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Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 5 11
4400.2.a.a 4400.a 1.a $1$ $35.134$ \(\Q\) None \(0\) \(-3\) \(0\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}-2q^{7}+6q^{9}+q^{11}+6q^{17}+\cdots\)
4400.2.a.b 4400.a 1.a $1$ $35.134$ \(\Q\) None \(0\) \(-3\) \(0\) \(-1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}-q^{7}+6q^{9}+q^{11}+5q^{17}+\cdots\)
4400.2.a.c 4400.a 1.a $1$ $35.134$ \(\Q\) None \(0\) \(-2\) \(0\) \(-4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{3}-4q^{7}+q^{9}-q^{11}-6q^{13}+\cdots\)
4400.2.a.d 4400.a 1.a $1$ $35.134$ \(\Q\) None \(0\) \(-2\) \(0\) \(-4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{3}-4q^{7}+q^{9}+q^{11}-5q^{13}+\cdots\)
4400.2.a.e 4400.a 1.a $1$ $35.134$ \(\Q\) None \(0\) \(-2\) \(0\) \(-4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{3}-4q^{7}+q^{9}+q^{11}+4q^{13}+\cdots\)
4400.2.a.f 4400.a 1.a $1$ $35.134$ \(\Q\) None \(0\) \(-2\) \(0\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{3}+q^{9}-q^{11}-2q^{13}+6q^{17}+\cdots\)
4400.2.a.g 4400.a 1.a $1$ $35.134$ \(\Q\) None \(0\) \(-2\) \(0\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{3}+q^{9}-q^{11}+3q^{13}-4q^{17}+\cdots\)
4400.2.a.h 4400.a 1.a $1$ $35.134$ \(\Q\) None \(0\) \(-2\) \(0\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{3}+2q^{7}+q^{9}+q^{11}+4q^{17}+\cdots\)
4400.2.a.i 4400.a 1.a $1$ $35.134$ \(\Q\) None \(0\) \(-1\) \(0\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{7}-2q^{9}-q^{11}-4q^{13}+\cdots\)
4400.2.a.j 4400.a 1.a $1$ $35.134$ \(\Q\) None \(0\) \(-1\) \(0\) \(1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{7}-2q^{9}+q^{11}-q^{17}-q^{19}+\cdots\)
4400.2.a.k 4400.a 1.a $1$ $35.134$ \(\Q\) None \(0\) \(-1\) \(0\) \(3\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+3q^{7}-2q^{9}-q^{11}-4q^{13}+\cdots\)
4400.2.a.l 4400.a 1.a $1$ $35.134$ \(\Q\) None \(0\) \(-1\) \(0\) \(3\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+3q^{7}-2q^{9}-q^{11}+6q^{13}+\cdots\)
4400.2.a.m 4400.a 1.a $1$ $35.134$ \(\Q\) None \(0\) \(0\) \(0\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{7}-3q^{9}-q^{11}+4q^{13}+4q^{17}+\cdots\)
4400.2.a.n 4400.a 1.a $1$ $35.134$ \(\Q\) None \(0\) \(0\) \(0\) \(-2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{7}-3q^{9}+q^{11}-6q^{13}-2q^{17}+\cdots\)
4400.2.a.o 4400.a 1.a $1$ $35.134$ \(\Q\) None \(0\) \(0\) \(0\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{7}-3q^{9}+q^{11}+8q^{19}-8q^{23}+\cdots\)
4400.2.a.p 4400.a 1.a $1$ $35.134$ \(\Q\) None \(0\) \(0\) \(0\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{9}+q^{11}-2q^{13}-6q^{17}+4q^{19}+\cdots\)
4400.2.a.q 4400.a 1.a $1$ $35.134$ \(\Q\) None \(0\) \(0\) \(0\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{7}-3q^{9}+q^{11}+6q^{13}+2q^{17}+\cdots\)
