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

• Label: 180.3.m
• Level: $180$
• Weight: $3$
• Character orbit: 180.m
• Rep. character: $\chi_{180}(107,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $48$
• Newform subspaces: $3$
• Sturm bound: $108$
• Trace bound: $10$

Defining parameters

Level:	\( N \)	\(=\)	\( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	180.m (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 60 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(108\)
Trace bound:			\(10\)
Distinguishing \(T_p\):			\(7\), \(13\)

Dimensions

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

	Total	New	Old
Modular forms	160	48	112
Cusp forms	128	48	80
Eisenstein series	32	0	32

Trace form

\( 48 q + O(q^{10}) \)

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.m.a	$180$	$3$	180.m	60.l	$4$	$4$	$2$	$4.905$	\(\Q(\zeta_{8})\)	\(\Q(\sqrt{-1}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{4}]$	\(q+2\zeta_{8}q^{2}+4\zeta_{8}^{2}q^{4}+(4\zeta_{8}+3\zeta_{8}^{3})q^{5}+\cdots\)
180.3.m.b	$180$	$3$	180.m	60.l	$4$	$4$	$2$	$4.905$	\(\Q(\zeta_{8})\)	\(\Q(\sqrt{-1}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{4}]$	\(q+2\zeta_{8}q^{2}+4\zeta_{8}^{2}q^{4}+(4\zeta_{8}-3\zeta_{8}^{3})q^{5}+\cdots\)
180.3.m.c	$180$	$3$	180.m	60.l	$4$	$40$	$20$	$4.905$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{3}^{\mathrm{old}}(180, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(180, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 2}\)