Space of modular forms of level 2960, weight 2, and trivial character

• Label: 2960.2.a
• Level: $2960$
• Weight: $2$
• Character orbit: 2960.a
• Rep. character: $\chi_{2960}(1,\cdot)$
• Character field: $\Q$
• Dimension: $72$
• Newform subspaces: $29$
• Sturm bound: $912$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 2960 = 2^{4} \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2960.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 29 \)
Sturm bound:			\(912\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(3\), \(7\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2960))\).

	Total	New	Old
Modular forms	468	72	396
Cusp forms	445	72	373
Eisenstein series	23	0	23

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

\(2\)	\(5\)	\(37\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	$+$	\(8\)
\(+\)	\(+\)	\(-\)	$-$	\(11\)
\(+\)	\(-\)	\(+\)	$-$	\(11\)
\(+\)	\(-\)	\(-\)	$+$	\(6\)
\(-\)	\(+\)	\(+\)	$-$	\(10\)
\(-\)	\(+\)	\(-\)	$+$	\(7\)
\(-\)	\(-\)	\(+\)	$+$	\(7\)
\(-\)	\(-\)	\(-\)	$-$	\(12\)
Plus space			\(+\)	\(28\)
Minus space			\(-\)	\(44\)

Trace form

\( 72 q + 80 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2960))\) 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	37
2960.2.a.a	$2960$	$2$	2960.a	1.a	$1$	$1$	$1$	$23.636$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-3\)	\(-1\)	\(3\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}-q^{5}+3q^{7}+6q^{9}-5q^{11}+\cdots\)
2960.2.a.b	$2960$	$2$	2960.a	1.a	$1$	$1$	$1$	$23.636$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(1\)	\(-3\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+q^{5}-3q^{7}+q^{9}-3q^{11}+\cdots\)
2960.2.a.c	$2960$	$2$	2960.a	1.a	$1$	$1$	$1$	$23.636$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(1\)	\(-1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+q^{5}-q^{7}+q^{9}-3q^{11}-2q^{15}+\cdots\)
2960.2.a.d	$2960$	$2$	2960.a	1.a	$1$	$1$	$1$	$23.636$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{7}-2q^{9}+3q^{11}-4q^{13}+\cdots\)
2960.2.a.e	$2960$	$2$	2960.a	1.a	$1$	$1$	$1$	$23.636$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(5\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+5q^{7}-2q^{9}-3q^{11}+\cdots\)
2960.2.a.f	$2960$	$2$	2960.a	1.a	$1$	$1$	$1$	$23.636$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{7}-2q^{9}+3q^{11}-q^{15}+\cdots\)
2960.2.a.g	$2960$	$2$	2960.a	1.a	$1$	$1$	$1$	$23.636$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-3q^{9}+4q^{11}+2q^{13}-2q^{17}+\cdots\)
2960.2.a.h	$2960$	$2$	2960.a	1.a	$1$	$1$	$1$	$23.636$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(1\)	\(-1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-q^{7}-2q^{9}+3q^{11}-6q^{13}+\cdots\)
2960.2.a.i	$2960$	$2$	2960.a	1.a	$1$	$1$	$1$	$23.636$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(1\)	\(3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+3q^{7}-2q^{9}+5q^{11}+\cdots\)
2960.2.a.j	$2960$	$2$	2960.a	1.a	$1$	$1$	$1$	$23.636$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(2\)	\(-1\)	\(1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-q^{5}+q^{7}+q^{9}-3q^{11}-4q^{13}+\cdots\)
2960.2.a.k	$2960$	$2$	2960.a	1.a	$1$	$1$	$1$	$23.636$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(2\)	\(-1\)	\(2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-q^{5}+2q^{7}+q^{9}-2q^{13}+\cdots\)
2960.2.a.l	$2960$	$2$	2960.a	1.a	$1$	$1$	$1$	$23.636$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(2\)	\(1\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+q^{5}-2q^{7}+q^{9}-6q^{13}+\cdots\)
2960.2.a.m	$2960$	$2$	2960.a	1.a	$1$	$1$	$1$	$23.636$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(2\)	\(1\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+q^{5}-2q^{7}+q^{9}+2q^{13}+\cdots\)
2960.2.a.n	$2960$	$2$	2960.a	1.a	$1$	$1$	$1$	$23.636$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(3\)	\(-1\)	\(5\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}-q^{5}+5q^{7}+6q^{9}+3q^{11}+\cdots\)
