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

• Label: 1512.1.bn
• Level: $1512$
• Weight: $1$
• Character orbit: 1512.bn
• Rep. character: $\chi_{1512}(181,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $8$
• Newform subspaces: $3$
• Sturm bound: $288$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1512.bn (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 504 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(288\)
Trace bound:			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	48	16	32
Cusp forms	24	8	16
Eisenstein series	24	8	16

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	8	0	0	0

Trace form

\( 8 q - 4 q^{4} + 4 q^{14} - 4 q^{16} - 4 q^{23} - 4 q^{25} - 4 q^{49} - 4 q^{50} + 4 q^{56} + 8 q^{64} - 4 q^{65} - 4 q^{92} + 8 q^{95}+O(q^{100}) \)

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.bn.a	$1512$	$1$	1512.bn	504.an	$6$	$2$	$1$	$0.755$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-14}) \)	None					504.1.bn.a	$4$	$0$	\(1\)	\(0\)	\(-1\)	\(-1\)	$1$		\(q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{5}-\zeta_{6}q^{7}+\cdots\)
1512.1.bn.b	$1512$	$1$	1512.bn	504.an	$6$	$2$	$1$	$0.755$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-14}) \)	None					504.1.bn.a	$4$	$0$	\(1\)	\(0\)	\(1\)	\(-1\)	$1$		\(q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{5}-\zeta_{6}q^{7}+\cdots\)
1512.1.bn.c	$1512$	$1$	1512.bn	504.an	$6$	$4$	$2$	$0.755$	\(\Q(\zeta_{12})\)	$D_{6}$	\(\Q(\sqrt{-14}) \)	None			✓		504.1.bn.c	$8$	$0$	\(-2\)	\(0\)	\(0\)	\(2\)	$3$		\(q+\zeta_{12}^{4}q^{2}-\zeta_{12}^{2}q^{4}+(\zeta_{12}+\zeta_{12}^{3}+\cdots)q^{5}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(1512, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 2}\)