Space of modular forms of level 20, weight 11, and Character 20.b

• Label: 20.11.b
• Level: $20$
• Weight: $11$
• Character orbit: 20.b
• Rep. character: $\chi_{20}(11,\cdot)$
• Character field: $\Q$
• Dimension: $20$
• Newform subspaces: $1$
• Sturm bound: $33$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 20 = 2^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	20.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 4 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(33\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(20, [\chi])\).

	Total	New	Old
Modular forms	32	20	12
Cusp forms	28	20	8
Eisenstein series	4	0	4

Trace form

20 * q + 22 * q^2 - 644 * q^4 - 14784 * q^6 + 3448 * q^8 - 414868 * q^9 - 31250 * q^10 + 1329640 * q^12 - 278864 * q^13 - 2240504 * q^14 + 4261360 * q^16 - 1921656 * q^17 - 3556082 * q^18 - 1187500 * q^20 + 4157512 * q^21 - 5811280 * q^22 - 19112144 * q^24 + 39062500 * q^25 + 25066884 * q^26 - 87415400 * q^28 - 66014888 * q^29 + 39875000 * q^30 - 33171328 * q^32 + 85980560 * q^33 - 27236084 * q^34 + 355456476 * q^36 - 153620656 * q^37 + 250352720 * q^38 - 112375000 * q^40 + 477406160 * q^41 - 570662040 * q^42 + 339141040 * q^44 - 140125000 * q^45 - 897549304 * q^46 - 479727360 * q^48 + 333772012 * q^49 + 42968750 * q^50 - 110465096 * q^52 - 1669491824 * q^53 + 706139792 * q^54 - 1362290224 * q^56 + 3973032960 * q^57 + 2075027916 * q^58 - 677375000 * q^60 - 4283166080 * q^61 + 1664032240 * q^62 + 340459456 * q^64 + 290125000 * q^65 + 1884031760 * q^66 + 3042411896 * q^68 - 5321669928 * q^69 - 2070000000 * q^70 + 1632326712 * q^72 + 2474287656 * q^73 + 188682276 * q^74 + 2323171200 * q^76 + 410885040 * q^77 - 19914223760 * q^78 + 3604750000 * q^80 + 9939722652 * q^81 - 3197757116 * q^82 + 2383099552 * q^84 + 4799500000 * q^85 + 19648321456 * q^86 + 2774318240 * q^88 + 3011851592 * q^89 - 2849906250 * q^90 - 27349072440 * q^92 - 11861394640 * q^93 + 15684681576 * q^94 - 1990377984 * q^96 - 39984502056 * q^97 + 38416891998 * q^98

Decomposition of \(S_{11}^{\mathrm{new}}(20, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
20.11.b.a	$20$	$11$	20.b	4.b	$2$	$20$	$20$	$12.707$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		✓	✓	✓	20.11.b.a	$2$	$0$	\(22\)	\(0\)	\(0\)	\(0\)	$2^{94}\cdot 3^{4}\cdot 5^{29}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1-\beta _{1})q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(-2^{5}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{11}^{\mathrm{old}}(20, [\chi])\) into lower level spaces

\( S_{11}^{\mathrm{old}}(20, [\chi]) \simeq \) \(S_{11}^{\mathrm{new}}(4, [\chi])\)\(^{\oplus 2}\)