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

• Label: 260.2.r
• Level: $260$
• Weight: $2$
• Character orbit: 260.r
• Rep. character: $\chi_{260}(177,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $14$
• Newform subspaces: $3$
• Sturm bound: $84$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	260.r (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 65 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(84\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	96	14	82
Cusp forms	72	14	58
Eisenstein series	24	0	24

Trace form

\( 14 q + 2 q^{5} + O(q^{10}) \)

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.r.a	$260$	$2$	260.r	65.f	$4$	$2$	$1$	$2.076$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(-4\)	\(4\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-2+2i)q^{3}+(2-i)q^{5}+4q^{7}+\cdots\)
260.2.r.b	$260$	$2$	260.r	65.f	$4$	$4$	$2$	$2.076$	\(\Q(i, \sqrt{5})\)	None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{3}q^{3}+(-1-\beta _{1}+\beta _{3})q^{5}+(\beta _{1}+\cdots)q^{9}+\cdots\)
260.2.r.c	$260$	$2$	260.r	65.f	$4$	$8$	$4$	$2.076$	8.0.\(\cdots\).2	None		$2$	$0$	\(0\)	\(2\)	\(-2\)	\(-8\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{3}q^{3}+(-\beta _{1}+\beta _{7})q^{5}+(-1-\beta _{2}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(260, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(260, [\chi]) \cong \)