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

• Label: 20.11.f
• Level: $20$
• Weight: $11$
• Character orbit: 20.f
• Rep. character: $\chi_{20}(13,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $10$
• 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.f (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q(i)\)
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	66	10	56
Cusp forms	54	10	44
Eisenstein series	12	0	12

Trace form

10 * q + 62 * q^3 + 894 * q^5 + 22286 * q^7 - 201700 * q^11 + 239298 * q^13 + 213662 * q^15 + 1045442 * q^17 + 4578860 * q^21 - 4097986 * q^23 - 4233934 * q^25 - 4817488 * q^27 + 23221660 * q^31 + 31816220 * q^33 - 55388242 * q^35 - 87811974 * q^37 + 29776460 * q^41 + 156325470 * q^43 - 144135236 * q^45 - 450750018 * q^47 + 1632585820 * q^51 + 701393866 * q^53 - 1301185140 * q^55 - 2564330416 * q^57 + 2991488220 * q^61 + 3352397678 * q^63 - 2867494182 * q^65 - 6990333394 * q^67 + 9915200380 * q^71 + 8401915018 * q^73 - 10170758642 * q^75 - 19825815140 * q^77 + 26071184290 * q^81 + 16998617454 * q^83 - 24280829854 * q^85 - 36065578576 * q^87 + 52347612540 * q^91 + 26277966572 * q^93 - 23431125296 * q^95 - 48945511254 * q^97

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.f.a	$20$	$11$	20.f	5.c	$4$	$10$	$5$	$12.707$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		✓	✓	✓	20.11.f.a	$2$	$0$	\(0\)	\(62\)	\(894\)	\(22286\)	$2^{22}\cdot 3^{2}\cdot 5^{6}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(6+6\beta _{1}-\beta _{2})q^{3}+(90-174\beta _{1}+\cdots)q^{5}+\cdots\)

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

\( S_{11}^{\mathrm{old}}(20, [\chi]) \simeq \) \(S_{11}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 2}\)