Space of modular forms of level 186, weight 4, and Character 186.p

• Label: 186.4.p
• Level: $186$
• Weight: $4$
• Character orbit: 186.p
• Rep. character: $\chi_{186}(11,\cdot)$
• Character field: $\Q(\zeta_{30})$
• Dimension: $256$
• Newform subspaces: $1$
• Sturm bound: $128$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 186 = 2 \cdot 3 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	186.p (of order \(30\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 93 \)
Character field:			\(\Q(\zeta_{30})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(128\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(186, [\chi])\).

	Total	New	Old
Modular forms	800	256	544
Cusp forms	736	256	480
Eisenstein series	64	0	64

Trace form

\( 256 q + 256 q^{4} - 8 q^{7} + 64 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(186, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
186.4.p.a	$186$	$4$	186.p	93.p	$30$	$256$	$32$	$10.974$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)		$\mathrm{SU}(2)[C_{30}]$

Decomposition of \(S_{4}^{\mathrm{old}}(186, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(186, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(93, [\chi])\)\(^{\oplus 2}\)