• Level: $3675$
• Weight: $1$
• Character orbit: 3675.cg
• Rep. character: $\chi_{3675}(326,\cdot)$
• Character field: $\Q(\zeta_{42})$
• Dimension: $24$
• Newform subspaces: $2$
• Sturm bound: $560$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 3675 = 3 \cdot 5^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3675.cg (of order \(42\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 147 \)
Character field:			\(\Q(\zeta_{42})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(560\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3675, [\chi])\).

	Total	New	Old
Modular forms	168	96	72
Cusp forms	24	24	0
Eisenstein series	144	72	72

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	24	0	0	0

Trace form

\( 24 q + 2 q^{4} + 2 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3675, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3675.1.cg.a	$3675$	$1$	3675.cg	147.n	$42$	$12$	$1$	$1.834$	\(\Q(\zeta_{21})\)	$D_{21}$	\(\Q(\sqrt{-3}) \)	None		$4$	$0$	\(0\)	\(-1\)	\(0\)	\(-1\)	$1$		\(q-\zeta_{42}^{2}q^{3}+\zeta_{42}^{20}q^{4}+\zeta_{42}^{17}q^{7}+\cdots\)
3675.1.cg.b	$3675$	$1$	3675.cg	147.n	$42$	$12$	$1$	$1.834$	\(\Q(\zeta_{21})\)	$D_{21}$	\(\Q(\sqrt{-3}) \)	None		$4$	$0$	\(0\)	\(1\)	\(0\)	\(1\)	$1$		\(q+\zeta_{42}^{2}q^{3}+\zeta_{42}^{20}q^{4}-\zeta_{42}^{17}q^{7}+\cdots\)