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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1815.1.g.a 1815.g 15.d $1$ $0.906$ \(\Q\) \(\Q(\sqrt{-15}) \) None \(-1\) \(-1\) \(-1\) \(0\) \(q-q^{2}-q^{3}-q^{5}+q^{6}+q^{8}+q^{9}+\cdots\)
1815.1.g.b 1815.g 15.d $1$ $0.906$ \(\Q\) \(\Q(\sqrt{-15}) \) None \(-1\) \(1\) \(1\) \(0\) \(q-q^{2}+q^{3}+q^{5}-q^{6}+q^{8}+q^{9}+\cdots\)
1815.1.g.c 1815.g 15.d $1$ $0.906$ \(\Q\) \(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-15}) \) \(\Q(\sqrt{165}) \) \(0\) \(-1\) \(1\) \(0\) \(q-q^{3}-q^{4}+q^{5}+q^{9}+q^{12}-q^{15}+\cdots\)
1815.1.g.d 1815.g 15.d $1$ $0.906$ \(\Q\) \(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-15}) \) \(\Q(\sqrt{165}) \) \(0\) \(1\) \(-1\) \(0\) \(q+q^{3}-q^{4}-q^{5}+q^{9}-q^{12}-q^{15}+\cdots\)
1815.1.g.e 1815.g 15.d $1$ $0.906$ \(\Q\) \(\Q(\sqrt{-15}) \) None \(1\) \(-1\) \(-1\) \(0\) \(q+q^{2}-q^{3}-q^{5}-q^{6}-q^{8}+q^{9}+\cdots\)
1815.1.g.f 1815.g 15.d $1$ $0.906$ \(\Q\) \(\Q(\sqrt{-15}) \) None \(1\) \(1\) \(1\) \(0\) \(q+q^{2}+q^{3}+q^{5}+q^{6}-q^{8}+q^{9}+\cdots\)
1815.1.g.g 1815.g 15.d $2$ $0.906$ \(\Q(\sqrt{3}) \) \(\Q(\sqrt{-15}) \) None \(0\) \(-2\) \(2\) \(0\) \(q-\beta q^{2}-q^{3}+2q^{4}+q^{5}+\beta q^{6}-\beta q^{8}+\cdots\)
1815.1.g.h 1815.g 15.d $2$ $0.906$ \(\Q(\sqrt{3}) \) \(\Q(\sqrt{-15}) \) None \(0\) \(2\) \(-2\) \(0\) \(q-\beta q^{2}+q^{3}+2q^{4}-q^{5}-\beta q^{6}-\beta q^{8}+\cdots\)
1815.1.o.a 1815.o 165.o $4$ $0.906$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-15}) \) None \(-1\) \(-1\) \(-1\) \(0\) \(q-\zeta_{10}^{3}q^{2}+\zeta_{10}^{4}q^{3}+\zeta_{10}^{2}q^{5}+\cdots\)
1815.1.o.b 1815.o 165.o $4$ $0.906$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-15}) \) None \(-1\) \(1\) \(1\) \(0\) \(q-\zeta_{10}^{3}q^{2}-\zeta_{10}^{4}q^{3}-\zeta_{10}^{2}q^{5}+\cdots\)
1815.1.o.c 1815.o 165.o $4$ $0.906$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-15}) \) \(\Q(\sqrt{165}) \) \(0\) \(-1\) \(1\) \(0\) \(q+\zeta_{10}^{4}q^{3}+\zeta_{10}q^{4}-\zeta_{10}^{2}q^{5}-\zeta_{10}^{3}q^{9}+\cdots\)
1815.1.o.d 1815.o 165.o $4$ $0.906$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-15}) \) \(\Q(\sqrt{165}) \) \(0\) \(1\) \(-1\) \(0\) \(q-\zeta_{10}^{4}q^{3}+\zeta_{10}q^{4}+\zeta_{10}^{2}q^{5}-\zeta_{10}^{3}q^{9}+\cdots\)
1815.1.o.e 1815.o 165.o $4$ $0.906$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-15}) \) None \(1\) \(-1\) \(-1\) \(0\) \(q+\zeta_{10}^{3}q^{2}+\zeta_{10}^{4}q^{3}+\zeta_{10}^{2}q^{5}+\cdots\)
1815.1.o.f 1815.o 165.o $4$ $0.906$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-15}) \) None \(1\) \(1\) \(1\) \(0\) \(q+\zeta_{10}^{3}q^{2}-\zeta_{10}^{4}q^{3}-\zeta_{10}^{2}q^{5}+\cdots\)
1815.1.o.g 1815.o 165.o $8$ $0.906$ 8.0.324000000.3 \(\Q(\sqrt{-15}) \) None \(0\) \(-2\) \(2\) \(0\) \(q-\beta _{7}q^{2}+\beta _{6}q^{3}+2\beta _{4}q^{4}+(1+\beta _{2}+\cdots)q^{5}+\cdots\)
1815.1.o.h 1815.o 165.o $8$ $0.906$ 8.0.324000000.3 \(\Q(\sqrt{-15}) \) None \(0\) \(2\) \(-2\) \(0\) \(q-\beta _{7}q^{2}-\beta _{6}q^{3}+2\beta _{4}q^{4}+(-1-\beta _{2}+\cdots)q^{5}+\cdots\)
