Space of modular forms of level 9660, weight 2, and trivial character

• Label: 9660.2.a
• Level: $9660$
• Weight: $2$
• Character orbit: 9660.a
• Rep. character: $\chi_{9660}(1,\cdot)$
• Character field: $\Q$
• Dimension: $88$
• Newform subspaces: $26$
• Sturm bound: $4608$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 9660 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9660.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 26 \)
Sturm bound:			\(4608\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(9660))\).

	Total	New	Old
Modular forms	2328	88	2240
Cusp forms	2281	88	2193
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.

\(2\)	\(3\)	\(5\)	\(7\)	\(23\)	Fricke	Dim
\(-\)	\(+\)	\(+\)	\(+\)	\(+\)	$-$	\(3\)
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)	$+$	\(7\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)	$+$	\(7\)
\(-\)	\(+\)	\(+\)	\(-\)	\(-\)	$-$	\(5\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)	$+$	\(7\)
\(-\)	\(+\)	\(-\)	\(+\)	\(-\)	$-$	\(5\)
\(-\)	\(+\)	\(-\)	\(-\)	\(+\)	$-$	\(5\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)	$+$	\(5\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)	$+$	\(6\)
\(-\)	\(-\)	\(+\)	\(+\)	\(-\)	$-$	\(6\)
\(-\)	\(-\)	\(+\)	\(-\)	\(+\)	$-$	\(6\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)	$+$	\(4\)
\(-\)	\(-\)	\(-\)	\(+\)	\(+\)	$-$	\(6\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)	$+$	\(4\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)	$+$	\(4\)
\(-\)	\(-\)	\(-\)	\(-\)	\(-\)	$-$	\(8\)
Plus space					\(+\)	\(44\)
Minus space					\(-\)	\(44\)