2960.2.a.o	$2960$	$2$	2960.a	1.a	$1$	$2$	$2$	$23.636$	\(\Q(\sqrt{33}) \)	None	✓	$1$	$0$	\(0\)	\(-4\)	\(2\)	\(3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+q^{5}+(2-\beta )q^{7}+q^{9}+\beta q^{11}+\cdots\)
2960.2.a.p	$2960$	$2$	2960.a	1.a	$1$	$2$	$2$	$23.636$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(2\)	\(-6\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}+q^{5}+(-3+\beta )q^{7}+(1+\cdots)q^{9}+\cdots\)
2960.2.a.q	$2960$	$2$	2960.a	1.a	$1$	$2$	$2$	$23.636$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(2\)	\(6\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}+q^{5}+(3-\beta )q^{7}+(1+2\beta )q^{9}+\cdots\)
2960.2.a.r	$2960$	$2$	2960.a	1.a	$1$	$3$	$3$	$23.636$	3.3.316.1	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-3\)	\(1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-q^{5}+\beta _{1}q^{7}+\beta _{2}q^{9}+(1+\cdots)q^{11}+\cdots\)
2960.2.a.s	$2960$	$2$	2960.a	1.a	$1$	$3$	$3$	$23.636$	3.3.568.1	None	✓	$1$	$1$	\(0\)	\(-1\)	\(3\)	\(1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+q^{5}+\beta _{1}q^{7}+(1+2\beta _{1}+\beta _{2})q^{9}+\cdots\)
2960.2.a.t	$2960$	$2$	2960.a	1.a	$1$	$3$	$3$	$23.636$	3.3.148.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(-3\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}-q^{5}+(-2\beta _{1}+\beta _{2})q^{7}+(-\beta _{1}+\cdots)q^{9}+\cdots\)
2960.2.a.u	$2960$	$2$	2960.a	1.a	$1$	$3$	$3$	$23.636$	3.3.892.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(-3\)	\(1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}-q^{5}+\beta _{1}q^{7}+(3+2\beta _{1})q^{9}+\cdots\)
2960.2.a.v	$2960$	$2$	2960.a	1.a	$1$	$4$	$4$	$23.636$	4.4.286164.1	None	✓	$1$	$0$	\(0\)	\(-3\)	\(4\)	\(5\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}+q^{5}+(1+\beta _{1})q^{7}+\cdots\)
2960.2.a.w	$2960$	$2$	2960.a	1.a	$1$	$5$	$5$	$23.636$	5.5.973904.1	None	✓	$1$	$1$	\(0\)	\(-3\)	\(-5\)	\(-11\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}-q^{5}+(-2-\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
2960.2.a.x	$2960$	$2$	2960.a	1.a	$1$	$5$	$5$	$23.636$	5.5.998068.1	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-5\)	\(2\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{4}q^{3}-q^{5}+\beta _{2}q^{7}+(2-\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots\)
2960.2.a.y	$2960$	$2$	2960.a	1.a	$1$	$5$	$5$	$23.636$	5.5.6397264.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(-5\)	\(-3\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-q^{5}+(-1-\beta _{1}+\beta _{3})q^{7}+\cdots\)
2960.2.a.z	$2960$	$2$	2960.a	1.a	$1$	$5$	$5$	$23.636$	5.5.935504.1	None	✓	$1$	$0$	\(0\)	\(1\)	\(-5\)	\(1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-q^{5}-\beta _{3}q^{7}+(\beta _{1}+\beta _{2}-\beta _{3}+\cdots)q^{9}+\cdots\)
2960.2.a.ba	$2960$	$2$	2960.a	1.a	$1$	$5$	$5$	$23.636$	5.5.368464.1	None	✓	$1$	$1$	\(0\)	\(1\)	\(5\)	\(-7\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{3}+q^{5}+(-1-\beta _{4})q^{7}+(-1+\cdots)q^{9}+\cdots\)
2960.2.a.bb	$2960$	$2$	2960.a	1.a	$1$	$5$	$5$	$23.636$	5.5.583504.1	None	✓	$1$	$0$	\(0\)	\(5\)	\(5\)	\(5\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}+q^{5}+(1+\beta _{2}-\beta _{4})q^{7}+\cdots\)
2960.2.a.bc	$2960$	$2$	2960.a	1.a	$1$	$6$	$6$	$23.636$	6.6.693982032.1	None	✓	$1$	$0$	\(0\)	\(-1\)	\(6\)	\(-8\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+q^{5}+(-1-\beta _{2})q^{7}+(2+\beta _{3}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2960))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2960)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(37))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(74))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(148))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(185))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(296))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(370))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(592))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(740))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1480))\)\(^{\oplus 2}\)