Space of modular forms of level 1512, weight 1, and Character 1512.ef

• Label: 1512.1.ef
• Level: $1512$
• Weight: $1$
• Character orbit: 1512.ef
• Rep. character: $\chi_{1512}(13,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $24$
• Newform subspaces: $3$
• Sturm bound: $288$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1512.ef (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1512 \)
Character field:			\(\Q(\zeta_{18})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(288\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1512, [\chi])\).

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

\( 24 q - 12 q^{15} - 12 q^{23} - 12 q^{50} - 12 q^{64} - 12 q^{65} + 24 q^{72} - 12 q^{78} - 12 q^{81} + 24 q^{92}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1512, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1512.1.ef.a	$1512$	$1$	1512.ef	1512.df	$18$	$6$	$1$	$0.755$	\(\Q(\zeta_{18})\)	$D_{9}$	\(\Q(\sqrt{-14}) \)	None		✓			1512.1.ef.a	$4$	$0$	\(0\)	\(-3\)	\(6\)	\(0\)	$1$		\(q-\zeta_{18}^{5}q^{2}+\zeta_{18}^{6}q^{3}-\zeta_{18}q^{4}+(1+\cdots)q^{5}+\cdots\)
1512.1.ef.b	$1512$	$1$	1512.ef	1512.df	$18$	$6$	$1$	$0.755$	\(\Q(\zeta_{18})\)	$D_{9}$	\(\Q(\sqrt{-14}) \)	None		✓			1512.1.ef.a	$4$	$0$	\(0\)	\(3\)	\(-6\)	\(0\)	$1$		\(q-\zeta_{18}^{5}q^{2}-\zeta_{18}^{6}q^{3}-\zeta_{18}q^{4}+(-1+\cdots)q^{5}+\cdots\)
1512.1.ef.c	$1512$	$1$	1512.ef	1512.df	$18$	$12$	$2$	$0.755$	\(\Q(\zeta_{36})\)	$D_{18}$	\(\Q(\sqrt{-14}) \)	None		✓	✓		1512.1.ef.c	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{36}^{10}q^{2}+\zeta_{36}^{3}q^{3}-\zeta_{36}^{2}q^{4}+\cdots\)