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

• Label: 130.2.m
• Level: $130$
• Weight: $2$
• Character orbit: 130.m
• Rep. character: $\chi_{130}(49,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $16$
• 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.m (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 65 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(42\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

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

Trace form

\( 16 q - 8 q^{4} + 16 q^{9} + O(q^{10}) \)

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.m.a	$130$	$2$	130.m	65.l	$6$	$8$	$4$	$1.038$	8.0.\(\cdots\).1	None		$2$	$0$	\(-4\)	\(0\)	\(3\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+\beta _{3})q^{2}-\beta _{2}q^{3}-\beta _{3}q^{4}-\beta _{7}q^{5}+\cdots\)
130.2.m.b	$130$	$2$	130.m	65.l	$6$	$8$	$4$	$1.038$	8.0.\(\cdots\).1	None		$2$	$0$	\(4\)	\(0\)	\(-3\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{3}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(-1+\beta _{3}+\cdots)q^{4}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(130, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 2}\)