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

• Label: 180.2.i
• Level: $180$
• Weight: $2$
• Character orbit: 180.i
• Rep. character: $\chi_{180}(61,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $8$
• Newform subspaces: $2$
• Sturm bound: $72$
• Trace bound: $1$

Defining parameters

Level:	$N$	$=$	$180 = 2^{2} \cdot 3^{2} \cdot 5$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	180.i (of order $3$ and degree $2$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$9$
Character field:			$\Q(\zeta_{3})$
Newform subspaces:			$2$
Sturm bound:			$72$
Trace bound:			$1$
Distinguishing $T_p$:			$7$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(180, [\chi])$.

	Total	New	Old
Modular forms	84	8	76
Cusp forms	60	8	52
Eisenstein series	24	0	24

Trace form

8 * q + 2 * q^3 + 2 * q^5 - 2 * q^7 + 8 * q^9 - 2 * q^13 - 2 * q^15 - 12 * q^17 + 16 * q^19 - 20 * q^21 + 6 * q^23 - 4 * q^25 + 2 * q^27 + 4 * q^31 + 12 * q^33 - 8 * q^35 + 4 * q^37 - 8 * q^39 - 12 * q^41 - 2 * q^43 - 8 * q^45 - 24 * q^47 - 12 * q^49 + 12 * q^51 - 24 * q^53 - 26 * q^57 - 20 * q^61 - 32 * q^63 + 10 * q^65 - 20 * q^67 + 24 * q^69 + 72 * q^71 + 40 * q^73 + 2 * q^75 - 6 * q^77 + 4 * q^79 + 20 * q^81 + 30 * q^83 + 6 * q^85 + 42 * q^87 + 8 * q^91 + 46 * q^93 + 4 * q^95 - 8 * q^97 + 12 * q^99

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.i.a	$180$	$2$	180.i	9.c	$3$	$2$	$1$	$1.437$	$\Q(\sqrt{-3})$	None		✓			180.2.i.a	$2$	$0$	$0$	$3$	$-1$	$1$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-\zeta_{6})q^{3}-\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+\cdots$
180.2.i.b	$180$	$2$	180.i	9.c	$3$	$6$	$3$	$1.437$	6.0.954288.1	None		✓	✓		180.2.i.b	$2$	$0$	$0$	$-1$	$3$	$-3$	$3$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{3}+(1+\beta _{2})q^{5}+(\beta _{2}-\beta _{3}-\beta _{4}+\cdots)q^{7}+\cdots$

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

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