Space of modular forms of level 180, weight 6, and Character 180.d

• Label: 180.6.d
• Level: $180$
• Weight: $6$
• Character orbit: 180.d
• Rep. character: $\chi_{180}(109,\cdot)$
• Character field: $\Q$
• Dimension: $12$
• Newform subspaces: $4$
• Sturm bound: $216$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	180.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(216\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(180, [\chi])\).

	Total	New	Old
Modular forms	192	12	180
Cusp forms	168	12	156
Eisenstein series	24	0	24

Trace form

\( 12 q + 48 q^{5} + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(180, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
180.6.d.a	$180$	$6$	180.d	5.b	$2$	$2$	$2$	$28.869$	\(\Q(\sqrt{-61}) \)	None		$2$	$1$	\(0\)	\(0\)	\(-80\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-40+5\beta )q^{5}+2^{4}\beta q^{7}-80q^{11}+\cdots\)
180.6.d.b	$180$	$6$	180.d	5.b	$2$	$2$	$2$	$28.869$	\(\Q(\sqrt{-31}) \)	None		$2$	$0$	\(0\)	\(0\)	\(10\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(5+5\beta )q^{5}-11\beta q^{7}+10^{2}q^{11}+\cdots\)
180.6.d.c	$180$	$6$	180.d	5.b	$2$	$2$	$2$	$28.869$	\(\Q(\sqrt{-61}) \)	None		$2$	$0$	\(0\)	\(0\)	\(80\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(40-5\beta )q^{5}+2^{4}\beta q^{7}+80q^{11}+\cdots\)
180.6.d.d	$180$	$6$	180.d	5.b	$2$	$6$	$6$	$28.869$	\(\mathbb{Q}[x]/(x^{6} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(38\)	\(0\)	$2^{7}\cdot 3^{4}\cdot 5^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(6+\beta _{2})q^{5}+(\beta _{1}+\beta _{2}+\beta _{5})q^{7}+(-7^{2}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(180, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(180, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 3}\)