1815.1.v.a 1815.v 165.u $8$ $0.906$ \(\Q(\zeta_{20})\) \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{20}^{7}q^{3}+\zeta_{20}^{3}q^{4}+\zeta_{20}q^{5}-\zeta_{20}^{4}q^{9}+\cdots\)
1815.1.v.b 1815.v 165.u $8$ $0.906$ \(\Q(\zeta_{20})\) \(\Q(\sqrt{-11}) \) None \(0\) \(2\) \(0\) \(0\) \(q+\zeta_{20}^{2}q^{3}+\zeta_{20}^{3}q^{4}-\zeta_{20}q^{5}+\zeta_{20}^{4}q^{9}+\cdots\)
1815.2.a.a 1815.a 1.a $1$ $14.493$ \(\Q\) None None \(-1\) \(1\) \(-1\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}-q^{4}-q^{5}-q^{6}-2q^{7}+\cdots\)
1815.2.a.b 1815.a 1.a $1$ $14.493$ \(\Q\) None None \(0\) \(1\) \(-1\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{4}-q^{5}-q^{7}+q^{9}-2q^{12}+\cdots\)
1815.2.a.c 1815.a 1.a $1$ $14.493$ \(\Q\) None None \(0\) \(1\) \(-1\) \(1\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{4}-q^{5}+q^{7}+q^{9}-2q^{12}+\cdots\)
1815.2.a.d 1815.a 1.a $1$ $14.493$ \(\Q\) None None \(1\) \(-1\) \(1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}-q^{4}+q^{5}-q^{6}-3q^{8}+\cdots\)
1815.2.a.e 1815.a 1.a $1$ $14.493$ \(\Q\) None None \(1\) \(1\) \(-1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}-q^{4}-q^{5}+q^{6}+2q^{7}+\cdots\)
1815.2.a.f 1815.a 1.a $2$ $14.493$ \(\Q(\sqrt{5}) \) None None \(-1\) \(-2\) \(-2\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}-q^{3}+(-1+\beta )q^{4}-q^{5}+\beta q^{6}+\cdots\)
1815.2.a.g 1815.a 1.a $2$ $14.493$ \(\Q(\sqrt{3}) \) None None \(0\) \(-2\) \(-2\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{4}-q^{5}-\beta q^{7}+q^{9}+2q^{12}+\cdots\)
1815.2.a.h 1815.a 1.a $2$ $14.493$ \(\Q(\sqrt{3}) \) None None \(0\) \(-2\) \(-2\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-q^{3}+q^{4}-q^{5}-\beta q^{6}-\beta q^{8}+\cdots\)
1815.2.a.i 1815.a 1.a $2$ $14.493$ \(\Q(\sqrt{3}) \) None None \(0\) \(2\) \(-2\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{3}+q^{4}-q^{5}+\beta q^{6}-2q^{7}+\cdots\)
1815.2.a.j 1815.a 1.a $2$ $14.493$ \(\Q(\sqrt{5}) \) None None \(1\) \(-2\) \(-2\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}-q^{5}-\beta q^{6}+\cdots\)
1815.2.a.k 1815.a 1.a $2$ $14.493$ \(\Q(\sqrt{2}) \) None None \(2\) \(-2\) \(-2\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}-q^{3}+(1+2\beta )q^{4}-q^{5}+\cdots\)
1815.2.a.l 1815.a 1.a $3$ $14.493$ 3.3.469.1 None None \(-1\) \(3\) \(3\) \(-3\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
1815.2.a.m 1815.a 1.a $3$ $14.493$ 3.3.148.1 None None \(1\) \(3\) \(3\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots\)
1815.2.a.n 1815.a 1.a $3$ $14.493$ 3.3.469.1 None None \(1\) \(3\) \(3\) \(3\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
1815.2.a.o 1815.a 1.a $4$ $14.493$ 4.4.725.1 None None \(-5\) \(4\) \(-4\) \(2\) $+$ $\mathrm{SU}(2)$ \(q+(-2+\beta _{1}+\beta _{2})q^{2}+q^{3}+(3-\beta _{1}+\cdots)q^{4}+\cdots\)
