Space of modular forms of level 180, weight 2, and Character 180.x

• Label: 180.2.x
• Level: $180$
• Weight: $2$
• Character orbit: 180.x
• Rep. character: $\chi_{180}(7,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $128$
• Newform subspaces: $1$
• Sturm bound: $72$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	180.x (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 180 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(72\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(180, [\chi])\).

	Total	New	Old
Modular forms	160	160	0
Cusp forms	128	128	0
Eisenstein series	32	32	0

Trace form

128 * q - 2 * q^2 - 4 * q^5 - 8 * q^6 - 8 * q^8 - 8 * q^10 + 2 * q^12 - 4 * q^13 - 4 * q^16 - 16 * q^17 - 36 * q^18 - 18 * q^20 - 24 * q^21 - 10 * q^22 - 4 * q^25 - 48 * q^26 + 8 * q^28 - 14 * q^30 + 18 * q^32 - 20 * q^33 - 40 * q^36 - 16 * q^37 - 34 * q^38 - 2 * q^40 - 8 * q^41 + 34 * q^42 - 28 * q^45 - 40 * q^46 - 22 * q^48 + 38 * q^50 - 18 * q^52 - 64 * q^53 - 32 * q^56 - 48 * q^57 - 10 * q^58 + 74 * q^60 - 8 * q^61 + 44 * q^62 + 12 * q^65 - 36 * q^66 + 58 * q^68 - 22 * q^70 + 78 * q^72 - 16 * q^73 - 32 * q^76 - 60 * q^77 + 114 * q^78 + 132 * q^80 + 24 * q^81 - 4 * q^85 + 32 * q^86 - 10 * q^88 + 138 * q^90 + 52 * q^92 - 68 * q^93 + 52 * q^96 - 4 * q^97 + 164 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(180, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
180.2.x.a	$180$	$2$	180.x	180.x	$12$	$128$	$32$	$1.437$		None		✓	✓	✓	180.2.x.a	$8$	$0$	\(-2\)	\(0\)	\(-4\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$