Space of modular forms of level 3780, weight 1, and Character 3780.ez

• Label: 3780.1.ez
• Level: $3780$
• Weight: $1$
• Character orbit: 3780.ez
• Rep. character: $\chi_{3780}(479,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $24$
• Newform subspaces: $2$
• Sturm bound: $864$
• Trace bound: $6$

Defining parameters

Level:	\( N \)	\(=\)	\( 3780 = 2^{2} \cdot 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3780.ez (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3780 \)
Character field:			\(\Q(\zeta_{18})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(864\)
Trace bound:			\(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3780, [\chi])\).

	Total	New	Old
Modular forms	72	72	0
Cusp forms	24	24	0
Eisenstein series	48	48	0

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

\( 24 q + 18 q^{6} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3780, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3780.1.ez.a	$3780$	$1$	3780.ez	3780.dz	$18$	$12$	$2$	$1.886$	\(\Q(\zeta_{36})\)	$D_{18}$	\(\Q(\sqrt{-5}) \)	None		✓			3780.1.ez.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{36}^{11}q^{2}+\zeta_{36}^{13}q^{3}-\zeta_{36}^{4}q^{4}+\cdots\)
3780.1.ez.b	$3780$	$1$	3780.ez	3780.dz	$18$	$12$	$2$	$1.886$	\(\Q(\zeta_{36})\)	$D_{18}$	\(\Q(\sqrt{-5}) \)	None		✓			3780.1.ez.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{36}^{11}q^{2}-\zeta_{36}^{7}q^{3}-\zeta_{36}^{4}q^{4}+\cdots\)