Space of modular forms of level 960, weight 4, and trivial character

• Label: 960.4.a
• Level: $960$
• Weight: $4$
• Character orbit: 960.a
• Rep. character: $\chi_{960}(1,\cdot)$
• Character field: $\Q$
• Dimension: $48$
• Newform subspaces: $42$
• Sturm bound: $768$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	960.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 42 \)
Sturm bound:			\(768\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(960))\).

	Total	New	Old
Modular forms	600	48	552
Cusp forms	552	48	504
Eisenstein series	48	0	48

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

\(2\)	\(3\)	\(5\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	$+$	\(6\)
\(+\)	\(+\)	\(-\)	$-$	\(5\)
\(+\)	\(-\)	\(+\)	$-$	\(6\)
\(+\)	\(-\)	\(-\)	$+$	\(7\)
\(-\)	\(+\)	\(+\)	$-$	\(6\)
\(-\)	\(+\)	\(-\)	$+$	\(7\)
\(-\)	\(-\)	\(+\)	$+$	\(6\)
\(-\)	\(-\)	\(-\)	$-$	\(5\)
Plus space			\(+\)	\(26\)
Minus space			\(-\)	\(22\)

Trace form

\( 48 q + 432 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(960))\) 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	3	5
960.4.a.a	$960$	$4$	960.a	1.a	$1$	$1$	$1$	$56.642$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-3\)	\(-5\)	\(-32\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}-5q^{5}-2^{5}q^{7}+9q^{9}+6^{2}q^{11}+\cdots\)
960.4.a.b	$960$	$4$	960.a	1.a	$1$	$1$	$1$	$56.642$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-3\)	\(-5\)	\(-24\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}-5q^{5}-24q^{7}+9q^{9}-52q^{11}+\cdots\)
960.4.a.c	$960$	$4$	960.a	1.a	$1$	$1$	$1$	$56.642$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-3\)	\(-5\)	\(-16\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}-5q^{5}-2^{4}q^{7}+9q^{9}+24q^{11}+\cdots\)
960.4.a.d	$960$	$4$	960.a	1.a	$1$	$1$	$1$	$56.642$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-3\)	\(-5\)	\(-12\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}-5q^{5}-12q^{7}+9q^{9}+24q^{11}+\cdots\)
960.4.a.e	$960$	$4$	960.a	1.a	$1$	$1$	$1$	$56.642$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-3\)	\(-5\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}-5q^{5}+9q^{9}+4q^{11}-54q^{13}+\cdots\)
960.4.a.f	$960$	$4$	960.a	1.a	$1$	$1$	$1$	$56.642$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-3\)	\(-5\)	\(4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}-5q^{5}+4q^{7}+9q^{9}+40q^{11}+\cdots\)
960.4.a.g	$960$	$4$	960.a	1.a	$1$	$1$	$1$	$56.642$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-3\)	\(-5\)	\(8\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}-5q^{5}+8q^{7}+9q^{9}-20q^{11}+\cdots\)
960.4.a.h	$960$	$4$	960.a	1.a	$1$	$1$	$1$	$56.642$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-3\)	\(-5\)	\(16\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}-5q^{5}+2^{4}q^{7}+9q^{9}-28q^{11}+\cdots\)
960.4.a.i	$960$	$4$	960.a	1.a	$1$	$1$	$1$	$56.642$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-3\)	\(-5\)	\(32\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}-5q^{5}+2^{5}q^{7}+9q^{9}-2^{6}q^{11}+\cdots\)
960.4.a.j	$960$	$4$	960.a	1.a	$1$	$1$	$1$	$56.642$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-3\)	\(-5\)	\(32\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}-5q^{5}+2^{5}q^{7}+9q^{9}+60q^{11}+\cdots\)
960.4.a.k	$960$	$4$	960.a	1.a	$1$	$1$	$1$	$56.642$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-3\)	\(5\)	\(-20\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}+5q^{5}-20q^{7}+9q^{9}-56q^{11}+\cdots\)
960.4.a.l	$960$	$4$	960.a	1.a	$1$	$1$	$1$	$56.642$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-3\)	\(5\)	\(-20\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}+5q^{5}-20q^{7}+9q^{9}-24q^{11}+\cdots\)
