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

• Label: 1260.1.de
• Level: $1260$
• Weight: $1$
• Character orbit: 1260.de
• Rep. character: $\chi_{1260}(59,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $8$
• Newform subspaces: $2$
• Sturm bound: $288$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1260.de (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1260 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(288\)
Trace bound:			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	24	24	0
Cusp forms	8	8	0
Eisenstein series	16	16	0

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

\( 8 q + 4 q^{4} - 2 q^{9} + O(q^{10}) \)

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.de.a	$1260$	$1$	1260.de	1260.ce	$6$	$4$	$2$	$0.629$	\(\Q(\zeta_{12})\)	$D_{6}$	\(\Q(\sqrt{-5}) \)	None		$8$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$		\(q+\zeta_{12}^{5}q^{2}+\zeta_{12}^{5}q^{3}-\zeta_{12}^{4}q^{4}+\cdots\)
1260.1.de.b	$1260$	$1$	1260.de	1260.ce	$6$	$4$	$2$	$0.629$	\(\Q(\zeta_{12})\)	$D_{6}$	\(\Q(\sqrt{-5}) \)	None		$8$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$		\(q-\zeta_{12}^{5}q^{2}-\zeta_{12}^{3}q^{3}-\zeta_{12}^{4}q^{4}+\cdots\)