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

• Label: 180.4.i
• Level: $180$
• Weight: $4$
• Character orbit: 180.i
• Rep. character: $\chi_{180}(61,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $24$
• Newform subspaces: $3$
• Sturm bound: $144$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	180.i (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(144\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(7\)

Dimensions

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

	Total	New	Old
Modular forms	228	24	204
Cusp forms	204	24	180
Eisenstein series	24	0	24

Trace form

24 * q + 2 * q^3 - 10 * q^5 + 12 * q^7 - 28 * q^9 - 54 * q^11 - 24 * q^13 - 20 * q^15 + 348 * q^17 - 60 * q^19 + 196 * q^21 - 84 * q^23 - 300 * q^25 - 592 * q^27 - 342 * q^29 - 60 * q^31 + 738 * q^33 + 280 * q^35 + 336 * q^37 - 308 * q^39 - 804 * q^41 - 258 * q^43 - 140 * q^45 - 276 * q^47 - 630 * q^49 + 1518 * q^51 + 3432 * q^53 + 178 * q^57 - 630 * q^59 + 822 * q^61 - 1976 * q^63 - 200 * q^65 - 186 * q^67 - 522 * q^69 - 216 * q^71 - 1500 * q^73 + 50 * q^75 - 96 * q^77 - 888 * q^79 - 412 * q^81 + 228 * q^83 - 360 * q^85 + 2700 * q^87 + 828 * q^89 + 24 * q^91 - 1376 * q^93 + 520 * q^95 - 546 * q^97 + 1512 * q^99

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
180.4.i.a	$180$	$4$	180.i	9.c	$3$	$2$	$1$	$10.620$	\(\Q(\sqrt{-3}) \)	None		✓			180.4.i.a	$2$	$0$	\(0\)	\(9\)	\(5\)	\(7\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(6-3\zeta_{6})q^{3}+5\zeta_{6}q^{5}+(7-7\zeta_{6})q^{7}+\cdots\)
180.4.i.b	$180$	$4$	180.i	9.c	$3$	$8$	$4$	$10.620$	8.0.\(\cdots\).1	None		✓			180.4.i.b	$2$	$0$	\(0\)	\(-12\)	\(20\)	\(13\)	$2^{2}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2-\beta _{5})q^{3}+5\beta _{2}q^{5}+(5-3\beta _{2}+\cdots)q^{7}+\cdots\)
180.4.i.c	$180$	$4$	180.i	9.c	$3$	$14$	$7$	$10.620$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None		✓	✓		180.4.i.c	$2$	$0$	\(0\)	\(5\)	\(-35\)	\(-8\)	$2^{10}\cdot 3^{9}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{3}+\beta _{5})q^{3}+(-5+5\beta _{2})q^{5}+\cdots\)

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

\( S_{4}^{\mathrm{old}}(180, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 2}\)