Properties

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 $13$

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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.

\(2\)\(3\)\(5\)\(7\)\(23\)FrickeDim.
\(-\)\(+\)\(+\)\(+\)\(+\)\(-\)\(3\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(+\)\(7\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(+\)\(7\)
\(-\)\(+\)\(+\)\(-\)\(-\)\(-\)\(5\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(+\)\(7\)
\(-\)\(+\)\(-\)\(+\)\(-\)\(-\)\(5\)
\(-\)\(+\)\(-\)\(-\)\(+\)\(-\)\(5\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(+\)\(5\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(+\)\(6\)
\(-\)\(-\)\(+\)\(+\)\(-\)\(-\)\(6\)
\(-\)\(-\)\(+\)\(-\)\(+\)\(-\)\(6\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(+\)\(4\)
\(-\)\(-\)\(-\)\(+\)\(+\)\(-\)\(6\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(+\)\(4\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(+\)\(4\)
\(-\)\(-\)\(-\)\(-\)\(-\)\(-\)\(8\)
Plus space\(+\)\(44\)
Minus space\(-\)\(44\)

Trace form

\( 88 q + 88 q^{9} + O(q^{10}) \) \( 88 q + 88 q^{9} + 88 q^{25} - 16 q^{31} - 16 q^{33} - 16 q^{37} - 16 q^{41} - 32 q^{43} - 16 q^{47} + 88 q^{49} - 16 q^{51} - 16 q^{53} + 32 q^{59} - 32 q^{61} + 32 q^{67} - 16 q^{73} + 48 q^{79} + 88 q^{81} + 16 q^{83} + 16 q^{85} + 16 q^{87} + 32 q^{89} + 16 q^{93} + 16 q^{95} + 16 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9660))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3 5 7 23
9660.2.a.a 9660.a 1.a $1$ $77.135$ \(\Q\) None \(0\) \(-1\) \(-1\) \(-1\) $-$ $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-q^{7}+q^{9}-2q^{11}+q^{15}+\cdots\)
9660.2.a.b 9660.a 1.a $1$ $77.135$ \(\Q\) None \(0\) \(-1\) \(-1\) \(1\) $-$ $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+q^{7}+q^{9}+4q^{11}+6q^{13}+\cdots\)
9660.2.a.c 9660.a 1.a $1$ $77.135$ \(\Q\) None \(0\) \(-1\) \(1\) \(1\) $-$ $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+q^{7}+q^{9}-q^{11}+4q^{13}+\cdots\)
9660.2.a.d 9660.a 1.a $1$ $77.135$ \(\Q\) None \(0\) \(1\) \(-1\) \(1\) $-$ $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+q^{7}+q^{9}-3q^{11}-4q^{13}+\cdots\)
9660.2.a.e 9660.a 1.a $1$ $77.135$ \(\Q\) None \(0\) \(1\) \(-1\) \(1\) $-$ $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+q^{7}+q^{9}+2q^{13}-q^{15}+\cdots\)
9660.2.a.f 9660.a 1.a $1$ $77.135$ \(\Q\) None \(0\) \(1\) \(1\) \(-1\) $-$ $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-q^{7}+q^{9}-5q^{11}+4q^{13}+\cdots\)
9660.2.a.g 9660.a 1.a $2$ $77.135$ \(\Q(\sqrt{13}) \) None \(0\) \(-2\) \(-2\) \(-2\) $-$ $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-q^{7}+q^{9}+\beta q^{11}+(1+\cdots)q^{13}+\cdots\)
9660.2.a.h 9660.a 1.a $2$ $77.135$ \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(-2\) \(2\) $-$ $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+q^{7}+q^{9}+(1-3\beta )q^{11}+\cdots\)
9660.2.a.i 9660.a 1.a $2$ $77.135$ \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(2\) \(-2\) $-$ $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-q^{7}+q^{9}+(-4+\beta )q^{11}+\cdots\)
9660.2.a.j 9660.a 1.a $2$ $77.135$ \(\Q(\sqrt{21}) \) None \(0\) \(2\) \(2\) \(-2\) $-$ $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-q^{7}+q^{9}+(3-\beta )q^{11}+\cdots\)
