Space of modular forms of level 20, weight 3, and Character 20.f

• Label: 20.3.f
• Level: $20$
• Weight: $3$
• Character orbit: 20.f
• Rep. character: $\chi_{20}(13,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $9$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 20 = 2^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	20.f (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(9\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(20, [\chi])\).

	Total	New	Old
Modular forms	18	2	16
Cusp forms	6	2	4
Eisenstein series	12	0	12

Trace form

2 * q + 2 * q^3 - 6 * q^5 - 14 * q^7 + 20 * q^11 + 18 * q^13 + 2 * q^15 + 2 * q^17 - 28 * q^21 - 46 * q^23 - 14 * q^25 + 32 * q^27 - 28 * q^31 + 20 * q^33 + 98 * q^35 + 66 * q^37 - 28 * q^41 - 30 * q^43 - 56 * q^45 - 78 * q^47 + 4 * q^51 - 14 * q^53 - 60 * q^55 - 16 * q^57 + 84 * q^61 + 98 * q^63 + 18 * q^65 - 14 * q^67 + 196 * q^71 + 98 * q^73 - 62 * q^75 - 140 * q^77 - 62 * q^81 - 126 * q^83 - 14 * q^85 - 16 * q^87 - 252 * q^91 - 28 * q^93 + 64 * q^95 + 66 * q^97

Decomposition of \(S_{3}^{\mathrm{new}}(20, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
20.3.f.a	$20$	$3$	20.f	5.c	$4$	$2$	$1$	$0.545$	\(\Q(\sqrt{-1}) \)	None		✓	✓	✓	20.3.f.a	$2$	$0$	\(0\)	\(2\)	\(-6\)	\(-14\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-i+1)q^{3}+(4 i-3)q^{5}+(-7 i-7)q^{7}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(20, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(20, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 2}\)