Space of modular forms of level 260, weight 2, and Character 260.bj

• Label: 260.2.bj
• Level: $260$
• Weight: $2$
• Character orbit: 260.bj
• Rep. character: $\chi_{260}(3,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $152$
• Newform subspaces: $3$
• Sturm bound: $84$
• Trace bound: $10$

Defining parameters

Level:	\( N \)	\(=\)	\( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	260.bj (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 260 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(84\)
Trace bound:			\(10\)
Distinguishing \(T_p\):			\(3\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(260, [\chi])\).

	Total	New	Old
Modular forms	184	184	0
Cusp forms	152	152	0
Eisenstein series	32	32	0

Trace form

\( 152 q - 2 q^{2} - 16 q^{5} - 4 q^{6} - 8 q^{8} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(260, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
260.2.bj.a	$260$	$2$	260.bj	260.aj	$12$	$4$	$1$	$2.076$	\(\Q(\zeta_{12})\)	\(\Q(\sqrt{-1}) \)		$4$	$0$	\(2\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{U}(1)[D_{12}]$	\(q+(-\zeta_{12}+\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}-2\zeta_{12}q^{4}+\cdots\)
260.2.bj.b	$260$	$2$	260.bj	260.aj	$12$	$4$	$1$	$2.076$	\(\Q(\zeta_{12})\)	\(\Q(\sqrt{-1}) \)		$4$	$0$	\(2\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{U}(1)[D_{12}]$	\(q+(-\zeta_{12}+\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}-2\zeta_{12}q^{4}+\cdots\)
260.2.bj.c	$260$	$2$	260.bj	260.aj	$12$	$144$	$36$	$2.076$		None		$8$	$0$	\(-6\)	\(0\)	\(-24\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$