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Label Char Prim Dim $A$ Field CM RM Minimal twist Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2535.1.e.a 2535.e 195.e $6$ $1.265$ 6.0.153664.1 \(\Q(\sqrt{-15}) \) None 2535.1.f.a \(0\) \(-6\) \(0\) \(0\) \(q+(-\beta _{1}+\beta _{3}+\beta _{5})q^{2}-q^{3}+(-\beta _{2}+\cdots)q^{4}+\cdots\)
2535.1.e.b 2535.e 195.e $6$ $1.265$ 6.0.153664.1 \(\Q(\sqrt{-15}) \) None 2535.1.f.a \(0\) \(6\) \(0\) \(0\) \(q+(-\beta _{1}+\beta _{3}+\beta _{5})q^{2}+q^{3}+(-\beta _{2}+\cdots)q^{4}+\cdots\)
2535.1.f.a 2535.f 15.d $3$ $1.265$ \(\Q(\zeta_{14})^+\) \(\Q(\sqrt{-15}) \) None 2535.1.f.a \(-1\) \(-3\) \(3\) \(0\) \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
2535.1.f.b 2535.f 15.d $3$ $1.265$ \(\Q(\zeta_{14})^+\) \(\Q(\sqrt{-15}) \) None 2535.1.f.a \(-1\) \(3\) \(3\) \(0\) \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
2535.1.f.c 2535.f 15.d $3$ $1.265$ \(\Q(\zeta_{14})^+\) \(\Q(\sqrt{-15}) \) None 2535.1.f.a \(1\) \(-3\) \(-3\) \(0\) \(q-\beta _{2}q^{2}-q^{3}+(\beta _{1}-\beta _{2})q^{4}-q^{5}+\cdots\)
2535.1.f.d 2535.f 15.d $3$ $1.265$ \(\Q(\zeta_{14})^+\) \(\Q(\sqrt{-15}) \) None 2535.1.f.a \(1\) \(3\) \(-3\) \(0\) \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
2535.1.f.e 2535.f 15.d $4$ $1.265$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-39}) \) None 195.1.e.a \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{8}-\zeta_{8}^{3})q^{2}+\zeta_{8}^{2}q^{3}+q^{4}+\zeta_{8}^{3}q^{5}+\cdots\)
2535.1.j.a 2535.j 195.j $8$ $1.265$ \(\Q(\zeta_{16})\) \(\Q(\sqrt{-39}) \) None 2535.1.j.a \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{16}-\zeta_{16}^{7})q^{2}-\zeta_{16}^{6}q^{3}+(-1+\cdots)q^{4}+\cdots\)
2535.1.u.a 2535.u 195.u $8$ $1.265$ \(\Q(\zeta_{16})\) \(\Q(\sqrt{-39}) \) None 2535.1.j.a \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{16}^{3}+\zeta_{16}^{5})q^{2}-\zeta_{16}^{6}q^{3}+\cdots\)
2535.1.x.a 2535.x 195.x $6$ $1.265$ 6.0.64827.1 \(\Q(\sqrt{-15}) \) None 2535.1.f.a \(-1\) \(-3\) \(-6\) \(0\) \(q+(\beta _{3}+\beta _{4})q^{2}-\beta _{5}q^{3}+(-1+\beta _{1}+\cdots)q^{4}+\cdots\)
2535.1.x.b 2535.x 195.x $6$ $1.265$ 6.0.64827.1 \(\Q(\sqrt{-15}) \) None 2535.1.f.a \(-1\) \(3\) \(-6\) \(0\) \(q+(\beta _{1}-\beta _{2})q^{2}+\beta _{5}q^{3}+(-\beta _{1}-\beta _{4}+\cdots)q^{4}+\cdots\)
2535.1.x.c 2535.x 195.x $6$ $1.265$ 6.0.64827.1 \(\Q(\sqrt{-15}) \) None 2535.1.f.a \(1\) \(-3\) \(6\) \(0\) \(q+(\beta _{1}-\beta _{2}+\beta _{3}+\beta _{4}+\beta _{5})q^{2}-\beta _{5}q^{3}+\cdots\)
2535.1.x.d 2535.x 195.x $6$ $1.265$ 6.0.64827.1 \(\Q(\sqrt{-15}) \) None 2535.1.f.a \(1\) \(3\) \(6\) \(0\) \(q+(-\beta _{3}-\beta _{4})q^{2}+\beta _{5}q^{3}+(-1+\beta _{1}+\cdots)q^{4}+\cdots\)
2535.1.x.e 2535.x 195.x $8$ $1.265$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-39}) \) None 195.1.e.a \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{24}^{5}+\zeta_{24}^{11})q^{2}+\zeta_{24}^{2}q^{3}-\zeta_{24}^{4}q^{4}+\cdots\)
2535.1.y.a 2535.y 195.y $8$ $1.265$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-39}) \) None 195.1.e.a \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{24}-\zeta_{24}^{7})q^{2}+\zeta_{24}^{10}q^{3}-\zeta_{24}^{8}q^{4}+\cdots\)
