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Level	Weight	Analytic conductor	$Nk^2$	Dim.

Bad $p$	Char.	Primitive character	Character order	Coefficient field

Self-twists	CM/RM discriminant	Inner twist count	Is self-dual	Analytic rank

Coefficient ring index	Coefficient ring gens.		Projective image	Projective image type
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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
1875.1.c.a	$1875$	$1$	1875.c	3.b	$2$	$2$	$2$	$0.936$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-3}) $	None	✓	$2$	$0$	$0$	$-2$	$0$	$1$		$1$		$q-q^{3}+q^{4}+(1-\beta )q^{7}+q^{9}-q^{12}+\cdots$
1875.1.c.b	$1875$	$1$	1875.c	3.b	$2$	$2$	$2$	$0.936$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-3}) $	None	✓	$2$	$0$	$0$	$2$	$0$	$-1$		$1$		$q+q^{3}+q^{4}+(-1+\beta )q^{7}+q^{9}+q^{12}+\cdots$
1875.1.d.a	$1875$	$1$	1875.d	15.d	$2$	$4$	$4$	$0.936$	$\Q(i, \sqrt{5})$	$D_{5}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\beta _{3}q^{3}-q^{4}-\beta _{1}q^{7}-q^{9}-\beta _{3}q^{12}+\cdots$
1875.1.h.a	$1875$	$1$	1875.h	75.h	$10$	$4$	$1$	$0.936$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$-3$	$1$	$0$	$0$		$1$		$q+(-1+\zeta_{10})q^{2}+\zeta_{10}q^{3}+(1-\zeta_{10}+\cdots)q^{4}+\cdots$
1875.1.h.b	$1875$	$1$	1875.h	75.h	$10$	$4$	$1$	$0.936$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$-2$	$-1$	$0$	$0$		$1$		$q+(\zeta_{10}^{2}+\zeta_{10}^{4})q^{2}-\zeta_{10}q^{3}+(-\zeta_{10}+\cdots)q^{4}+\cdots$
1875.1.h.c	$1875$	$1$	1875.h	75.h	$10$	$4$	$1$	$0.936$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$2$	$1$	$0$	$0$		$1$		$q+(-\zeta_{10}^{2}-\zeta_{10}^{4})q^{2}+\zeta_{10}q^{3}+(-\zeta_{10}+\cdots)q^{4}+\cdots$
1875.1.h.d	$1875$	$1$	1875.h	75.h	$10$	$4$	$1$	$0.936$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$3$	$-1$	$0$	$0$		$1$		$q+(1-\zeta_{10})q^{2}-\zeta_{10}q^{3}+(1-\zeta_{10}+\cdots)q^{4}+\cdots$
1875.1.h.e	$1875$	$1$	1875.h	75.h	$10$	$8$	$2$	$0.936$	$\Q(\zeta_{20})$	$D_{5}$	$\Q(\sqrt{-3}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{20}^{7}q^{3}+\zeta_{20}^{2}q^{4}+(\zeta_{20}+\zeta_{20}^{9}+\cdots)q^{7}+\cdots$
1875.1.h.f	$1875$	$1$	1875.h	75.h	$10$	$8$	$2$	$0.936$	$\Q(\zeta_{20})$	$D_{5}$	$\Q(\sqrt{-3}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{20}^{7}q^{3}+\zeta_{20}^{2}q^{4}+(-\zeta_{20}^{3}-\zeta_{20}^{7}+\cdots)q^{7}+\cdots$
1875.1.j.a	$1875$	$1$	1875.j	75.j	$10$	$4$	$1$	$0.936$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-2$		$1$		$q+\zeta_{10}^{2}q^{3}+\zeta_{10}^{2}q^{4}+(-\zeta_{10}+\zeta_{10}^{4}+\cdots)q^{7}+\cdots$
1875.1.j.b	$1875$	$1$	1875.j	75.j	$10$	$4$	$1$	$0.936$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-2$		$1$		$q+\zeta_{10}^{2}q^{3}+\zeta_{10}^{2}q^{4}+(\zeta_{10}^{2}-\zeta_{10}^{3}+\cdots)q^{7}+\cdots$
1875.1.j.c	$1875$	$1$	1875.j	75.j	$10$	$4$	$1$	$0.936$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$2$		$1$		$q-\zeta_{10}^{2}q^{3}+\zeta_{10}^{2}q^{4}+(-\zeta_{10}^{2}+\zeta_{10}^{3}+\cdots)q^{7}+\cdots$
1875.1.j.d	$1875$	$1$	1875.j	75.j	$10$	$4$	$1$	$0.936$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$2$		$1$		$q-\zeta_{10}^{2}q^{3}+\zeta_{10}^{2}q^{4}+(\zeta_{10}-\zeta_{10}^{4}+\cdots)q^{7}+\cdots$
1875.1.j.e	$1875$	$1$	1875.j	75.j	$10$	$8$	$2$	$0.936$	$\Q(\zeta_{20})$	$D_{5}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{20}^{5}+\zeta_{20}^{9})q^{2}-\zeta_{20}^{9}q^{3}+(-1+\cdots)q^{4}+\cdots$
1875.1.j.f	$1875$	$1$	1875.j	75.j	$10$	$8$	$2$	$0.936$	$\Q(\zeta_{20})$	$D_{5}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{20}-\zeta_{20}^{3})q^{2}-\zeta_{20}^{9}q^{3}+(\zeta_{20}^{2}+\cdots)q^{4}+\cdots$
1875.2.a.a	$1875$	$2$	1875.a	1.a	$1$	$2$	$2$	$14.972$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$-2$	$-2$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}-q^{4}+q^{6}+(2-4\beta )q^{7}+\cdots$
