Space of modular forms of level 130, weight 2, and Character 130.c

• Label: 130.2.c
• Level: $130$
• Weight: $2$
• Character orbit: 130.c
• Rep. character: $\chi_{130}(129,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $2$
• Sturm bound: $42$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 130 = 2 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	130.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 65 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(42\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(130, [\chi])\).

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

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(130, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
130.2.c.a	$130$	$2$	130.c	65.d	$2$	$4$	$4$	$1.038$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None		$2$	$0$	\(-4\)	\(0\)	\(3\)	\(2\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}-\beta _{2}q^{3}+q^{4}+(1-\beta _{3})q^{5}+\beta _{2}q^{6}+\cdots\)
130.2.c.b	$130$	$2$	130.c	65.d	$2$	$4$	$4$	$1.038$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None		$2$	$0$	\(4\)	\(0\)	\(-3\)	\(-2\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}-\beta _{2}q^{3}+q^{4}+(-1+\beta _{3})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(130, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(130, [\chi]) \cong \)