4400.2.a.r 4400.a 1.a $1$ $35.134$ \(\Q\) None \(0\) \(0\) \(0\) \(4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+4q^{7}-3q^{9}+q^{11}-6q^{13}+6q^{17}+\cdots\)
4400.2.a.s 4400.a 1.a $1$ $35.134$ \(\Q\) None \(0\) \(1\) \(0\) \(-3\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-3q^{7}-2q^{9}-q^{11}+4q^{13}+\cdots\)
4400.2.a.t 4400.a 1.a $1$ $35.134$ \(\Q\) None \(0\) \(1\) \(0\) \(-1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{7}-2q^{9}+q^{11}-2q^{13}+\cdots\)
4400.2.a.u 4400.a 1.a $1$ $35.134$ \(\Q\) None \(0\) \(1\) \(0\) \(-1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{7}-2q^{9}+q^{11}+q^{17}-q^{19}+\cdots\)
4400.2.a.v 4400.a 1.a $1$ $35.134$ \(\Q\) None \(0\) \(1\) \(0\) \(2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{7}-2q^{9}+q^{11}+4q^{13}+\cdots\)
4400.2.a.w 4400.a 1.a $1$ $35.134$ \(\Q\) None \(0\) \(1\) \(0\) \(5\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+5q^{7}-2q^{9}-q^{11}-2q^{13}+\cdots\)
4400.2.a.x 4400.a 1.a $1$ $35.134$ \(\Q\) None \(0\) \(2\) \(0\) \(-2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{3}-2q^{7}+q^{9}+q^{11}-4q^{17}+\cdots\)
4400.2.a.y 4400.a 1.a $1$ $35.134$ \(\Q\) None \(0\) \(2\) \(0\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{3}+q^{9}-q^{11}-3q^{13}+4q^{17}+\cdots\)
4400.2.a.z 4400.a 1.a $1$ $35.134$ \(\Q\) None \(0\) \(2\) \(0\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{3}+q^{9}-q^{11}+4q^{17}+4q^{19}+\cdots\)
4400.2.a.ba 4400.a 1.a $1$ $35.134$ \(\Q\) None \(0\) \(2\) \(0\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{3}+q^{9}-q^{11}+2q^{13}-6q^{17}+\cdots\)
4400.2.a.bb 4400.a 1.a $1$ $35.134$ \(\Q\) None \(0\) \(2\) \(0\) \(4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{3}+4q^{7}+q^{9}-q^{11}+6q^{13}+\cdots\)
4400.2.a.bc 4400.a 1.a $1$ $35.134$ \(\Q\) None \(0\) \(2\) \(0\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{3}+4q^{7}+q^{9}+q^{11}+5q^{13}+\cdots\)
4400.2.a.bd 4400.a 1.a $1$ $35.134$ \(\Q\) None \(0\) \(3\) \(0\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+q^{7}+6q^{9}+q^{11}-5q^{17}+\cdots\)
4400.2.a.be 4400.a 1.a $1$ $35.134$ \(\Q\) None \(0\) \(3\) \(0\) \(1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+q^{7}+6q^{9}+q^{11}+6q^{13}+\cdots\)
4400.2.a.bf 4400.a 1.a $2$ $35.134$ \(\Q(\sqrt{13}) \) None \(0\) \(-3\) \(0\) \(-5\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{3}+(-2-\beta )q^{7}+(1+3\beta )q^{9}+\cdots\)
4400.2.a.bg 4400.a 1.a $2$ $35.134$ \(\Q(\sqrt{5}) \) None \(0\) \(-3\) \(0\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{3}+(-2+3\beta )q^{7}+(-1+\cdots)q^{9}+\cdots\)
4400.2.a.bh 4400.a 1.a $2$ $35.134$ \(\Q(\sqrt{13}) \) None \(0\) \(-1\) \(0\) \(-5\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(-3+\beta )q^{7}+\beta q^{9}+q^{11}+\cdots\)
4400.2.a.bi 4400.a 1.a $2$ $35.134$ \(\Q(\sqrt{21}) \) None \(0\) \(-1\) \(0\) \(-5\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(-3+\beta )q^{7}+(2+\beta )q^{9}+q^{11}+\cdots\)