1875.2.a.b	$1875$	$2$	1875.a	1.a	$1$	$2$	$2$	$14.972$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$-1$	$-2$	$0$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}-q^{3}+(-1+\beta )q^{4}+\beta q^{6}+\cdots$
1875.2.a.c	$1875$	$2$	1875.a	1.a	$1$	$2$	$2$	$14.972$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$1$	$2$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{3}+(-1+\beta )q^{4}+\beta q^{6}+\cdots$
1875.2.a.d	$1875$	$2$	1875.a	1.a	$1$	$2$	$2$	$14.972$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$2$	$2$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}-q^{4}+q^{6}+(-2+4\beta )q^{7}+\cdots$
1875.2.a.e	$1875$	$2$	1875.a	1.a	$1$	$4$	$4$	$14.972$	4.4.5125.1	$_{}$	None	None	✓	$1$	$1$	$-2$	$-4$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(2+\beta _{1}+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots$
1875.2.a.f	$1875$	$2$	1875.a	1.a	$1$	$4$	$4$	$14.972$	$\Q(\zeta_{15})^+$	$_{}$	None	None	✓	$1$	$1$	$-1$	$4$	$0$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q+(\beta _{2}+\beta _{3})q^{2}+q^{3}+\beta _{1}q^{4}+(\beta _{2}+\beta _{3})q^{6}+\cdots$
1875.2.a.g	$1875$	$2$	1875.a	1.a	$1$	$4$	$4$	$14.972$	$\Q(\zeta_{15})^+$	$_{}$	None	None	✓	$1$	$1$	$1$	$-4$	$0$	$5$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-\beta _{2}-\beta _{3})q^{2}-q^{3}+\beta _{1}q^{4}+(\beta _{2}+\cdots)q^{6}+\cdots$
1875.2.a.h	$1875$	$2$	1875.a	1.a	$1$	$4$	$4$	$14.972$	4.4.5125.1	$_{}$	None	None	✓	$1$	$0$	$2$	$4$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(2+\beta _{1}+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots$
1875.2.a.i	$1875$	$2$	1875.a	1.a	$1$	$6$	$6$	$14.972$	6.6.46840000.1	$_{}$	None	None	✓	$1$	$0$	$-1$	$6$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots$
1875.2.a.j	$1875$	$2$	1875.a	1.a	$1$	$6$	$6$	$14.972$	6.6.44400625.1	$_{}$	None	None	✓	$1$	$1$	$0$	$-6$	$0$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1-\beta _{3}+\beta _{4})q^{4}+\beta _{1}q^{6}+\cdots$
1875.2.a.k	$1875$	$2$	1875.a	1.a	$1$	$6$	$6$	$14.972$	6.6.44400625.1	$_{}$	None	None	✓	$1$	$0$	$0$	$6$	$0$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(1-\beta _{3}+\beta _{4})q^{4}+\beta _{1}q^{6}+\cdots$
1875.2.a.l	$1875$	$2$	1875.a	1.a	$1$	$6$	$6$	$14.972$	6.6.46840000.1	$_{}$	None	None	✓	$1$	$0$	$1$	$-6$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots$
1875.2.a.m	$1875$	$2$	1875.a	1.a	$1$	$8$	$8$	$14.972$	8.8.5444000000.1	$_{}$	None	None	✓	$1$	$1$	$-4$	$8$	$0$	$-8$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
1875.2.a.n	$1875$	$2$	1875.a	1.a	$1$	$8$	$8$	$14.972$	8.8.$\cdots$.1	$_{}$	None	None	✓	$1$	$0$	$-1$	$-8$	$0$	$-12$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{4}+\beta _{5})q^{4}+\beta _{1}q^{6}+\cdots$
1875.2.a.o	$1875$	$2$	1875.a	1.a	$1$	$8$	$8$	$14.972$	8.8.$\cdots$.1	$_{}$	None	None	✓	$1$	$0$	$1$	$8$	$0$	$12$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(1+\beta _{4}+\beta _{5})q^{4}+\beta _{1}q^{6}+\cdots$
1875.2.a.p	$1875$	$2$	1875.a	1.a	$1$	$8$	$8$	$14.972$	8.8.5444000000.1	$_{}$	None	None	✓	$1$	$0$	$4$	$-8$	$0$	$8$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(\beta _{1}+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots$
1875.2.b.a	$1875$	$2$	1875.b	5.b	$2$	$4$	$4$	$14.972$	$\Q(i, \sqrt{5})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{2})q^{4}-\beta _{2}q^{6}+\cdots$
1875.2.b.b	$1875$	$2$	1875.b	5.b	$2$	$4$	$4$	$14.972$	$\Q(i, \sqrt{5})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{2}-\beta _{3}q^{3}+q^{4}+q^{6}+(-4\beta _{1}+\cdots)q^{7}+\cdots$
1875.2.b.c	$1875$	$2$	1875.b	5.b	$2$	$8$	$8$	$14.972$	8.0.$\cdots$.12	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{3}q^{3}+(-2+\beta _{5}+\beta _{6}+\cdots)q^{4}+\cdots$
