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Label Char Prim Dim $A$ Field CM RM Minimal twist Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2175.1.b.a 2175.b 435.b $2$ $1.085$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-87}) \) None 87.1.d.a \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-iq^{3}-q^{6}-iq^{7}-iq^{8}+\cdots\)
2175.1.b.b 2175.b 435.b $2$ $1.085$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-87}) \) None 87.1.d.a \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-iq^{3}-q^{6}+iq^{7}-iq^{8}+\cdots\)
2175.1.b.c 2175.b 435.b $6$ $1.085$ 6.0.419904.1 \(\Q(\sqrt{-87}) \) None 2175.1.h.c \(0\) \(0\) \(0\) \(0\) \(q+\beta _{5}q^{2}-\beta _{3}q^{3}+(-1-\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\)
2175.1.b.d 2175.b 435.b $6$ $1.085$ 6.0.419904.1 \(\Q(\sqrt{-87}) \) None 2175.1.h.c \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(-1+\beta _{2})q^{4}+(\beta _{2}+\cdots)q^{6}+\cdots\)
2175.1.h.a 2175.h 87.d $1$ $1.085$ \(\Q\) \(\Q(\sqrt{-87}) \) None 87.1.d.a \(-1\) \(1\) \(0\) \(1\) \(q-q^{2}+q^{3}-q^{6}+q^{7}+q^{8}+q^{9}+\cdots\)
2175.1.h.b 2175.h 87.d $1$ $1.085$ \(\Q\) \(\Q(\sqrt{-87}) \) None 87.1.d.a \(1\) \(-1\) \(0\) \(1\) \(q+q^{2}-q^{3}-q^{6}+q^{7}-q^{8}+q^{9}+\cdots\)
2175.1.h.c 2175.h 87.d $3$ $1.085$ \(\Q(\zeta_{18})^+\) \(\Q(\sqrt{-87}) \) None 2175.1.h.c \(0\) \(-3\) \(0\) \(0\) \(q+(-\beta _{1}+\beta _{2})q^{2}-q^{3}+(1-\beta _{1})q^{4}+\cdots\)
2175.1.h.d 2175.h 87.d $3$ $1.085$ \(\Q(\zeta_{18})^+\) \(\Q(\sqrt{-87}) \) None 2175.1.h.c \(0\) \(-3\) \(0\) \(0\) \(q+(-\beta _{1}+\beta _{2})q^{2}-q^{3}+(1-\beta _{1})q^{4}+\cdots\)
2175.1.h.e 2175.h 87.d $3$ $1.085$ \(\Q(\zeta_{18})^+\) \(\Q(\sqrt{-87}) \) None 2175.1.h.c \(0\) \(3\) \(0\) \(0\) \(q+(\beta _{1}-\beta _{2})q^{2}+q^{3}+(1-\beta _{1})q^{4}+(\beta _{1}+\cdots)q^{6}+\cdots\)
2175.1.h.f 2175.h 87.d $3$ $1.085$ \(\Q(\zeta_{18})^+\) \(\Q(\sqrt{-87}) \) None 2175.1.h.c \(0\) \(3\) \(0\) \(0\) \(q+(\beta _{1}-\beta _{2})q^{2}+q^{3}+(1-\beta _{1})q^{4}+(\beta _{1}+\cdots)q^{6}+\cdots\)
2175.1.h.g 2175.h 87.d $4$ $1.085$ \(\Q(\zeta_{8})\) None \(\Q(\sqrt{145}) \) 435.1.b.a \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{8}+\zeta_{8}^{3})q^{2}-\zeta_{8}q^{3}+q^{4}+(1+\cdots)q^{6}+\cdots\)
2175.2.a.a 2175.a 1.a $1$ $17.367$ \(\Q\) None None 435.2.c.a \(-2\) \(1\) \(0\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+q^{3}+2q^{4}-2q^{6}-2q^{7}+\cdots\)
2175.2.a.b 2175.a 1.a $1$ $17.367$ \(\Q\) None None 435.2.a.d \(-1\) \(-1\) \(0\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-q^{4}+q^{6}-4q^{7}+3q^{8}+\cdots\)
2175.2.a.c 2175.a 1.a $1$ $17.367$ \(\Q\) None None 435.2.c.b \(-1\) \(-1\) \(0\) \(2\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-q^{4}+q^{6}+2q^{7}+3q^{8}+\cdots\)
2175.2.a.d 2175.a 1.a $1$ $17.367$ \(\Q\) None None 435.2.a.c \(0\) \(-1\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{4}-2q^{7}+q^{9}+3q^{11}+\cdots\)
2175.2.a.e 2175.a 1.a $1$ $17.367$ \(\Q\) None None 2175.2.a.e \(0\) \(-1\) \(0\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{4}+q^{7}+q^{9}-2q^{11}+2q^{12}+\cdots\)
