Space of modular forms of level 20, weight 8, and Character 20.c

• Label: 20.8.c
• Level: $20$
• Weight: $8$
• Character orbit: 20.c
• Rep. character: $\chi_{20}(9,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $24$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 20 = 2^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	20.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(24\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(20, [\chi])\).

	Total	New	Old
Modular forms	24	4	20
Cusp forms	18	4	14
Eisenstein series	6	0	6

Trace form

4 * q - 156 * q^5 - 2036 * q^9 - 2640 * q^11 + 5552 * q^15 - 36336 * q^19 + 63104 * q^21 + 162036 * q^25 - 481896 * q^29 + 161344 * q^31 + 691248 * q^35 - 2366496 * q^39 + 1129464 * q^41 + 2391244 * q^45 - 4312452 * q^49 + 1978688 * q^51 + 4726640 * q^55 - 7747152 * q^59 + 4305128 * q^61 + 3389568 * q^65 - 9357248 * q^69 - 1206048 * q^71 + 3265888 * q^75 + 5716992 * q^79 + 570116 * q^81 - 8256064 * q^85 + 13641576 * q^89 - 7864224 * q^91 - 12453936 * q^95 + 47580560 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(20, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
20.8.c.a	$20$	$8$	20.c	5.b	$2$	$4$	$4$	$6.248$	\(\mathbb{Q}[x]/(x^{4} + \cdots)\)	None		✓	✓	✓	20.8.c.a	$2$	$0$	\(0\)	\(0\)	\(-156\)	\(0\)	$2^{7}\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(-39-\beta _{1}+\beta _{2})q^{5}+(-5\beta _{1}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{8}^{\mathrm{old}}(20, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(20, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 2}\)