Space of modular forms of level 20, weight 4, and trivial character

• Label: 20.4.a
• Level: $20$
• Weight: $4$
• Character orbit: 20.a
• Rep. character: $\chi_{20}(1,\cdot)$
• Character field: $\Q$
• Dimension: $1$
• Newform subspaces: $1$
• Sturm bound: $12$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 20 = 2^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	20.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(12\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(20))\).

	Total	New	Old
Modular forms	12	1	11
Cusp forms	6	1	5
Eisenstein series	6	0	6

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)	\(5\)	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(4\)	\(0\)	\(4\)		\(2\)	\(0\)	\(2\)		\(2\)	\(0\)	\(2\)
\(+\)	\(-\)	\(-\)		\(3\)	\(0\)	\(3\)		\(1\)	\(0\)	\(1\)		\(2\)	\(0\)	\(2\)
\(-\)	\(+\)	\(-\)		\(2\)	\(0\)	\(2\)		\(1\)	\(0\)	\(1\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)		\(3\)	\(1\)	\(2\)		\(2\)	\(1\)	\(1\)		\(1\)	\(0\)	\(1\)
Plus space		\(+\)		\(7\)	\(1\)	\(6\)		\(4\)	\(1\)	\(3\)		\(3\)	\(0\)	\(3\)
Minus space		\(-\)		\(5\)	\(0\)	\(5\)		\(2\)	\(0\)	\(2\)		\(3\)	\(0\)	\(3\)

Trace form

q + 4 * q^3 + 5 * q^5 - 16 * q^7 - 11 * q^9 - 60 * q^11 + 86 * q^13 + 20 * q^15 + 18 * q^17 + 44 * q^19 - 64 * q^21 + 48 * q^23 + 25 * q^25 - 152 * q^27 - 186 * q^29 + 176 * q^31 - 240 * q^33 - 80 * q^35 + 254 * q^37 + 344 * q^39 + 186 * q^41 - 100 * q^43 - 55 * q^45 + 168 * q^47 - 87 * q^49 + 72 * q^51 - 498 * q^53 - 300 * q^55 + 176 * q^57 - 252 * q^59 - 58 * q^61 + 176 * q^63 + 430 * q^65 - 1036 * q^67 + 192 * q^69 + 168 * q^71 + 506 * q^73 + 100 * q^75 + 960 * q^77 + 272 * q^79 - 311 * q^81 + 948 * q^83 + 90 * q^85 - 744 * q^87 - 1014 * q^89 - 1376 * q^91 + 704 * q^93 + 220 * q^95 - 766 * q^97 + 660 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(20))\) 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					A-L signs		Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	5
20.4.a.a	$20$	$4$	20.a	1.a	$1$	$1$	$1$	$1.180$	\(\Q\)	None	✓	✓	✓	✓	20.4.a.a	$1$	$0$	\(0\)	\(4\)	\(5\)	\(-16\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+4q^{3}+5q^{5}-2^{4}q^{7}-11q^{9}-60q^{11}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(20))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(20)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(10))\)\(^{\oplus 2}\)