Space of modular forms of level 160, weight 6, and trivial character

• Label: 160.6.a
• Level: $160$
• Weight: $6$
• Character orbit: 160.a
• Rep. character: $\chi_{160}(1,\cdot)$
• Character field: $\Q$
• Dimension: $20$
• Newform subspaces: $8$
• Sturm bound: $144$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 160 = 2^{5} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	160.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(144\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(160))\).

	Total	New	Old
Modular forms	128	20	108
Cusp forms	112	20	92
Eisenstein series	16	0	16

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	Dim
\(+\)	\(+\)	$+$	\(5\)
\(+\)	\(-\)	$-$	\(6\)
\(-\)	\(+\)	$-$	\(5\)
\(-\)	\(-\)	$+$	\(4\)
Plus space		\(+\)	\(9\)
Minus space		\(-\)	\(11\)

Trace form

\( 20 q + 1532 q^{9} + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(160))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	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
160.6.a.a	$160$	$6$	160.a	1.a	$1$	$2$	$2$	$25.661$	\(\Q(\sqrt{70}) \)	None	✓	$1$	$1$	\(0\)	\(-8\)	\(50\)	\(-104\)		$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-4+\beta )q^{3}+5^{2}q^{5}+(-52-\beta )q^{7}+\cdots\)
160.6.a.b	$160$	$6$	160.a	1.a	$1$	$2$	$2$	$25.661$	\(\Q(\sqrt{5}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(-50\)	\(0\)		$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-3\beta q^{3}-5^{2}q^{5}-31\beta q^{7}-63q^{9}+\cdots\)
160.6.a.c	$160$	$6$	160.a	1.a	$1$	$2$	$2$	$25.661$	\(\Q(\sqrt{85}) \)	None	✓	$2$	$1$	\(0\)	\(0\)	\(-50\)	\(0\)		$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta q^{3}-5^{2}q^{5}+3\beta q^{7}+97q^{9}+26\beta q^{11}+\cdots\)
160.6.a.d	$160$	$6$	160.a	1.a	$1$	$2$	$2$	$25.661$	\(\Q(\sqrt{10}) \)	None	✓	$2$	$1$	\(0\)	\(0\)	\(50\)	\(0\)		$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+5^{2}q^{5}+7\beta q^{7}-203q^{9}+\cdots\)
160.6.a.e	$160$	$6$	160.a	1.a	$1$	$2$	$2$	$25.661$	\(\Q(\sqrt{70}) \)	None	✓	$1$	$0$	\(0\)	\(8\)	\(50\)	\(104\)		$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(4+\beta )q^{3}+5^{2}q^{5}+(52-\beta )q^{7}+(53+\cdots)q^{9}+\cdots\)
160.6.a.f	$160$	$6$	160.a	1.a	$1$	$3$	$3$	$25.661$	3.3.39180.1	None	✓	$1$	$1$	\(0\)	\(-10\)	\(-75\)	\(6\)		$+$	$+$	$+$	$2^{6}$	$\mathrm{SU}(2)$	\(q+(-3-\beta _{1})q^{3}-5^{2}q^{5}+(2+\beta _{1}-\beta _{2})q^{7}+\cdots\)
160.6.a.g	$160$	$6$	160.a	1.a	$1$	$3$	$3$	$25.661$	3.3.39180.1	None	✓	$1$	$0$	\(0\)	\(10\)	\(-75\)	\(-6\)		$-$	$+$	$-$	$2^{6}$	$\mathrm{SU}(2)$	\(q+(3+\beta _{1})q^{3}-5^{2}q^{5}+(-2-\beta _{1}+\beta _{2})q^{7}+\cdots\)
160.6.a.h	$160$	$6$	160.a	1.a	$1$	$4$	$4$	$25.661$	4.4.81998080.1	None	✓	$2$	$0$	\(0\)	\(0\)	\(100\)	\(0\)		$+$	$-$	$-$	$2^{11}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+5^{2}q^{5}+(-6\beta _{1}+\beta _{2})q^{7}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(160))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(160)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(10))\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 2}\)