Space of modular forms of level 3645, weight 1, and Character 3645.n

• Label: 3645.1.n
• Level: $3645$
• Weight: $1$
• Character orbit: 3645.n
• Rep. character: $\chi_{3645}(404,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $48$
• Newform subspaces: $8$
• Sturm bound: $486$
• Trace bound: $16$

Defining parameters

Level:	\( N \)	\(=\)	\( 3645 = 3^{6} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3645.n (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 135 \)
Character field:			\(\Q(\zeta_{18})\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(486\)
Trace bound:			\(16\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3645, [\chi])\).

	Total	New	Old
Modular forms	264	84	180
Cusp forms	48	48	0
Eisenstein series	216	36	180

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	48	0	0	0

Trace form

\( 48 q + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3645, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3645.1.n.a	$3645$	$1$	3645.n	135.n	$18$	$6$	$1$	$1.819$	\(\Q(\zeta_{18})\)	$D_{9}$	\(\Q(\sqrt{-15}) \)	None		$4$	$0$	\(-6\)	\(0\)	\(0\)	\(0\)	$1$		\(q+(-1+\zeta_{18}^{7})q^{2}+(1-\zeta_{18}^{5}-\zeta_{18}^{7}+\cdots)q^{4}+\cdots\)
3645.1.n.b	$3645$	$1$	3645.n	135.n	$18$	$6$	$1$	$1.819$	\(\Q(\zeta_{18})\)	$D_{9}$	\(\Q(\sqrt{-15}) \)	None		$4$	$0$	\(-3\)	\(0\)	\(0\)	\(0\)	$1$		\(q+(-\zeta_{18}^{3}+\zeta_{18}^{4})q^{2}+(\zeta_{18}^{6}-\zeta_{18}^{7}+\cdots)q^{4}+\cdots\)
3645.1.n.c	$3645$	$1$	3645.n	135.n	$18$	$6$	$1$	$1.819$	\(\Q(\zeta_{18})\)	$D_{9}$	\(\Q(\sqrt{-15}) \)	None		$4$	$0$	\(-3\)	\(0\)	\(0\)	\(0\)	$1$		\(q+(-\zeta_{18}+\zeta_{18}^{6})q^{2}+(\zeta_{18}^{2}-\zeta_{18}^{3}+\cdots)q^{4}+\cdots\)
3645.1.n.d	$3645$	$1$	3645.n	135.n	$18$	$6$	$1$	$1.819$	\(\Q(\zeta_{18})\)	$D_{3}$	\(\Q(\sqrt{-15}) \)	None		$12$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{18}^{8}q^{2}+\zeta_{18}^{4}q^{5}+\zeta_{18}^{6}q^{8}+\cdots\)
3645.1.n.e	$3645$	$1$	3645.n	135.n	$18$	$6$	$1$	$1.819$	\(\Q(\zeta_{18})\)	$D_{3}$	\(\Q(\sqrt{-15}) \)	None		$12$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{18}^{8}q^{2}-\zeta_{18}^{4}q^{5}-\zeta_{18}^{6}q^{8}+\cdots\)
3645.1.n.f	$3645$	$1$	3645.n	135.n	$18$	$6$	$1$	$1.819$	\(\Q(\zeta_{18})\)	$D_{9}$	\(\Q(\sqrt{-15}) \)	None		$4$	$0$	\(3\)	\(0\)	\(0\)	\(0\)	$1$		\(q+(\zeta_{18}^{3}-\zeta_{18}^{4})q^{2}+(\zeta_{18}^{6}-\zeta_{18}^{7}+\cdots)q^{4}+\cdots\)
3645.1.n.g	$3645$	$1$	3645.n	135.n	$18$	$6$	$1$	$1.819$	\(\Q(\zeta_{18})\)	$D_{9}$	\(\Q(\sqrt{-15}) \)	None		$4$	$0$	\(3\)	\(0\)	\(0\)	\(0\)	$1$		\(q+(\zeta_{18}-\zeta_{18}^{6})q^{2}+(\zeta_{18}^{2}-\zeta_{18}^{3}+\cdots)q^{4}+\cdots\)
3645.1.n.h	$3645$	$1$	3645.n	135.n	$18$	$6$	$1$	$1.819$	\(\Q(\zeta_{18})\)	$D_{9}$	\(\Q(\sqrt{-15}) \)	None		$4$	$0$	\(6\)	\(0\)	\(0\)	\(0\)	$1$		\(q+(1-\zeta_{18}^{7})q^{2}+(1-\zeta_{18}^{5}-\zeta_{18}^{7}+\cdots)q^{4}+\cdots\)