Trace form

\( 88 q + 88 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9660))\) 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	7	23
9660.2.a.a	$9660$	$2$	9660.a	1.a	$1$	$1$	$1$	$77.135$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(-1\)		$-$	$+$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-q^{7}+q^{9}-2q^{11}+q^{15}+\cdots\)
9660.2.a.b	$9660$	$2$	9660.a	1.a	$1$	$1$	$1$	$77.135$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(1\)		$-$	$+$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{7}+q^{9}+4q^{11}+6q^{13}+\cdots\)
9660.2.a.c	$9660$	$2$	9660.a	1.a	$1$	$1$	$1$	$77.135$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(1\)		$-$	$+$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{7}+q^{9}-q^{11}+4q^{13}+\cdots\)
9660.2.a.d	$9660$	$2$	9660.a	1.a	$1$	$1$	$1$	$77.135$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(1\)		$-$	$-$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{7}+q^{9}-3q^{11}-4q^{13}+\cdots\)
9660.2.a.e	$9660$	$2$	9660.a	1.a	$1$	$1$	$1$	$77.135$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(1\)		$-$	$-$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{7}+q^{9}+2q^{13}-q^{15}+\cdots\)
9660.2.a.f	$9660$	$2$	9660.a	1.a	$1$	$1$	$1$	$77.135$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(1\)	\(-1\)		$-$	$-$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-q^{7}+q^{9}-5q^{11}+4q^{13}+\cdots\)
9660.2.a.g	$9660$	$2$	9660.a	1.a	$1$	$2$	$2$	$77.135$	\(\Q(\sqrt{13}) \)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(-2\)	\(-2\)		$-$	$+$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-q^{7}+q^{9}+\beta q^{11}+(1+\cdots)q^{13}+\cdots\)
9660.2.a.h	$9660$	$2$	9660.a	1.a	$1$	$2$	$2$	$77.135$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(2\)	\(-2\)	\(2\)		$-$	$-$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{7}+q^{9}+(1-3\beta )q^{11}+\cdots\)
9660.2.a.i	$9660$	$2$	9660.a	1.a	$1$	$2$	$2$	$77.135$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(0\)	\(2\)	\(2\)	\(-2\)		$-$	$-$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-q^{7}+q^{9}+(-4+\beta )q^{11}+\cdots\)
9660.2.a.j	$9660$	$2$	9660.a	1.a	$1$	$2$	$2$	$77.135$	\(\Q(\sqrt{21}) \)	None	✓	$1$	$1$	\(0\)	\(2\)	\(2\)	\(-2\)		$-$	$-$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-q^{7}+q^{9}+(3-\beta )q^{11}+\cdots\)
9660.2.a.k	$9660$	$2$	9660.a	1.a	$1$	$2$	$2$	$77.135$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(2\)	\(-2\)		$-$	$-$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-q^{7}+q^{9}+(3-\beta )q^{11}+\cdots\)
9660.2.a.l	$9660$	$2$	9660.a	1.a	$1$	$2$	$2$	$77.135$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$1$	\(0\)	\(2\)	\(2\)	\(2\)		$-$	$-$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{7}+q^{9}+(-3+\beta )q^{11}+\cdots\)
9660.2.a.m	$9660$	$2$	9660.a	1.a	$1$	$2$	$2$	$77.135$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(2\)	\(2\)	\(2\)		$-$	$-$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{7}+q^{9}+(-1-\beta )q^{11}+\cdots\)
9660.2.a.n	$9660$	$2$	9660.a	1.a	$1$	$3$	$3$	$77.135$	3.3.1101.1	None	✓	$1$	$0$	\(0\)	\(3\)	\(-3\)	\(3\)		$-$	$-$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{7}+q^{9}+(-2-\beta _{1}+\cdots)q^{11}+\cdots\)
9660.2.a.o	$9660$	$2$	9660.a	1.a	$1$	$3$	$3$	$77.135$	3.3.564.1	None	✓	$1$	$0$	\(0\)	\(3\)	\(-3\)	\(3\)		$-$	$-$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{7}+q^{9}+(2-\beta _{1}-\beta _{2})q^{11}+\cdots\)
9660.2.a.p	$9660$	$2$	9660.a	1.a	$1$	$3$	$3$	$77.135$	3.3.3252.1	None	✓	$1$	$0$	\(0\)	\(3\)	\(3\)	\(-3\)		$-$	$-$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-q^{7}+q^{9}+(1+\beta _{1})q^{11}+\cdots\)
9660.2.a.q	$9660$	$2$	9660.a	1.a	$1$	$4$	$4$	$77.135$	4.4.118732.1	None	✓	$1$	$0$	\(0\)	\(-4\)	\(4\)	\(4\)		$-$	$+$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{7}+q^{9}+(2+\beta _{1})q^{11}+\cdots\)
9660.2.a.r	$9660$	$2$	9660.a	1.a	$1$	$5$	$5$	$77.135$	5.5.746052.1	None	✓	$1$	$0$	\(0\)	\(-5\)	\(-5\)	\(5\)		$-$	$+$	$+$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{7}+q^{9}+(1-\beta _{3}+\beta _{4})q^{11}+\cdots\)
9660.2.a.s	$9660$	$2$	9660.a	1.a	$1$	$5$	$5$	$77.135$	5.5.10241256.1	None	✓	$1$	$0$	\(0\)	\(-5\)	\(5\)	\(-5\)		$-$	$+$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-q^{7}+q^{9}+(1-\beta _{4})q^{11}+\cdots\)
9660.2.a.t	$9660$	$2$	9660.a	1.a	$1$	$5$	$5$	$77.135$	5.5.3015492.1	None	✓	$1$	$1$	\(0\)	\(-5\)	\(5\)	\(5\)		$-$	$+$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{7}+q^{9}+(-1-\beta _{1}+\cdots)q^{11}+\cdots\)
9660.2.a.u	$9660$	$2$	9660.a	1.a	$1$	$6$	$6$	$77.135$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-6\)	\(-6\)	\(6\)		$-$	$+$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{7}+q^{9}+(-1+\beta _{5})q^{11}+\cdots\)
9660.2.a.v	$9660$	$2$	9660.a	1.a	$1$	$6$	$6$	$77.135$	6.6.914299812.1	None	✓	$1$	$0$	\(0\)	\(6\)	\(-6\)	\(-6\)		$-$	$-$	$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-q^{7}+q^{9}+\beta _{2}q^{11}+(1+\cdots)q^{13}+\cdots\)
9660.2.a.w	$9660$	$2$	9660.a	1.a	$1$	$6$	$6$	$77.135$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(6\)	\(-6\)	\(-6\)		$-$	$-$	$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-q^{7}+q^{9}+\beta _{2}q^{11}+(-1+\cdots)q^{13}+\cdots\)
9660.2.a.x	$9660$	$2$	9660.a	1.a	$1$	$7$	$7$	$77.135$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-7\)	\(-7\)	\(-7\)		$-$	$+$	$+$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-q^{7}+q^{9}+(1-\beta _{4})q^{11}+\cdots\)
9660.2.a.y	$9660$	$2$	9660.a	1.a	$1$	$7$	$7$	$77.135$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-7\)	\(7\)	\(-7\)		$-$	$+$	$-$	$+$	$+$	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-q^{7}+q^{9}+(-1+\beta _{4}+\cdots)q^{11}+\cdots\)
9660.2.a.z	$9660$	$2$	9660.a	1.a	$1$	$8$	$8$	$77.135$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(8\)	\(8\)	\(8\)		$-$	$-$	$-$	$-$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{7}+q^{9}+(1+\beta _{4})q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9660))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(9660)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(28))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(60))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(69))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(92))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(105))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(115))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(138))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(140))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(161))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(210))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(230))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(276))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(322))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(345))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(420))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(460))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(483))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(644))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(690))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(805))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(966))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1380))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1610))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1932))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2415))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3220))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4830))\)\(^{\oplus 2}\)