Space of modular forms of level 186, weight 2, and Character 186.c

• Label: 186.2.c
• Level: $186$
• Weight: $2$
• Character orbit: 186.c
• Rep. character: $\chi_{186}(185,\cdot)$
• Character field: $\Q$
• Dimension: $12$
• Newform subspaces: $2$
• Sturm bound: $64$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 186 = 2 \cdot 3 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	186.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 93 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(64\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(186, [\chi])\).

	Total	New	Old
Modular forms	36	12	24
Cusp forms	28	12	16
Eisenstein series	8	0	8

Trace form

\( 12 q - 12 q^{4} + 8 q^{7} + 4 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(186, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
186.2.c.a	$186$	$2$	186.c	93.c	$2$	$4$	$4$	$1.485$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{12}q^{2}+\zeta_{12}^{3}q^{3}-q^{4}-3\zeta_{12}q^{5}+\cdots\)
186.2.c.b	$186$	$2$	186.c	93.c	$2$	$8$	$8$	$1.485$	8.0.\(\cdots\).8	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{2}+\beta _{4}q^{3}-q^{4}+2\beta _{3}q^{5}+\beta _{5}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(186, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(186, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(93, [\chi])\)\(^{\oplus 2}\)