9660.2.a.k 9660.a 1.a $2$ $77.135$ \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(2\) \(-2\) $-$ $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-q^{7}+q^{9}+(3-\beta )q^{11}+\cdots\)
9660.2.a.l 9660.a 1.a $2$ $77.135$ \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(2\) \(2\) $-$ $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+q^{7}+q^{9}+(-3+\beta )q^{11}+\cdots\)
9660.2.a.m 9660.a 1.a $2$ $77.135$ \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(2\) \(2\) $-$ $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+q^{7}+q^{9}+(-1-\beta )q^{11}+\cdots\)
9660.2.a.n 9660.a 1.a $3$ $77.135$ 3.3.1101.1 None \(0\) \(3\) \(-3\) \(3\) $-$ $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+q^{7}+q^{9}+(-2-\beta _{1}+\cdots)q^{11}+\cdots\)
9660.2.a.o 9660.a 1.a $3$ $77.135$ 3.3.564.1 None \(0\) \(3\) \(-3\) \(3\) $-$ $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+q^{7}+q^{9}+(2-\beta _{1}-\beta _{2})q^{11}+\cdots\)
9660.2.a.p 9660.a 1.a $3$ $77.135$ 3.3.3252.1 None \(0\) \(3\) \(3\) \(-3\) $-$ $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-q^{7}+q^{9}+(1+\beta _{1})q^{11}+\cdots\)
9660.2.a.q 9660.a 1.a $4$ $77.135$ 4.4.118732.1 None \(0\) \(-4\) \(4\) \(4\) $-$ $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+q^{7}+q^{9}+(2+\beta _{1})q^{11}+\cdots\)
9660.2.a.r 9660.a 1.a $5$ $77.135$ 5.5.746052.1 None \(0\) \(-5\) \(-5\) \(5\) $-$ $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+q^{7}+q^{9}+(1-\beta _{3}+\beta _{4})q^{11}+\cdots\)
9660.2.a.s 9660.a 1.a $5$ $77.135$ 5.5.10241256.1 None \(0\) \(-5\) \(5\) \(-5\) $-$ $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-q^{7}+q^{9}+(1-\beta _{4})q^{11}+\cdots\)
9660.2.a.t 9660.a 1.a $5$ $77.135$ 5.5.3015492.1 None \(0\) \(-5\) \(5\) \(5\) $-$ $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+q^{7}+q^{9}+(-1-\beta _{1}+\cdots)q^{11}+\cdots\)
9660.2.a.u 9660.a 1.a $6$ $77.135$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(-6\) \(-6\) \(6\) $-$ $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+q^{7}+q^{9}+(-1+\beta _{5})q^{11}+\cdots\)
9660.2.a.v 9660.a 1.a $6$ $77.135$ 6.6.914299812.1 None \(0\) \(6\) \(-6\) \(-6\) $-$ $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-q^{7}+q^{9}+\beta _{2}q^{11}+(1+\cdots)q^{13}+\cdots\)
9660.2.a.w 9660.a 1.a $6$ $77.135$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(6\) \(-6\) \(-6\) $-$ $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-q^{7}+q^{9}+\beta _{2}q^{11}+(-1+\cdots)q^{13}+\cdots\)
9660.2.a.x 9660.a 1.a $7$ $77.135$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(-7\) \(-7\) \(-7\) $-$ $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-q^{7}+q^{9}+(1-\beta _{4})q^{11}+\cdots\)
9660.2.a.y 9660.a 1.a $7$ $77.135$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(-7\) \(7\) \(-7\) $-$ $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-q^{7}+q^{9}+(-1+\beta _{4}+\cdots)q^{11}+\cdots\)
9660.2.a.z 9660.a 1.a $8$ $77.135$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(8\) \(8\) \(8\) $-$ $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+q^{7}+q^{9}+(1+\beta _{4})q^{11}+\cdots\)

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

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