2175.2.a.f 2175.a 1.a $1$ $17.367$ \(\Q\) None None 2175.2.a.e \(0\) \(1\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{4}-q^{7}+q^{9}-2q^{11}-2q^{12}+\cdots\)
2175.2.a.g 2175.a 1.a $1$ $17.367$ \(\Q\) None None 435.2.a.b \(0\) \(1\) \(0\) \(2\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{4}+2q^{7}+q^{9}+q^{11}-2q^{12}+\cdots\)
2175.2.a.h 2175.a 1.a $1$ $17.367$ \(\Q\) None None 435.2.a.a \(1\) \(-1\) \(0\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}-q^{4}-q^{6}+4q^{7}-3q^{8}+\cdots\)
2175.2.a.i 2175.a 1.a $1$ $17.367$ \(\Q\) None None 435.2.c.b \(1\) \(1\) \(0\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}-q^{4}+q^{6}-2q^{7}-3q^{8}+\cdots\)
2175.2.a.j 2175.a 1.a $1$ $17.367$ \(\Q\) None None 435.2.c.a \(2\) \(-1\) \(0\) \(2\) $+$ $\mathrm{SU}(2)$ \(q+2q^{2}-q^{3}+2q^{4}-2q^{6}+2q^{7}+\cdots\)
2175.2.a.k 2175.a 1.a $2$ $17.367$ \(\Q(\sqrt{2}) \) None None 435.2.c.c \(-2\) \(2\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}-q^{4}-q^{6}-\beta q^{7}+3q^{8}+\cdots\)
2175.2.a.l 2175.a 1.a $2$ $17.367$ \(\Q(\sqrt{5}) \) None None 87.2.a.a \(-1\) \(-2\) \(0\) \(4\) $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}-q^{3}+(-1+\beta )q^{4}+\beta q^{6}+\cdots\)
2175.2.a.m 2175.a 1.a $2$ $17.367$ \(\Q(\sqrt{17}) \) None None 435.2.a.h \(-1\) \(-2\) \(0\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}-q^{3}+(2+\beta )q^{4}+\beta q^{6}+(-2+\cdots)q^{7}+\cdots\)
2175.2.a.n 2175.a 1.a $2$ $17.367$ \(\Q(\sqrt{2}) \) None None 2175.2.a.n \(0\) \(-2\) \(0\) \(2\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-q^{3}-\beta q^{6}+q^{7}-2\beta q^{8}+\cdots\)
2175.2.a.o 2175.a 1.a $2$ $17.367$ \(\Q(\sqrt{5}) \) None None 435.2.a.g \(0\) \(-2\) \(0\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}-q^{3}+3q^{4}+\beta q^{6}-2q^{7}+\cdots\)
2175.2.a.p 2175.a 1.a $2$ $17.367$ \(\Q(\sqrt{2}) \) None None 2175.2.a.n \(0\) \(2\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{3}+\beta q^{6}-q^{7}-2\beta q^{8}+\cdots\)
2175.2.a.q 2175.a 1.a $2$ $17.367$ \(\Q(\sqrt{5}) \) None None 435.2.a.e \(1\) \(-2\) \(0\) \(6\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}-\beta q^{6}+\cdots\)
2175.2.a.r 2175.a 1.a $2$ $17.367$ \(\Q(\sqrt{21}) \) None None 435.2.a.f \(1\) \(-2\) \(0\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-q^{3}+(3+\beta )q^{4}-\beta q^{6}-q^{7}+\cdots\)
2175.2.a.s 2175.a 1.a $2$ $17.367$ \(\Q(\sqrt{2}) \) None None 435.2.c.c \(2\) \(-2\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}-q^{4}-q^{6}+\beta q^{7}-3q^{8}+\cdots\)
2175.2.a.t 2175.a 1.a $3$ $17.367$ 3.3.229.1 None None 87.2.a.b \(-2\) \(3\) \(0\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{2}+q^{3}+(2+\beta _{1})q^{4}+\cdots\)
2175.2.a.u 2175.a 1.a $3$ $17.367$ 3.3.469.1 None None 435.2.a.i \(-1\) \(3\) \(0\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
2175.2.a.v 2175.a 1.a $4$ $17.367$ 4.4.2225.1 None None 435.2.a.j \(3\) \(4\) \(0\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