960.4.a.m	$960$	$4$	960.a	1.a	$1$	$1$	$1$	$56.642$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-3\)	\(5\)	\(-8\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}+5q^{5}-8q^{7}+9q^{9}-4q^{11}+\cdots\)
960.4.a.n	$960$	$4$	960.a	1.a	$1$	$1$	$1$	$56.642$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-3\)	\(5\)	\(-4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}+5q^{5}-4q^{7}+9q^{9}+48q^{11}+\cdots\)
960.4.a.o	$960$	$4$	960.a	1.a	$1$	$1$	$1$	$56.642$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-3\)	\(5\)	\(-4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}+5q^{5}-4q^{7}+9q^{9}+72q^{11}+\cdots\)
960.4.a.p	$960$	$4$	960.a	1.a	$1$	$1$	$1$	$56.642$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-3\)	\(5\)	\(12\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}+5q^{5}+12q^{7}+9q^{9}+20q^{11}+\cdots\)
960.4.a.q	$960$	$4$	960.a	1.a	$1$	$1$	$1$	$56.642$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-3\)	\(5\)	\(20\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}+5q^{5}+20q^{7}+9q^{9}-2^{4}q^{11}+\cdots\)
960.4.a.r	$960$	$4$	960.a	1.a	$1$	$1$	$1$	$56.642$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-3\)	\(5\)	\(28\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}+5q^{5}+28q^{7}+9q^{9}-24q^{11}+\cdots\)
960.4.a.s	$960$	$4$	960.a	1.a	$1$	$1$	$1$	$56.642$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(3\)	\(-5\)	\(-32\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}-5q^{5}-2^{5}q^{7}+9q^{9}-60q^{11}+\cdots\)
960.4.a.t	$960$	$4$	960.a	1.a	$1$	$1$	$1$	$56.642$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(3\)	\(-5\)	\(-32\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}-5q^{5}-2^{5}q^{7}+9q^{9}+2^{6}q^{11}+\cdots\)
960.4.a.u	$960$	$4$	960.a	1.a	$1$	$1$	$1$	$56.642$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(3\)	\(-5\)	\(-16\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}-5q^{5}-2^{4}q^{7}+9q^{9}+28q^{11}+\cdots\)
960.4.a.v	$960$	$4$	960.a	1.a	$1$	$1$	$1$	$56.642$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(3\)	\(-5\)	\(-8\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}-5q^{5}-8q^{7}+9q^{9}+20q^{11}+\cdots\)
960.4.a.w	$960$	$4$	960.a	1.a	$1$	$1$	$1$	$56.642$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(3\)	\(-5\)	\(-4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}-5q^{5}-4q^{7}+9q^{9}-40q^{11}+\cdots\)
960.4.a.x	$960$	$4$	960.a	1.a	$1$	$1$	$1$	$56.642$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(3\)	\(-5\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}-5q^{5}+9q^{9}-4q^{11}-54q^{13}+\cdots\)
960.4.a.y	$960$	$4$	960.a	1.a	$1$	$1$	$1$	$56.642$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(3\)	\(-5\)	\(12\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}-5q^{5}+12q^{7}+9q^{9}-24q^{11}+\cdots\)
960.4.a.z	$960$	$4$	960.a	1.a	$1$	$1$	$1$	$56.642$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(3\)	\(-5\)	\(16\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}-5q^{5}+2^{4}q^{7}+9q^{9}-24q^{11}+\cdots\)
960.4.a.ba	$960$	$4$	960.a	1.a	$1$	$1$	$1$	$56.642$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(3\)	\(-5\)	\(24\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}-5q^{5}+24q^{7}+9q^{9}+52q^{11}+\cdots\)
960.4.a.bb	$960$	$4$	960.a	1.a	$1$	$1$	$1$	$56.642$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(3\)	\(-5\)	\(32\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}-5q^{5}+2^{5}q^{7}+9q^{9}-6^{2}q^{11}+\cdots\)
960.4.a.bc	$960$	$4$	960.a	1.a	$1$	$1$	$1$	$56.642$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(3\)	\(5\)	\(-28\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}+5q^{5}-28q^{7}+9q^{9}+24q^{11}+\cdots\)
