Properties

Label 8664.2.a
Level $8664$
Weight $2$
Character orbit 8664.a
Rep. character $\chi_{8664}(1,\cdot)$
Character field $\Q$
Dimension $171$
Newform subspaces $45$
Sturm bound $3040$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 8664 = 2^{3} \cdot 3 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8664.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 45 \)
Sturm bound: \(3040\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(7\), \(13\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8664))\).

Total New Old
Modular forms 1600 171 1429
Cusp forms 1441 171 1270
Eisenstein series 159 0 159

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

\(2\)\(3\)\(19\)FrickeDim
\(+\)\(+\)\(+\)\(+\)\(22\)
\(+\)\(+\)\(-\)\(-\)\(20\)
\(+\)\(-\)\(+\)\(-\)\(23\)
\(+\)\(-\)\(-\)\(+\)\(20\)
\(-\)\(+\)\(+\)\(-\)\(27\)
\(-\)\(+\)\(-\)\(+\)\(16\)
\(-\)\(-\)\(+\)\(+\)\(18\)
\(-\)\(-\)\(-\)\(-\)\(25\)
Plus space\(+\)\(76\)
Minus space\(-\)\(95\)

Trace form

\( 171 q + q^{3} - 2 q^{5} + 4 q^{7} + 171 q^{9} - 4 q^{11} - 2 q^{13} + 2 q^{15} - 6 q^{17} + 8 q^{23} + 161 q^{25} + q^{27} - 2 q^{29} + 4 q^{31} - 8 q^{33} - 10 q^{37} + 6 q^{39} + 10 q^{41} - 8 q^{43}+ \cdots - 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8664))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3 19
8664.2.a.a 8664.a 1.a $1$ $69.182$ \(\Q\) None 456.2.a.c \(0\) \(-1\) \(-3\) \(-3\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-3q^{5}-3q^{7}+q^{9}-q^{11}+2q^{13}+\cdots\)
8664.2.a.b 8664.a 1.a $1$ $69.182$ \(\Q\) None 456.2.q.c \(0\) \(-1\) \(-2\) \(-5\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{5}-5q^{7}+q^{9}-4q^{11}+\cdots\)
8664.2.a.c 8664.a 1.a $1$ $69.182$ \(\Q\) None 8664.2.a.c \(0\) \(-1\) \(-2\) \(-4\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{5}-4q^{7}+q^{9}+2q^{11}+\cdots\)
8664.2.a.d 8664.a 1.a $1$ $69.182$ \(\Q\) None 456.2.q.b \(0\) \(-1\) \(0\) \(3\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+3q^{7}+q^{9}+2q^{11}-q^{13}+\cdots\)
8664.2.a.e 8664.a 1.a $1$ $69.182$ \(\Q\) None 456.2.q.a \(0\) \(-1\) \(2\) \(-3\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{5}-3q^{7}+q^{9}-5q^{13}+\cdots\)
8664.2.a.f 8664.a 1.a $1$ $69.182$ \(\Q\) None 456.2.a.d \(0\) \(-1\) \(2\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{5}+q^{9}-2q^{13}-2q^{15}+\cdots\)
8664.2.a.g 8664.a 1.a $1$ $69.182$ \(\Q\) None 8664.2.a.g \(0\) \(-1\) \(3\) \(1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+3q^{5}+q^{7}+q^{9}-3q^{11}-3q^{15}+\cdots\)
8664.2.a.h 8664.a 1.a $1$ $69.182$ \(\Q\) None 456.2.q.c \(0\) \(1\) \(-2\) \(-5\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{5}-5q^{7}+q^{9}-4q^{11}+\cdots\)
8664.2.a.i 8664.a 1.a $1$ $69.182$ \(\Q\) None 8664.2.a.c \(0\) \(1\) \(-2\) \(-4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{5}-4q^{7}+q^{9}+2q^{11}+\cdots\)
8664.2.a.j 8664.a 1.a $1$ $69.182$ \(\Q\) None 24.2.a.a \(0\) \(1\) \(-2\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{5}+q^{9}+4q^{11}+2q^{13}+\cdots\)
8664.2.a.k 8664.a 1.a $1$ $69.182$ \(\Q\) None 456.2.q.b \(0\) \(1\) \(0\) \(3\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+3q^{7}+q^{9}+2q^{11}+q^{13}+\cdots\)
8664.2.a.l 8664.a 1.a $1$ $69.182$ \(\Q\) None 456.2.a.a \(0\) \(1\) \(1\) \(-3\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-3q^{7}+q^{9}-5q^{11}+2q^{13}+\cdots\)
8664.2.a.m 8664.a 1.a $1$ $69.182$ \(\Q\) None 456.2.q.a \(0\) \(1\) \(2\) \(-3\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{5}-3q^{7}+q^{9}+5q^{13}+\cdots\)
8664.2.a.n 8664.a 1.a $1$ $69.182$ \(\Q\) None 8664.2.a.g \(0\) \(1\) \(3\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+3q^{5}+q^{7}+q^{9}-3q^{11}+3q^{15}+\cdots\)
