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

• Label: 180.2.j
• Level: $180$
• Weight: $2$
• Character orbit: 180.j
• Rep. character: $\chi_{180}(17,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $4$
• 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.j (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 15 \)
Character field:			\(\Q(i)\)
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	96	4	92
Cusp forms	48	4	44
Eisenstein series	48	0	48

Trace form

\( 4 q + 8 q^{7} + 12 q^{13} - 16 q^{25} - 32 q^{31} - 12 q^{37} - 24 q^{55} + 32 q^{67} + 28 q^{73} + 8 q^{85} + 48 q^{91} + 12 q^{97}+O(q^{100}) \)

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.j.a	$180$	$2$	180.j	15.e	$4$	$4$	$2$	$1.437$	\(\Q(\zeta_{8})\)	None		✓	✓	✓	180.2.j.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-2\zeta_{8}-\zeta_{8}^{3})q^{5}+(2-2\zeta_{8}^{2})q^{7}+\cdots\)

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

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