2175.2.a.w 2175.a 1.a $5$ $17.367$ 5.5.246832.1 None None 435.2.c.e \(-3\) \(-5\) \(0\) \(-8\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}-q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
2175.2.a.x 2175.a 1.a $5$ $17.367$ 5.5.331312.1 None None 435.2.c.d \(-2\) \(5\) \(0\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{2}+q^{3}+(1+\beta _{1}-\beta _{3}-\beta _{4})q^{4}+\cdots\)
2175.2.a.y 2175.a 1.a $5$ $17.367$ 5.5.331312.1 None None 435.2.c.d \(2\) \(-5\) \(0\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{3}q^{2}-q^{3}+(1+\beta _{1}-\beta _{3}-\beta _{4})q^{4}+\cdots\)
2175.2.a.z 2175.a 1.a $5$ $17.367$ 5.5.246832.1 None None 435.2.c.e \(3\) \(5\) \(0\) \(8\) $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+q^{3}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots\)
2175.2.a.ba 2175.a 1.a $7$ $17.367$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None None 2175.2.a.ba \(-2\) \(-7\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
2175.2.a.bb 2175.a 1.a $7$ $17.367$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None None 2175.2.a.ba \(2\) \(7\) \(0\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
2175.2.a.bc 2175.a 1.a $8$ $17.367$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None 2175.2.a.bc \(-2\) \(-8\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
2175.2.a.bd 2175.a 1.a $8$ $17.367$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None 2175.2.a.bc \(2\) \(8\) \(0\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
2175.2.c.a 2175.c 5.b $2$ $17.367$ \(\Q(\sqrt{-1}) \) None None 435.2.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+iq^{3}+q^{4}-q^{6}+4iq^{7}+\cdots\)
2175.2.c.b 2175.c 5.b $2$ $17.367$ \(\Q(\sqrt{-1}) \) None None 435.2.a.d \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-iq^{3}+q^{4}+q^{6}+4iq^{7}+\cdots\)
2175.2.c.c 2175.c 5.b $2$ $17.367$ \(\Q(\sqrt{-1}) \) None None 2175.2.a.e \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{3}+2q^{4}-iq^{7}-q^{9}-2q^{11}+\cdots\)
2175.2.c.d 2175.c 5.b $2$ $17.367$ \(\Q(\sqrt{-1}) \) None None 435.2.a.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{3}+2q^{4}+2iq^{7}-q^{9}+q^{11}+\cdots\)
2175.2.c.e 2175.c 5.b $2$ $17.367$ \(\Q(\sqrt{-1}) \) None None 435.2.a.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+2q^{4}-2iq^{7}-q^{9}+3q^{11}+\cdots\)
2175.2.c.f 2175.c 5.b $4$ $17.367$ \(\Q(i, \sqrt{21})\) None None 435.2.a.f \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-\beta _{2}q^{3}+(-4+\beta _{3})q^{4}+(-1+\cdots)q^{6}+\cdots\)
2175.2.c.g 2175.c 5.b $4$ $17.367$ \(\Q(i, \sqrt{5})\) None None 435.2.a.g \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}+\beta _{1}q^{3}-3q^{4}-\beta _{3}q^{6}-2\beta _{1}q^{7}+\cdots\)
2175.2.c.h 2175.c 5.b $4$ $17.367$ \(\Q(i, \sqrt{17})\) None None 435.2.a.h \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{2}q^{3}+(-3+\beta _{3})q^{4}+(1+\cdots)q^{6}+\cdots\)
2175.2.c.i 2175.c 5.b $4$ $17.367$ \(\Q(\zeta_{8})\) None None 2175.2.a.n \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{8}^{2}q^{2}+\zeta_{8}q^{3}-\zeta_{8}^{3}q^{6}+\zeta_{8}q^{7}+\cdots\)
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