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

• Label: 20.11.d
• Level: $20$
• Weight: $11$
• Character orbit: 20.d
• Rep. character: $\chi_{20}(19,\cdot)$
• Character field: $\Q$
• Dimension: $28$
• Newform subspaces: $4$
• Sturm bound: $33$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 20 = 2^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	20.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 20 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(33\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

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

Trace form

28 * q + 608 * q^4 + 1556 * q^5 - 4480 * q^6 + 472388 * q^9 + 24176 * q^10 + 429280 * q^14 - 539072 * q^16 - 4283104 * q^20 + 2717440 * q^21 + 25657280 * q^24 + 9050876 * q^25 + 9191136 * q^26 - 19342184 * q^29 + 56416160 * q^30 - 219292864 * q^34 - 162566752 * q^36 - 354837824 * q^40 + 56406856 * q^41 + 766329600 * q^44 - 199216564 * q^45 + 358329120 * q^46 + 358309988 * q^49 + 859922976 * q^50 - 803131840 * q^54 - 442489280 * q^56 + 296160000 * q^60 + 805559656 * q^61 - 1875284992 * q^64 - 253539648 * q^65 - 1440259200 * q^66 - 1495456640 * q^69 - 3430157760 * q^70 + 12198320736 * q^74 + 828422400 * q^76 + 4686174656 * q^80 - 5200597732 * q^81 - 11943818240 * q^84 - 6830251648 * q^85 - 6150898880 * q^86 + 9743437816 * q^89 - 4978675824 * q^90 + 6264221280 * q^94 + 10220645120 * q^96

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.d.a	$20$	$11$	20.d	20.d	$2$	$1$	$1$	$12.707$	\(\Q\)	\(\Q(\sqrt{-5}) \)	✓	✓			20.11.d.a	$2$	$0$	\(-32\)	\(-236\)	\(-3125\)	\(-33364\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-2^{5}q^{2}-236q^{3}+2^{10}q^{4}-5^{5}q^{5}+\cdots\)
20.11.d.b	$20$	$11$	20.d	20.d	$2$	$1$	$1$	$12.707$	\(\Q\)	\(\Q(\sqrt{-5}) \)	✓	✓			20.11.d.a	$2$	$0$	\(32\)	\(236\)	\(-3125\)	\(33364\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+2^{5}q^{2}+236q^{3}+2^{10}q^{4}-5^{5}q^{5}+\cdots\)
20.11.d.c	$20$	$11$	20.d	20.d	$2$	$2$	$2$	$12.707$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)		✓			20.11.d.c	$4$	$0$	\(0\)	\(0\)	\(-474\)	\(0\)	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+8\beta q^{2}-1024 q^{4}+(779\beta-237)q^{5}+\cdots\)
20.11.d.d	$20$	$11$	20.d	20.d	$2$	$24$	$24$	$12.707$		None		✓	✓		20.11.d.d	$4$	$0$	\(0\)	\(0\)	\(8280\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$