Space of modular forms of level 180, weight 4, and Character 180.d

• Label: 180.4.d
• Level: $180$
• Weight: $4$
• Character orbit: 180.d
• Rep. character: $\chi_{180}(109,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $3$
• Sturm bound: $144$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	180.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(144\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(180, [\chi])\).

	Total	New	Old
Modular forms	120	8	112
Cusp forms	96	8	88
Eisenstein series	24	0	24

Trace form

\( 8 q + 6 q^{5} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(180, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
180.4.d.a	$180$	$4$	180.d	5.b	$2$	$2$	$2$	$10.620$	\(\Q(\sqrt{-19}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-14\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-7-\beta )q^{5}+\beta q^{7}-20q^{11}+6\beta q^{13}+\cdots\)
180.4.d.b	$180$	$4$	180.d	5.b	$2$	$2$	$2$	$10.620$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(20\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(10+5i)q^{5}-22iq^{7}+14q^{11}+\cdots\)
180.4.d.c	$180$	$4$	180.d	5.b	$2$	$4$	$4$	$10.620$	\(\Q(\sqrt{10}, \sqrt{-34})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{5}\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{5}-\beta _{1}q^{7}+(-3\beta _{2}+\beta _{3})q^{11}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(180, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(180, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 3}\)