Space of modular forms of level 160, weight 2, and trivial character

• Label: 160.2.a
• Level: $160$
• Weight: $2$
• Character orbit: 160.a
• Rep. character: $\chi_{160}(1,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $3$
• Sturm bound: $48$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 160 = 2^{5} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	160.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(48\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(160))\).

	Total	New	Old
Modular forms	32	4	28
Cusp forms	17	4	13
Eisenstein series	15	0	15

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
\(+\)	\(+\)	\(+\)		\(7\)	\(1\)	\(6\)		\(4\)	\(1\)	\(3\)		\(3\)	\(0\)	\(3\)
\(+\)	\(-\)	\(-\)		\(9\)	\(2\)	\(7\)		\(5\)	\(2\)	\(3\)		\(4\)	\(0\)	\(4\)
\(-\)	\(+\)	\(-\)		\(9\)	\(1\)	\(8\)		\(5\)	\(1\)	\(4\)		\(4\)	\(0\)	\(4\)
\(-\)	\(-\)	\(+\)		\(7\)	\(0\)	\(7\)		\(3\)	\(0\)	\(3\)		\(4\)	\(0\)	\(4\)
Plus space		\(+\)		\(14\)	\(1\)	\(13\)		\(7\)	\(1\)	\(6\)		\(7\)	\(0\)	\(7\)
Minus space		\(-\)		\(18\)	\(3\)	\(15\)		\(10\)	\(3\)	\(7\)		\(8\)	\(0\)	\(8\)

Trace form

4 * q + 12 * q^9 - 16 * q^13 + 8 * q^17 - 8 * q^21 + 4 * q^25 + 8 * q^29 - 16 * q^33 - 16 * q^37 - 16 * q^41 + 8 * q^45 - 4 * q^49 + 16 * q^53 - 32 * q^57 + 8 * q^65 + 40 * q^69 + 8 * q^73 + 48 * q^77 - 20 * q^81 + 8 * q^89 + 16 * q^93 + 24 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(160))\) 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
160.2.a.a	$160$	$2$	160.a	1.a	$1$	$1$	$1$	$1.278$	\(\Q\)	None	✓	✓	✓	✓	160.2.a.a	$1$	$1$	\(0\)	\(-2\)	\(-1\)	\(-2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-q^{5}-2q^{7}+q^{9}-4q^{11}+\cdots\)
160.2.a.b	$160$	$2$	160.a	1.a	$1$	$1$	$1$	$1.278$	\(\Q\)	None	✓	✓	✓	✓	160.2.a.a	$1$	$0$	\(0\)	\(2\)	\(-1\)	\(2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-q^{5}+2q^{7}+q^{9}+4q^{11}+\cdots\)
160.2.a.c	$160$	$2$	160.a	1.a	$1$	$2$	$2$	$1.278$	\(\Q(\sqrt{2}) \)	None	✓	✓	✓	✓	160.2.a.c	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)		$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+q^{5}-\beta q^{7}+5q^{9}-2\beta q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(160))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(160)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 2}\)