1815.2.a.p 1815.a 1.a $4$ $14.493$ 4.4.725.1 None None \(-3\) \(4\) \(4\) \(-6\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+q^{3}+(-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
1815.2.a.q 1815.a 1.a $4$ $14.493$ \(\Q(\zeta_{15})^+\) None None \(-1\) \(-4\) \(4\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+(\beta _{2}+\beta _{3})q^{2}-q^{3}+\beta _{1}q^{4}+q^{5}+\cdots\)
1815.2.a.r 1815.a 1.a $4$ $14.493$ 4.4.5725.1 None None \(-1\) \(-4\) \(-4\) \(8\) $-$ $\mathrm{SU}(2)$ \(q+(\beta _{1}-\beta _{2})q^{2}-q^{3}+(3-\beta _{2}-\beta _{3})q^{4}+\cdots\)
1815.2.a.s 1815.a 1.a $4$ $14.493$ 4.4.8112.1 None None \(0\) \(-4\) \(4\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}-q^{3}+(2-\beta _{3})q^{4}+q^{5}+\beta _{2}q^{6}+\cdots\)
1815.2.a.t 1815.a 1.a $4$ $14.493$ \(\Q(\sqrt{3}, \sqrt{7})\) None None \(0\) \(4\) \(-4\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{2}+q^{3}-\beta _{2}q^{4}-q^{5}+\beta _{3}q^{6}+\cdots\)
1815.2.a.u 1815.a 1.a $4$ $14.493$ \(\Q(\zeta_{15})^+\) None None \(1\) \(-4\) \(4\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+(-\beta _{2}-\beta _{3})q^{2}-q^{3}+\beta _{1}q^{4}+q^{5}+\cdots\)
1815.2.a.v 1815.a 1.a $4$ $14.493$ 4.4.5725.1 None None \(1\) \(-4\) \(-4\) \(-8\) $+$ $\mathrm{SU}(2)$ \(q+(-\beta _{1}+\beta _{2})q^{2}-q^{3}+(3-\beta _{2}-\beta _{3})q^{4}+\cdots\)
1815.2.a.w 1815.a 1.a $4$ $14.493$ 4.4.725.1 None None \(3\) \(4\) \(4\) \(6\) $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+q^{3}+(-\beta _{1}+\beta _{2})q^{4}+\cdots\)
1815.2.a.x 1815.a 1.a $4$ $14.493$ 4.4.725.1 None None \(5\) \(4\) \(-4\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+(2-\beta _{1}-\beta _{2})q^{2}+q^{3}+(3-\beta _{1}-2\beta _{2}+\cdots)q^{4}+\cdots\)
1815.2.a.y 1815.a 1.a $6$ $14.493$ 6.6.437199552.1 None None \(0\) \(-6\) \(6\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
1815.2.c.a 1815.c 5.b $2$ $14.493$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+iq^{3}+q^{4}+(-1-2i)q^{5}+\cdots\)
1815.2.c.b 1815.c 5.b $2$ $14.493$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-iq^{3}+q^{4}+(-1+2i)q^{5}+\cdots\)
1815.2.c.c 1815.c 5.b $4$ $14.493$ \(\Q(i, \sqrt{5})\) None None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}-\beta _{1}q^{3}-3q^{4}+(-1-2\beta _{1}+\cdots)q^{5}+\cdots\)
1815.2.c.d 1815.c 5.b $6$ $14.493$ 6.0.350464.1 None None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{3}-\beta _{5})q^{2}-\beta _{3}q^{3}+(-2-\beta _{1}+\cdots)q^{4}+\cdots\)
1815.2.c.e 1815.c 5.b $6$ $14.493$ 6.0.350464.1 None None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{4}q^{2}-\beta _{3}q^{3}+(-\beta _{1}+\beta _{2})q^{4}+\cdots\)
1815.2.c.f 1815.c 5.b $8$ $14.493$ 8.0.49787136.1 None None \(0\) \(0\) \(16\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{6}q^{2}-\beta _{3}q^{3}+\beta _{4}q^{4}+(2-\beta _{3}+\cdots)q^{5}+\cdots\)
1815.2.c.g 1815.c 5.b $8$ $14.493$ \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\zeta_{24}+\zeta_{24}^{5})q^{2}+\zeta_{24}^{3}q^{3}+(-1+\cdots)q^{5}+\cdots\)
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