1875.2.b.d	$1875$	$2$	1875.b	5.b	$2$	$8$	$8$	$14.972$	8.0.324000000.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{3}-\beta _{7})q^{2}+\beta _{5}q^{3}-\beta _{4}q^{4}+\cdots$
1875.2.b.e	$1875$	$2$	1875.b	5.b	$2$	$12$	$12$	$14.972$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-\beta _{6}q^{3}+(-2+\beta _{2})q^{4}+\beta _{11}q^{6}+\cdots$
1875.2.b.f	$1875$	$2$	1875.b	5.b	$2$	$12$	$12$	$14.972$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-\beta _{9}q^{3}+(-1+\beta _{4}+\beta _{6}+\cdots)q^{4}+\cdots$
1875.2.b.g	$1875$	$2$	1875.b	5.b	$2$	$16$	$16$	$14.972$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}+\beta _{2})q^{2}+\beta _{11}q^{3}+(-1-\beta _{3}+\cdots)q^{4}+\cdots$
1875.2.b.h	$1875$	$2$	1875.b	5.b	$2$	$16$	$16$	$14.972$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{1}-\beta _{9})q^{2}-\beta _{9}q^{3}+(-1-\beta _{14}+\cdots)q^{4}+\cdots$
1875.4.a.a	$1875$	$4$	1875.a	1.a	$1$	$10$	$10$	$110.629$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-1$	$-30$	$0$	$51$	$-$	$2^{2}\cdot 5$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-3q^{3}+(4+\beta _{2}-\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots$
1875.4.a.b	$1875$	$4$	1875.a	1.a	$1$	$10$	$10$	$110.629$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$-1$	$30$	$0$	$21$	$+$	$5$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+3q^{3}+(2+\beta _{2}-\beta _{3})q^{4}+\cdots$
1875.4.a.c	$1875$	$4$	1875.a	1.a	$1$	$10$	$10$	$110.629$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$1$	$-30$	$0$	$-21$	$+$	$5$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-3q^{3}+(2+\beta _{2}-\beta _{3})q^{4}+\cdots$
1875.4.a.d	$1875$	$4$	1875.a	1.a	$1$	$10$	$10$	$110.629$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$1$	$30$	$0$	$-51$	$-$	$2^{2}\cdot 5$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+3q^{3}+(4+\beta _{2}-\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots$
1875.4.a.e	$1875$	$4$	1875.a	1.a	$1$	$14$	$14$	$110.629$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-8$	$42$	$0$	$-29$	$-$	$2^{2}\cdot 5^{3}$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+3q^{3}+(4-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
1875.4.a.f	$1875$	$4$	1875.a	1.a	$1$	$14$	$14$	$110.629$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$0$	$-42$	$0$	$27$	$+$	$2^{2}\cdot 5^{3}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-3q^{3}+(4+\beta _{2})q^{4}+3\beta _{1}q^{6}+\cdots$
1875.4.a.g	$1875$	$4$	1875.a	1.a	$1$	$14$	$14$	$110.629$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$0$	$42$	$0$	$-27$	$-$	$2^{2}\cdot 5^{3}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+3q^{3}+(4+\beta _{2})q^{4}+3\beta _{1}q^{6}+\cdots$
1875.4.a.h	$1875$	$4$	1875.a	1.a	$1$	$14$	$14$	$110.629$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$8$	$-42$	$0$	$29$	$+$	$2^{2}\cdot 5^{3}$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}-3q^{3}+(4-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
1875.4.a.i	$1875$	$4$	1875.a	1.a	$1$	$16$	$16$	$110.629$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-1$	$48$	$0$	$-52$	$-$	$2^{4}\cdot 5^{6}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+3q^{3}+(2+\beta _{2})q^{4}-3\beta _{1}q^{6}+\cdots$
1875.4.a.j	$1875$	$4$	1875.a	1.a	$1$	$16$	$16$	$110.629$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$1$	$-48$	$0$	$52$	$-$	$2^{4}\cdot 5^{6}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-3q^{3}+(2+\beta _{2})q^{4}-3\beta _{1}q^{6}+\cdots$
1875.4.a.k	$1875$	$4$	1875.a	1.a	$1$	$24$	$24$	$110.629$		$_{}$	None	None	✓	$1$	$0$	$-1$	$-72$	$0$	$-62$	$+$		$\mathrm{SU}(2)$

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.