8664.2.a.o 8664.a 1.a $1$ $69.182$ \(\Q\) None 456.2.a.b \(0\) \(1\) \(4\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+4q^{5}+4q^{7}+q^{9}-4q^{11}+\cdots\)
8664.2.a.p 8664.a 1.a $2$ $69.182$ \(\Q(\sqrt{5}) \) None 8664.2.a.p \(0\) \(-2\) \(-3\) \(-1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+(-1-\beta )q^{5}+(-1+\beta )q^{7}+\cdots\)
8664.2.a.q 8664.a 1.a $2$ $69.182$ \(\Q(\sqrt{5}) \) None 456.2.q.d \(0\) \(-2\) \(-2\) \(4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+(-1-\beta )q^{5}+(2-\beta )q^{7}+q^{9}+\cdots\)
8664.2.a.r 8664.a 1.a $2$ $69.182$ \(\Q(\sqrt{17}) \) None 456.2.a.f \(0\) \(-2\) \(1\) \(1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+\beta q^{5}+\beta q^{7}+q^{9}+(4-\beta )q^{11}+\cdots\)
8664.2.a.s 8664.a 1.a $2$ $69.182$ \(\Q(\sqrt{5}) \) None 456.2.q.e \(0\) \(-2\) \(2\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+(1+\beta )q^{5}-\beta q^{7}+q^{9}+(3+\beta )q^{11}+\cdots\)
8664.2.a.t 8664.a 1.a $2$ $69.182$ \(\Q(\sqrt{5}) \) None 8664.2.a.p \(0\) \(2\) \(-3\) \(-1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+(-1-\beta )q^{5}+(-1+\beta )q^{7}+\cdots\)
8664.2.a.u 8664.a 1.a $2$ $69.182$ \(\Q(\sqrt{5}) \) None 456.2.q.d \(0\) \(2\) \(-2\) \(4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+(-1-\beta )q^{5}+(2-\beta )q^{7}+q^{9}+\cdots\)
8664.2.a.v 8664.a 1.a $2$ $69.182$ \(\Q(\sqrt{41}) \) None 456.2.a.e \(0\) \(2\) \(-1\) \(-3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-\beta q^{5}+(-2+\beta )q^{7}+q^{9}+(2+\cdots)q^{11}+\cdots\)
8664.2.a.w 8664.a 1.a $2$ $69.182$ \(\Q(\sqrt{5}) \) None 456.2.q.e \(0\) \(2\) \(2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+(1+\beta )q^{5}-\beta q^{7}+q^{9}+(3+\beta )q^{11}+\cdots\)
8664.2.a.x 8664.a 1.a $3$ $69.182$ \(\Q(\zeta_{18})^+\) None 456.2.q.f \(0\) \(-3\) \(0\) \(3\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-\beta _{1}q^{5}+(1+\beta _{1})q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots\)
8664.2.a.y 8664.a 1.a $3$ $69.182$ 3.3.316.1 None 8664.2.a.y \(0\) \(-3\) \(3\) \(1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+(1-\beta _{1})q^{5}-\beta _{2}q^{7}+q^{9}+(-2\beta _{1}+\cdots)q^{11}+\cdots\)
8664.2.a.z 8664.a 1.a $3$ $69.182$ \(\Q(\zeta_{18})^+\) None 456.2.q.f \(0\) \(3\) \(0\) \(3\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-\beta _{1}q^{5}+(1+\beta _{1})q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots\)
8664.2.a.ba 8664.a 1.a $3$ $69.182$ 3.3.316.1 None 8664.2.a.y \(0\) \(3\) \(3\) \(1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+(1-\beta _{1})q^{5}-\beta _{2}q^{7}+q^{9}+(-2\beta _{1}+\cdots)q^{11}+\cdots\)
8664.2.a.bb 8664.a 1.a $4$ $69.182$ 4.4.34025.1 None 8664.2.a.bb \(0\) \(-4\) \(-2\) \(-1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+\beta _{2}q^{5}+(\beta _{2}-\beta _{3})q^{7}+q^{9}+\cdots\)
8664.2.a.bc 8664.a 1.a $4$ $69.182$ 4.4.5225.1 None 8664.2.a.bc \(0\) \(-4\) \(2\) \(2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+\beta _{3}q^{5}+\beta _{3}q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots\)
8664.2.a.bd 8664.a 1.a $4$ $69.182$ 4.4.34025.1 None 8664.2.a.bb \(0\) \(4\) \(-2\) \(-1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+\beta _{2}q^{5}+(\beta _{2}-\beta _{3})q^{7}+q^{9}+\cdots\)
8664.2.a.be 8664.a 1.a $4$ $69.182$ 4.4.5225.1 None 8664.2.a.bc \(0\) \(4\) \(2\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+\beta _{3}q^{5}+\beta _{3}q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots\)
8664.2.a.bf 8664.a 1.a $6$ $69.182$ 6.6.1528713.1 None 456.2.bg.a \(0\) \(-6\) \(-3\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-\beta _{1}q^{5}+(-1+2\beta _{1}+\beta _{2})q^{7}+\cdots\)
