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

• Label: 20.3.d
• Level: $20$
• Weight: $3$
• Character orbit: 20.d
• Rep. character: $\chi_{20}(19,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $3$
• Sturm bound: $9$
• Trace bound: $2$

Defining parameters

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

Dimensions

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

	Total	New	Old
Modular forms	8	8	0
Cusp forms	4	4	0
Eisenstein series	4	4	0

Trace form

4 * q - 4 * q^5 - 16 * q^6 - 4 * q^9 + 16 * q^10 + 16 * q^14 + 64 * q^16 - 64 * q^20 - 32 * q^21 - 64 * q^24 + 36 * q^25 - 96 * q^26 + 40 * q^29 + 80 * q^30 + 64 * q^34 + 128 * q^36 - 64 * q^40 + 88 * q^41 - 124 * q^45 - 176 * q^46 - 164 * q^49 + 96 * q^50 + 32 * q^54 + 64 * q^56 - 72 * q^61 + 192 * q^65 + 352 * q^69 - 80 * q^70 - 96 * q^74 - 64 * q^80 - 28 * q^81 - 128 * q^84 - 128 * q^85 + 304 * q^86 - 440 * q^89 - 144 * q^90 + 16 * q^94 - 256 * q^96

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.d.a	$20$	$3$	20.d	20.d	$2$	$1$	$1$	$0.545$	\(\Q\)	\(\Q(\sqrt{-5}) \)	✓	✓			20.3.d.a	$2$	$0$	\(-2\)	\(4\)	\(-5\)	\(-4\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-2q^{2}+4q^{3}+4q^{4}-5q^{5}-8q^{6}+\cdots\)
20.3.d.b	$20$	$3$	20.d	20.d	$2$	$1$	$1$	$0.545$	\(\Q\)	\(\Q(\sqrt{-5}) \)	✓	✓			20.3.d.a	$2$	$0$	\(2\)	\(-4\)	\(-5\)	\(4\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+2q^{2}-4q^{3}+4q^{4}-5q^{5}-8q^{6}+\cdots\)
20.3.d.c	$20$	$3$	20.d	20.d	$2$	$2$	$2$	$0.545$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)		✓	✓		20.3.d.c	$4$	$0$	\(0\)	\(0\)	\(6\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta q^{2}-4 q^{4}+(-2\beta+3)q^{5}-4\beta q^{8}+\cdots\)