Space of modular forms of level 1260, weight 1, and Character 1260.eb

• Label: 1260.1.eb
• Level: $1260$
• Weight: $1$
• Character orbit: 1260.eb
• Rep. character: $\chi_{1260}(223,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $16$
• Newform subspaces: $2$
• Sturm bound: $288$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1260.eb (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1260 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(288\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1260, [\chi])\).

	Total	New	Old
Modular forms	48	48	0
Cusp forms	16	16	0
Eisenstein series	32	32	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	0	0	16	0

Trace form

\( 16 q - 4 q^{2} + 8 q^{8} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1260, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1260.1.eb.a	$1260$	$1$	1260.eb	1260.db	$12$	$8$	$2$	$0.629$	\(\Q(\zeta_{24})\)	$S_{4}$	None	None		$8$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{24}^{4}q^{2}+\zeta_{24}^{3}q^{3}+\zeta_{24}^{8}q^{4}+\cdots\)
1260.1.eb.b	$1260$	$1$	1260.eb	1260.db	$12$	$8$	$2$	$0.629$	\(\Q(\zeta_{24})\)	$S_{4}$	None	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{24}^{10}q^{2}+\zeta_{24}^{3}q^{3}-\zeta_{24}^{8}q^{4}+\cdots\)