4400.2.a.bj 4400.a 1.a $2$ $35.134$ \(\Q(\sqrt{17}) \) None \(0\) \(-1\) \(0\) \(-1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}-\beta q^{7}+(1+\beta )q^{9}-q^{11}-2q^{13}+\cdots\)
4400.2.a.bk 4400.a 1.a $2$ $35.134$ \(\Q(\sqrt{5}) \) None \(0\) \(-1\) \(0\) \(1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(1-\beta )q^{7}+(-2+\beta )q^{9}+q^{11}+\cdots\)
4400.2.a.bl 4400.a 1.a $2$ $35.134$ \(\Q(\sqrt{33}) \) None \(0\) \(-1\) \(0\) \(1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+\beta q^{7}+(5+\beta )q^{9}+q^{11}-2q^{13}+\cdots\)
4400.2.a.bm 4400.a 1.a $2$ $35.134$ \(\Q(\sqrt{5}) \) None \(0\) \(-1\) \(0\) \(3\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(1+\beta )q^{7}+(-2+\beta )q^{9}-q^{11}+\cdots\)
4400.2.a.bn 4400.a 1.a $2$ $35.134$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(-4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-2q^{7}+5q^{9}-q^{11}+(4+\beta )q^{13}+\cdots\)
4400.2.a.bo 4400.a 1.a $2$ $35.134$ \(\Q(\sqrt{5}) \) None \(0\) \(1\) \(0\) \(-3\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(-1-\beta )q^{7}+(-2+\beta )q^{9}+\cdots\)
4400.2.a.bp 4400.a 1.a $2$ $35.134$ \(\Q(\sqrt{17}) \) None \(0\) \(1\) \(0\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-2\beta q^{7}+(1+\beta )q^{9}+q^{11}+\cdots\)
4400.2.a.bq 4400.a 1.a $2$ $35.134$ \(\Q(\sqrt{5}) \) None \(0\) \(1\) \(0\) \(-1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(-1+\beta )q^{7}+(-2+\beta )q^{9}+\cdots\)
4400.2.a.br 4400.a 1.a $2$ $35.134$ \(\Q(\sqrt{17}) \) None \(0\) \(1\) \(0\) \(3\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(2-\beta )q^{7}+(1+\beta )q^{9}-q^{11}+\cdots\)
4400.2.a.bs 4400.a 1.a $2$ $35.134$ \(\Q(\sqrt{13}) \) None \(0\) \(1\) \(0\) \(5\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(3-\beta )q^{7}+\beta q^{9}+q^{11}-5q^{13}+\cdots\)
4400.2.a.bt 4400.a 1.a $2$ $35.134$ \(\Q(\sqrt{17}) \) None \(0\) \(1\) \(0\) \(5\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(2+\beta )q^{7}+(1+\beta )q^{9}+q^{11}+\cdots\)
4400.2.a.bu 4400.a 1.a $2$ $35.134$ \(\Q(\sqrt{21}) \) None \(0\) \(1\) \(0\) \(5\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(3-\beta )q^{7}+(2+\beta )q^{9}+q^{11}+\cdots\)
4400.2.a.bv 4400.a 1.a $2$ $35.134$ \(\Q(\sqrt{5}) \) None \(0\) \(3\) \(0\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+(2-3\beta )q^{7}+(-1+3\beta )q^{9}+\cdots\)
4400.2.a.bw 4400.a 1.a $2$ $35.134$ \(\Q(\sqrt{13}) \) None \(0\) \(3\) \(0\) \(5\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+(2+\beta )q^{7}+(1+3\beta )q^{9}+\cdots\)
4400.2.a.bx 4400.a 1.a $3$ $35.134$ 3.3.837.1 None \(0\) \(-3\) \(0\) \(-3\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+(-1+\beta _{2})q^{7}+(2+\cdots)q^{9}+\cdots\)
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