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

• Label: 180.2.d
• Level: $180$
• Weight: $2$
• Character orbit: 180.d
• Rep. character: $\chi_{180}(109,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• 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.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
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	48	2	46
Cusp forms	24	2	22
Eisenstein series	24	0	24

Trace form

\( 2 q - 2 q^{5} + 8 q^{11} - 6 q^{25} - 12 q^{29} + 8 q^{31} - 16 q^{35} + 20 q^{41} - 18 q^{49} - 8 q^{55} + 8 q^{59} + 4 q^{61} + 24 q^{79} + 16 q^{85} - 20 q^{89}+O(q^{100}) \)

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.d.a	$180$	$2$	180.d	5.b	$2$	$2$	$2$	$1.437$	\(\Q(\sqrt{-1}) \)	None			✓	✓	60.2.d.a	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta-1)q^{5}+2\beta q^{7}+4 q^{11}-2\beta q^{17}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(180, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(180, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 2}\)