Space of modular forms of level 960, weight 2, and trivial character

• Label: 960.2.a
• Level: $960$
• Weight: $2$
• Character orbit: 960.a
• Rep. character: $\chi_{960}(1,\cdot)$
• Character field: $\Q$
• Dimension: $16$
• Newform subspaces: $16$
• Sturm bound: $384$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	960.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 16 \)
Sturm bound:			\(384\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(7\), \(11\), \(13\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(960))\).

	Total	New	Old
Modular forms	216	16	200
Cusp forms	169	16	153
Eisenstein series	47	0	47

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
\(+\)	\(+\)	\(+\)	\(+\)	\(2\)
\(+\)	\(+\)	\(-\)	\(-\)	\(3\)
\(+\)	\(-\)	\(+\)	\(-\)	\(2\)
\(+\)	\(-\)	\(-\)	\(+\)	\(1\)
\(-\)	\(+\)	\(+\)	\(-\)	\(2\)
\(-\)	\(+\)	\(-\)	\(+\)	\(1\)
\(-\)	\(-\)	\(+\)	\(+\)	\(2\)
\(-\)	\(-\)	\(-\)	\(-\)	\(3\)
Plus space			\(+\)	\(6\)
Minus space			\(-\)	\(10\)

Trace form

\( 16 q + 16 q^{9} - 16 q^{13} - 16 q^{21} + 16 q^{25} + 32 q^{29} + 16 q^{37} + 16 q^{49} + 32 q^{53} + 16 q^{69} + 32 q^{77} + 16 q^{81} + 16 q^{85} - 16 q^{93}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(960))\) 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	3	5
960.2.a.a	$960$	$2$	960.a	1.a	$1$	$1$	$1$	$7.666$	\(\Q\)	None	✓				15.2.a.a	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{9}-4q^{11}+2q^{13}+\cdots\)
960.2.a.b	$960$	$2$	960.a	1.a	$1$	$1$	$1$	$7.666$	\(\Q\)	None	✓				480.2.a.d	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{9}-2q^{13}+q^{15}+6q^{17}+\cdots\)
960.2.a.c	$960$	$2$	960.a	1.a	$1$	$1$	$1$	$7.666$	\(\Q\)	None	✓				120.2.a.b	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{9}+4q^{11}-6q^{13}+\cdots\)
960.2.a.d	$960$	$2$	960.a	1.a	$1$	$1$	$1$	$7.666$	\(\Q\)	None	✓				480.2.a.c	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+4q^{7}+q^{9}+2q^{13}+q^{15}+\cdots\)
960.2.a.e	$960$	$2$	960.a	1.a	$1$	$1$	$1$	$7.666$	\(\Q\)	None	✓				30.2.a.a	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(-4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-4q^{7}+q^{9}-2q^{13}-q^{15}+\cdots\)
960.2.a.f	$960$	$2$	960.a	1.a	$1$	$1$	$1$	$7.666$	\(\Q\)	None	✓		✓	✓	480.2.a.b	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots\)
960.2.a.g	$960$	$2$	960.a	1.a	$1$	$1$	$1$	$7.666$	\(\Q\)	None	✓				120.2.a.a	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+4q^{7}+q^{9}+6q^{13}-q^{15}+\cdots\)
960.2.a.h	$960$	$2$	960.a	1.a	$1$	$1$	$1$	$7.666$	\(\Q\)	None	✓				480.2.a.a	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+4q^{7}+q^{9}+4q^{11}-6q^{13}+\cdots\)
960.2.a.i	$960$	$2$	960.a	1.a	$1$	$1$	$1$	$7.666$	\(\Q\)	None	✓				480.2.a.c	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(-4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-4q^{7}+q^{9}+2q^{13}-q^{15}+\cdots\)
960.2.a.j	$960$	$2$	960.a	1.a	$1$	$1$	$1$	$7.666$	\(\Q\)	None	✓				120.2.a.b	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{9}-4q^{11}-6q^{13}+\cdots\)
960.2.a.k	$960$	$2$	960.a	1.a	$1$	$1$	$1$	$7.666$	\(\Q\)	None	✓				480.2.a.d	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{9}-2q^{13}-q^{15}+6q^{17}+\cdots\)
960.2.a.l	$960$	$2$	960.a	1.a	$1$	$1$	$1$	$7.666$	\(\Q\)	None	✓				15.2.a.a	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{9}+4q^{11}+2q^{13}+\cdots\)
960.2.a.m	$960$	$2$	960.a	1.a	$1$	$1$	$1$	$7.666$	\(\Q\)	None	✓		✓	✓	480.2.a.a	$1$	$1$	\(0\)	\(1\)	\(1\)	\(-4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-4q^{7}+q^{9}-4q^{11}-6q^{13}+\cdots\)
960.2.a.n	$960$	$2$	960.a	1.a	$1$	$1$	$1$	$7.666$	\(\Q\)	None	✓				120.2.a.a	$1$	$0$	\(0\)	\(1\)	\(1\)	\(-4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-4q^{7}+q^{9}+6q^{13}+q^{15}+\cdots\)
960.2.a.o	$960$	$2$	960.a	1.a	$1$	$1$	$1$	$7.666$	\(\Q\)	None	✓				480.2.a.b	$1$	$0$	\(0\)	\(1\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots\)
960.2.a.p	$960$	$2$	960.a	1.a	$1$	$1$	$1$	$7.666$	\(\Q\)	None	✓				30.2.a.a	$1$	$0$	\(0\)	\(1\)	\(1\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+4q^{7}+q^{9}-2q^{13}+q^{15}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(960))\) into lower level spaces

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