2535.1.y.b 2535.y 195.y $12$ $1.265$ 12.0.\(\cdots\).1 \(\Q(\sqrt{-15}) \) None 2535.1.f.a \(0\) \(-6\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-1+\beta _{7})q^{3}+(1-\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
2535.1.y.c 2535.y 195.y $12$ $1.265$ 12.0.\(\cdots\).1 \(\Q(\sqrt{-15}) \) None 2535.1.f.a \(0\) \(6\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(1-\beta _{7})q^{3}+(1-\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
2535.1.bc.a 2535.bc 195.ac $16$ $1.265$ \(\Q(\zeta_{48})\) \(\Q(\sqrt{-39}) \) None 2535.1.j.a \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{48}^{5}-\zeta_{48}^{11})q^{2}+\zeta_{48}^{2}q^{3}+\cdots\)
2535.1.bn.a 2535.bn 195.an $16$ $1.265$ \(\Q(\zeta_{48})\) \(\Q(\sqrt{-39}) \) None 2535.1.j.a \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{48}^{17}-\zeta_{48}^{23})q^{2}+\zeta_{48}^{2}q^{3}+\cdots\)
2535.2.a.a 2535.a 1.a $1$ $20.242$ \(\Q\) None None 195.2.a.b \(-2\) \(-1\) \(-1\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}-q^{3}+2q^{4}-q^{5}+2q^{6}-3q^{7}+\cdots\)
2535.2.a.b 2535.a 1.a $1$ $20.242$ \(\Q\) None None 195.2.a.d \(-2\) \(1\) \(-1\) \(3\) $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+q^{3}+2q^{4}-q^{5}-2q^{6}+3q^{7}+\cdots\)
2535.2.a.c 2535.a 1.a $1$ $20.242$ \(\Q\) None None 195.2.i.a \(-2\) \(1\) \(1\) \(-5\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+q^{3}+2q^{4}+q^{5}-2q^{6}-5q^{7}+\cdots\)
2535.2.a.d 2535.a 1.a $1$ $20.242$ \(\Q\) None None 195.2.a.c \(-2\) \(1\) \(1\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+q^{3}+2q^{4}+q^{5}-2q^{6}+q^{7}+\cdots\)
2535.2.a.e 2535.a 1.a $1$ $20.242$ \(\Q\) None None 195.2.b.b \(-1\) \(1\) \(-1\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}-q^{4}-q^{5}-q^{6}-2q^{7}+\cdots\)
2535.2.a.f 2535.a 1.a $1$ $20.242$ \(\Q\) None None 195.2.b.a \(0\) \(-1\) \(-1\) \(3\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{4}-q^{5}+3q^{7}+q^{9}-3q^{11}+\cdots\)
2535.2.a.g 2535.a 1.a $1$ $20.242$ \(\Q\) None None 195.2.b.a \(0\) \(-1\) \(1\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{4}+q^{5}-3q^{7}+q^{9}+3q^{11}+\cdots\)
2535.2.a.h 2535.a 1.a $1$ $20.242$ \(\Q\) None None 195.2.i.b \(0\) \(1\) \(-1\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{4}-q^{5}-q^{7}+q^{9}+6q^{11}+\cdots\)
2535.2.a.i 2535.a 1.a $1$ $20.242$ \(\Q\) None None 195.2.i.b \(0\) \(1\) \(1\) \(1\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{4}+q^{5}+q^{7}+q^{9}-6q^{11}+\cdots\)
2535.2.a.j 2535.a 1.a $1$ $20.242$ \(\Q\) None None 15.2.a.a \(1\) \(-1\) \(-1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}-q^{4}-q^{5}-q^{6}-3q^{8}+\cdots\)
2535.2.a.k 2535.a 1.a $1$ $20.242$ \(\Q\) None None 195.2.a.a \(1\) \(1\) \(-1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}-q^{4}-q^{5}+q^{6}-3q^{8}+\cdots\)
2535.2.a.l 2535.a 1.a $1$ $20.242$ \(\Q\) None None 195.2.b.b \(1\) \(1\) \(1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}-q^{4}+q^{5}+q^{6}+2q^{7}+\cdots\)
2535.2.a.m 2535.a 1.a $1$ $20.242$ \(\Q\) None None 195.2.i.a \(2\) \(1\) \(-1\) \(5\) $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+q^{3}+2q^{4}-q^{5}+2q^{6}+5q^{7}+\cdots\)
2535.2.a.n 2535.a 1.a $2$ $20.242$ \(\Q(\sqrt{3}) \) None None 195.2.bb.a \(-2\) \(2\) \(-2\) \(2\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+q^{3}+(2-2\beta )q^{4}-q^{5}+\cdots\)