960.4.a.bd	$960$	$4$	960.a	1.a	$1$	$1$	$1$	$56.642$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(3\)	\(5\)	\(-20\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}+5q^{5}-20q^{7}+9q^{9}+2^{4}q^{11}+\cdots\)
960.4.a.be	$960$	$4$	960.a	1.a	$1$	$1$	$1$	$56.642$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(3\)	\(5\)	\(-12\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}+5q^{5}-12q^{7}+9q^{9}-20q^{11}+\cdots\)
960.4.a.bf	$960$	$4$	960.a	1.a	$1$	$1$	$1$	$56.642$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(3\)	\(5\)	\(4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}+5q^{5}+4q^{7}+9q^{9}-72q^{11}+\cdots\)
960.4.a.bg	$960$	$4$	960.a	1.a	$1$	$1$	$1$	$56.642$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(3\)	\(5\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}+5q^{5}+4q^{7}+9q^{9}-48q^{11}+\cdots\)
960.4.a.bh	$960$	$4$	960.a	1.a	$1$	$1$	$1$	$56.642$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(3\)	\(5\)	\(8\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}+5q^{5}+8q^{7}+9q^{9}+4q^{11}+\cdots\)
960.4.a.bi	$960$	$4$	960.a	1.a	$1$	$1$	$1$	$56.642$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(3\)	\(5\)	\(20\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}+5q^{5}+20q^{7}+9q^{9}+24q^{11}+\cdots\)
960.4.a.bj	$960$	$4$	960.a	1.a	$1$	$1$	$1$	$56.642$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(3\)	\(5\)	\(20\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}+5q^{5}+20q^{7}+9q^{9}+56q^{11}+\cdots\)
960.4.a.bk	$960$	$4$	960.a	1.a	$1$	$2$	$2$	$56.642$	\(\Q(\sqrt{89}) \)	None	✓	$1$	$1$	\(0\)	\(-6\)	\(-10\)	\(12\)		$-$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-3q^{3}-5q^{5}+(6+\beta )q^{7}+9q^{9}+(-12+\cdots)q^{11}+\cdots\)
960.4.a.bl	$960$	$4$	960.a	1.a	$1$	$2$	$2$	$56.642$	\(\Q(\sqrt{201}) \)	None	✓	$1$	$1$	\(0\)	\(-6\)	\(10\)	\(4\)		$+$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-3q^{3}+5q^{5}+(2+\beta )q^{7}+9q^{9}-20q^{11}+\cdots\)
960.4.a.bm	$960$	$4$	960.a	1.a	$1$	$2$	$2$	$56.642$	\(\Q(\sqrt{41}) \)	None	✓	$1$	$0$	\(0\)	\(-6\)	\(10\)	\(12\)		$-$	$+$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q-3q^{3}+5q^{5}+(6+\beta )q^{7}+9q^{9}+(12+\cdots)q^{11}+\cdots\)
960.4.a.bn	$960$	$4$	960.a	1.a	$1$	$2$	$2$	$56.642$	\(\Q(\sqrt{89}) \)	None	✓	$1$	$0$	\(0\)	\(6\)	\(-10\)	\(-12\)		$-$	$-$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+3q^{3}-5q^{5}+(-6-\beta )q^{7}+9q^{9}+\cdots\)
960.4.a.bo	$960$	$4$	960.a	1.a	$1$	$2$	$2$	$56.642$	\(\Q(\sqrt{41}) \)	None	✓	$1$	$1$	\(0\)	\(6\)	\(10\)	\(-12\)		$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+3q^{3}+5q^{5}+(-6-\beta )q^{7}+9q^{9}+\cdots\)
960.4.a.bp	$960$	$4$	960.a	1.a	$1$	$2$	$2$	$56.642$	\(\Q(\sqrt{201}) \)	None	✓	$1$	$0$	\(0\)	\(6\)	\(10\)	\(-4\)		$+$	$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+3q^{3}+5q^{5}+(-2-\beta )q^{7}+9q^{9}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(960))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(960)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 14}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(10))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(12))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 7}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(60))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(160))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(192))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(240))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(320))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(480))\)\(^{\oplus 2}\)