Space of modular forms of level 160, weight 4, and trivial character

• Label: 160.4.a
• Level: $160$
• Weight: $4$
• Character orbit: 160.a
• Rep. character: $\chi_{160}(1,\cdot)$
• Character field: $\Q$
• Dimension: $12$
• Newform subspaces: $7$
• Sturm bound: $96$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 160 = 2^{5} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	160.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(96\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(160))\).

	Total	New	Old
Modular forms	80	12	68
Cusp forms	64	12	52
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
\(+\)	\(+\)	\(+\)	\(3\)
\(+\)	\(-\)	\(-\)	\(2\)
\(-\)	\(+\)	\(-\)	\(3\)
\(-\)	\(-\)	\(+\)	\(4\)
Plus space		\(+\)	\(7\)
Minus space		\(-\)	\(5\)

Trace form

12 * q + 68 * q^9 + 144 * q^13 + 152 * q^17 - 376 * q^21 + 300 * q^25 + 56 * q^29 + 1232 * q^33 - 1008 * q^37 - 176 * q^41 + 440 * q^45 + 1204 * q^49 - 784 * q^53 + 416 * q^57 - 2560 * q^61 + 280 * q^65 - 1064 * q^69 - 2088 * q^73 - 944 * q^77 - 1020 * q^81 + 2648 * q^89 - 3472 * q^93 - 2488 * q^97

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(160))\) 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
160.4.a.a	$160$	$4$	160.a	1.a	$1$	$1$	$1$	$9.440$	\(\Q\)	None	✓	✓			160.4.a.a	$1$	$0$	\(0\)	\(-2\)	\(-5\)	\(6\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-5q^{5}+6q^{7}-23q^{9}+60q^{11}+\cdots\)
160.4.a.b	$160$	$4$	160.a	1.a	$1$	$1$	$1$	$9.440$	\(\Q\)	None	✓	✓			160.4.a.a	$1$	$1$	\(0\)	\(2\)	\(-5\)	\(-6\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-5q^{5}-6q^{7}-23q^{9}-60q^{11}+\cdots\)
160.4.a.c	$160$	$4$	160.a	1.a	$1$	$2$	$2$	$9.440$	\(\Q(\sqrt{6}) \)	None	✓	✓	✓	✓	160.4.a.c	$1$	$1$	\(0\)	\(-8\)	\(10\)	\(-8\)		$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-4+\beta )q^{3}+5q^{5}+(-4-5\beta )q^{7}+\cdots\)
160.4.a.d	$160$	$4$	160.a	1.a	$1$	$2$	$2$	$9.440$	\(\Q(\sqrt{5}) \)	None	✓	✓	✓		160.4.a.d	$2$	$1$	\(0\)	\(0\)	\(-10\)	\(0\)		$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta q^{3}-5q^{5}+7\beta q^{7}-7q^{9}+2\beta q^{11}+\cdots\)
160.4.a.e	$160$	$4$	160.a	1.a	$1$	$2$	$2$	$9.440$	\(\Q(\sqrt{13}) \)	None	✓	✓	✓		160.4.a.e	$2$	$0$	\(0\)	\(0\)	\(-10\)	\(0\)		$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta q^{3}-5q^{5}-\beta q^{7}+5^{2}q^{9}-6\beta q^{11}+\cdots\)
160.4.a.f	$160$	$4$	160.a	1.a	$1$	$2$	$2$	$9.440$	\(\Q(\sqrt{10}) \)	None	✓	✓			160.4.a.f	$2$	$0$	\(0\)	\(0\)	\(10\)	\(0\)		$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+5q^{5}+3\beta q^{7}+13q^{9}-2\beta q^{11}+\cdots\)
160.4.a.g	$160$	$4$	160.a	1.a	$1$	$2$	$2$	$9.440$	\(\Q(\sqrt{6}) \)	None	✓	✓			160.4.a.c	$1$	$0$	\(0\)	\(8\)	\(10\)	\(8\)		$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(4+\beta )q^{3}+5q^{5}+(4-5\beta )q^{7}+(13+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(160))\) into lower level spaces

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