2535.2.a.o 2535.a 1.a $2$ $20.242$ \(\Q(\sqrt{3}) \) None None 195.2.i.c \(-2\) \(2\) \(2\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+q^{3}+(2-2\beta )q^{4}+q^{5}+\cdots\)
2535.2.a.p 2535.a 1.a $2$ $20.242$ \(\Q(\sqrt{17}) \) None None 195.2.b.c \(-1\) \(2\) \(-2\) \(3\) $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+q^{3}+(2+\beta )q^{4}-q^{5}-\beta q^{6}+\cdots\)
2535.2.a.q 2535.a 1.a $2$ $20.242$ \(\Q(\sqrt{17}) \) None None 195.2.b.c \(1\) \(2\) \(2\) \(-3\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{3}+(2+\beta )q^{4}+q^{5}+\beta q^{6}+\cdots\)
2535.2.a.r 2535.a 1.a $2$ $20.242$ \(\Q(\sqrt{3}) \) None None 195.2.i.c \(2\) \(2\) \(-2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+q^{3}+(2+2\beta )q^{4}-q^{5}+\cdots\)
2535.2.a.s 2535.a 1.a $2$ $20.242$ \(\Q(\sqrt{3}) \) None None 195.2.bb.a \(2\) \(2\) \(2\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+q^{3}+(2+2\beta )q^{4}+q^{5}+\cdots\)
2535.2.a.t 2535.a 1.a $3$ $20.242$ \(\Q(\zeta_{14})^+\) None None 2535.2.a.t \(-3\) \(3\) \(3\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1}+\beta _{2})q^{2}+q^{3}+(4-\beta _{1}+\cdots)q^{4}+\cdots\)
2535.2.a.u 2535.a 1.a $3$ $20.242$ \(\Q(\zeta_{14})^+\) None None 2535.2.a.u \(-2\) \(3\) \(-3\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}+\cdots\)
2535.2.a.v 2535.a 1.a $3$ $20.242$ \(\Q(\zeta_{14})^+\) None None 2535.2.a.v \(-1\) \(-3\) \(3\) \(2\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+\beta _{2}q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
2535.2.a.w 2535.a 1.a $3$ $20.242$ \(\Q(\zeta_{14})^+\) None None 2535.2.a.w \(-1\) \(3\) \(-3\) \(4\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
2535.2.a.x 2535.a 1.a $3$ $20.242$ \(\Q(\zeta_{14})^+\) None None 2535.2.a.x \(-1\) \(3\) \(3\) \(12\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
2535.2.a.y 2535.a 1.a $3$ $20.242$ 3.3.148.1 None None 195.2.i.e \(0\) \(-3\) \(-3\) \(-5\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}-q^{3}+(1-\beta _{1}-\beta _{2})q^{4}-q^{5}+\cdots\)
2535.2.a.z 2535.a 1.a $3$ $20.242$ 3.3.148.1 None None 195.2.i.e \(0\) \(-3\) \(3\) \(5\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{2}-q^{3}+(1-\beta _{1}-\beta _{2})q^{4}+q^{5}+\cdots\)
2535.2.a.ba 2535.a 1.a $3$ $20.242$ 3.3.756.1 None None 195.2.i.d \(0\) \(-3\) \(-3\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
2535.2.a.bb 2535.a 1.a $3$ $20.242$ 3.3.756.1 None None 195.2.i.d \(0\) \(-3\) \(3\) \(3\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
2535.2.a.bc 2535.a 1.a $3$ $20.242$ 3.3.316.1 None None 195.2.a.e \(0\) \(-3\) \(3\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(3+\beta _{2})q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
2535.2.a.bd 2535.a 1.a $3$ $20.242$ \(\Q(\zeta_{14})^+\) None None 2535.2.a.v \(1\) \(-3\) \(-3\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+\beta _{2}q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
2535.2.a.be 2535.a 1.a $3$ $20.242$ \(\Q(\zeta_{14})^+\) None None 2535.2.a.x \(1\) \(3\) \(-3\) \(-12\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
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