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

• Label: 1512.1.l
• Level: $1512$
• Weight: $1$
• Character orbit: 1512.l
• Rep. character: $\chi_{1512}(1189,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $288$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1512.l (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 56 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(288\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	26	4	22
Cusp forms	14	4	10
Eisenstein series	12	0	12

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

\( 4 q - 4 q^{4} - 2 q^{7} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1512.1.l.a	$1512$	$1$	1512.l	56.h	$2$	$4$	$4$	$0.755$	\(\Q(\zeta_{12})\)	$D_{6}$	\(\Q(\sqrt{-6}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$		\(q-\zeta_{12}^{3}q^{2}-q^{4}+(\zeta_{12}-\zeta_{12}^{5})q^{5}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1512, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1512, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 2}\)