Space of modular forms of level 20, weight 4, and Character 20.e

• Label: 20.4.e
• Level: $20$
• Weight: $4$
• Character orbit: 20.e
• Rep. character: $\chi_{20}(3,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $14$
• Newform subspaces: $2$
• Sturm bound: $12$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 20 = 2^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	20.e (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 20 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(12\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(20, [\chi])\).

	Total	New	Old
Modular forms	22	22	0
Cusp forms	14	14	0
Eisenstein series	8	8	0

Trace form

14 * q - 2 * q^2 - 4 * q^5 + 8 * q^6 - 44 * q^8 - 74 * q^10 - 80 * q^12 + 42 * q^13 + 184 * q^16 - 134 * q^17 + 306 * q^18 + 316 * q^20 - 144 * q^21 + 360 * q^22 + 106 * q^25 - 460 * q^26 - 880 * q^28 - 1240 * q^30 - 632 * q^32 + 80 * q^33 + 892 * q^36 + 326 * q^37 + 1600 * q^38 + 1836 * q^40 + 288 * q^41 + 1160 * q^42 + 586 * q^45 - 1432 * q^46 - 2720 * q^48 - 2214 * q^50 - 1524 * q^52 - 698 * q^53 + 2048 * q^56 - 960 * q^57 + 2712 * q^58 + 3280 * q^60 - 1832 * q^61 + 2440 * q^62 - 1778 * q^65 - 1680 * q^66 - 2428 * q^68 - 3040 * q^70 - 2172 * q^72 + 1942 * q^73 + 800 * q^76 + 3120 * q^77 + 3720 * q^78 + 2096 * q^80 + 4530 * q^81 + 536 * q^82 + 2282 * q^85 - 2552 * q^86 - 2400 * q^88 - 2154 * q^90 - 1840 * q^92 - 3280 * q^93 + 1088 * q^96 - 5994 * q^97 + 326 * q^98

Decomposition of \(S_{4}^{\mathrm{new}}(20, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
20.4.e.a	$20$	$4$	20.e	20.e	$4$	$2$	$1$	$1.180$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)		✓			20.4.e.a	$4$	$0$	\(4\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{U}(1)[D_{4}]$	\(q+(2 i+2)q^{2}+8 i q^{4}+(-11 i-2)q^{5}+\cdots\)
20.4.e.b	$20$	$4$	20.e	20.e	$4$	$12$	$6$	$1.180$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓	✓		20.4.e.b	$4$	$0$	\(-6\)	\(0\)	\(0\)	\(0\)	$2^{14}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(\beta _{1}-\beta _{5})q^{2}-\beta _{9}q^{3}+(2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)