Space of modular forms of level 180, weight 3, and Character 180.v

• Label: 180.3.v
• Level: $180$
• Weight: $3$
• Character orbit: 180.v
• Rep. character: $\chi_{180}(23,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $272$
• Newform subspaces: $1$
• Sturm bound: $108$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	180.v (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 180 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(108\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(180, [\chi])\).

	Total	New	Old
Modular forms	304	304	0
Cusp forms	272	272	0
Eisenstein series	32	32	0

Trace form

\( 272 q - 6 q^{2} - 12 q^{5} - 8 q^{6} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(180, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
180.3.v.a	$180$	$3$	180.v	180.v	$12$	$272$	$68$	$4.905$		None		$8$	$0$	\(-6\)	\(0\)	\(-12\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$