8664.2.a.bg 8664.a 1.a $6$ $69.182$ 6.6.142368125.1 None 8664.2.a.bg \(0\) \(-6\) \(1\) \(2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+\beta _{5}q^{5}+\beta _{2}q^{7}+q^{9}+(\beta _{1}+\beta _{2}+\cdots)q^{11}+\cdots\)
8664.2.a.bh 8664.a 1.a $6$ $69.182$ 6.6.65669049.1 None 456.2.bg.b \(0\) \(-6\) \(3\) \(6\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+(1-\beta _{1})q^{5}+(1+\beta _{4})q^{7}+q^{9}+\cdots\)
8664.2.a.bi 8664.a 1.a $6$ $69.182$ 6.6.1528713.1 None 456.2.bg.a \(0\) \(6\) \(-3\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-\beta _{1}q^{5}+(-1+2\beta _{1}+\beta _{2})q^{7}+\cdots\)
8664.2.a.bj 8664.a 1.a $6$ $69.182$ 6.6.142368125.1 None 8664.2.a.bg \(0\) \(6\) \(1\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+\beta _{5}q^{5}+\beta _{2}q^{7}+q^{9}+(\beta _{1}+\beta _{2}+\cdots)q^{11}+\cdots\)
8664.2.a.bk 8664.a 1.a $6$ $69.182$ 6.6.65669049.1 None 456.2.bg.b \(0\) \(6\) \(3\) \(6\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+(1-\beta _{1})q^{5}+(1+\beta _{4})q^{7}+q^{9}+\cdots\)
8664.2.a.bl 8664.a 1.a $8$ $69.182$ 8.8.\(\cdots\).1 None 8664.2.a.bl \(0\) \(-8\) \(-6\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+(-1-\beta _{2})q^{5}-\beta _{1}q^{7}+q^{9}+\cdots\)
8664.2.a.bm 8664.a 1.a $8$ $69.182$ 8.8.\(\cdots\).1 None 8664.2.a.bl \(0\) \(8\) \(-6\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+(-1-\beta _{2})q^{5}-\beta _{1}q^{7}+q^{9}+\cdots\)
8664.2.a.bn 8664.a 1.a $9$ $69.182$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None 456.2.bg.d \(0\) \(-9\) \(-3\) \(-6\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+(-\beta _{1}-\beta _{3}+\beta _{5})q^{5}+(-1+\cdots)q^{7}+\cdots\)
8664.2.a.bo 8664.a 1.a $9$ $69.182$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None 456.2.bg.c \(0\) \(-9\) \(3\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+\beta _{1}q^{5}+\beta _{7}q^{7}+q^{9}+(1-\beta _{1}+\cdots)q^{11}+\cdots\)
8664.2.a.bp 8664.a 1.a $9$ $69.182$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None 456.2.bg.d \(0\) \(9\) \(-3\) \(-6\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+(-\beta _{1}-\beta _{3}+\beta _{5})q^{5}+(-1+\cdots)q^{7}+\cdots\)
8664.2.a.bq 8664.a 1.a $9$ $69.182$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None 456.2.bg.c \(0\) \(9\) \(3\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+\beta _{1}q^{5}+\beta _{7}q^{7}+q^{9}+(1-\beta _{1}+\cdots)q^{11}+\cdots\)
8664.2.a.br 8664.a 1.a $12$ $69.182$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None 8664.2.a.br \(0\) \(-12\) \(2\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+\beta _{1}q^{5}+\beta _{10}q^{7}+q^{9}+(1+\beta _{4}+\cdots)q^{11}+\cdots\)
8664.2.a.bs 8664.a 1.a $12$ $69.182$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None 8664.2.a.br \(0\) \(12\) \(2\) \(4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+\beta _{1}q^{5}+\beta _{10}q^{7}+q^{9}+(1+\beta _{4}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8664))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8664)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(76))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(114))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(152))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(228))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(361))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(456))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(722))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1083))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1444))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2166))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2888))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4332))\)\(^{\oplus 2}\)