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

• Label: 180.2.e
• Level: $180$
• Weight: $2$
• Character orbit: 180.e
• Rep. character: $\chi_{180}(71,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $1$
• Sturm bound: $72$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	180.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 12 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(72\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	44	8	36
Cusp forms	28	8	20
Eisenstein series	16	0	16

Trace form

8 * q + 4 * q^4 + 4 * q^10 + 16 * q^13 + 4 * q^16 - 16 * q^22 - 8 * q^25 - 32 * q^28 + 16 * q^34 - 16 * q^37 - 4 * q^40 - 40 * q^46 - 56 * q^49 - 8 * q^52 + 24 * q^58 + 16 * q^61 + 52 * q^64 + 24 * q^70 + 48 * q^73 + 48 * q^76 - 8 * q^82 - 32 * q^85 - 64 * q^88 + 48 * q^94 + 48 * q^97

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.e.a	$180$	$2$	180.e	12.b	$2$	$8$	$8$	$1.437$	8.0.18939904.2	None		✓	✓	✓	180.2.e.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{2}+\beta _{6})q^{2}+(\beta _{4}-\beta _{5}+\beta _{7})q^{4}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(180, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 2}\)