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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	CM	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	CM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
6003.2.a.i	$6003$	$2$	6003.a	1.a	$1$	$7$	$7$	$47.934$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$1$	$1$	$0$	$5$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{2}+(1+\beta _{4}+\beta _{5})q^{4}+(1-\beta _{3}+\cdots)q^{5}+\cdots$
6003.2.a.j	$6003$	$2$	6003.a	1.a	$1$	$7$	$7$	$47.934$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$1$	$3$	$0$	$3$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+\beta _{4}q^{5}+(-1+\cdots)q^{7}+\cdots$
6003.2.a.k	$6003$	$2$	6003.a	1.a	$1$	$10$	$10$	$47.934$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$1$	$-3$	$0$	$-6$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{3}q^{2}+(2+\beta _{6})q^{4}+(-1-\beta _{4})q^{5}+\cdots$
6003.2.a.l	$6003$	$2$	6003.a	1.a	$1$	$10$	$10$	$47.934$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$0$	$3$	$0$	$10$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1+\beta _{7})q^{5}+\cdots$
6004.2.a.d	$6004$	$2$	6004.a	1.a	$1$	$8$	$8$	$47.942$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$0$	$0$	$0$	$4$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{5}-\beta _{4}q^{7}-3q^{9}+(-1+\beta _{1}+\cdots)q^{11}+\cdots$
6006.2.a.cf	$6006$	$2$	6006.a	1.a	$1$	$6$	$6$	$47.958$	6.6.72306708.1	None	✓	$1$	$0$	$6$	$-6$	$0$	$6$	$-$	$2^{4}$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+\beta _{2}q^{5}-q^{6}+q^{7}+\cdots$
6006.2.a.cg	$6006$	$2$	6006.a	1.a	$1$	$7$	$7$	$47.958$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$0$	$7$	$7$	$2$	$7$	$-$	$2^{6}$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-\beta _{1}q^{5}+q^{6}+q^{7}+\cdots$
6012.2.a.g	$6012$	$2$	6012.a	1.a	$1$	$7$	$7$	$48.006$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$1$	$0$	$0$	$2$	$-12$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-\beta _{1}+\beta _{2}-\beta _{3})q^{5}+(-2-\beta _{1}+\cdots)q^{7}+\cdots$
6012.2.a.h	$6012$	$2$	6012.a	1.a	$1$	$9$	$9$	$48.006$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$1$	$0$	$0$	$-9$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{5}-\beta _{6}q^{7}+(-1+\beta _{5}+\cdots)q^{11}+\cdots$
6012.2.a.i	$6012$	$2$	6012.a	1.a	$1$	$9$	$9$	$48.006$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$0$	$0$	$0$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{5}+(-\beta _{3}-\beta _{6})q^{7}+(1+\beta _{7}+\cdots)q^{11}+\cdots$
6012.2.a.j	$6012$	$2$	6012.a	1.a	$1$	$10$	$10$	$48.006$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$1$	$0$	$0$	$-6$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{3})q^{5}+\beta _{1}q^{7}+(-\beta _{2}+\beta _{3}+\cdots)q^{11}+\cdots$
6012.2.a.k	$6012$	$2$	6012.a	1.a	$1$	$10$	$10$	$48.006$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$0$	$0$	$0$	$6$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{3})q^{5}+\beta _{1}q^{7}+(\beta _{2}-\beta _{3}-\beta _{6}+\cdots)q^{11}+\cdots$
6016.2.a.e	$6016$	$2$	6016.a	1.a	$1$	$8$	$8$	$48.038$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$1$	$0$	$-2$	$-4$	$6$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(-1-\beta _{2})q^{5}+(1+\beta _{6})q^{7}+\cdots$
6016.2.a.f	$6016$	$2$	6016.a	1.a	$1$	$8$	$8$	$48.038$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$1$	$0$	$-2$	$4$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(1+\beta _{2})q^{5}+(-1-\beta _{6})q^{7}+\cdots$
6016.2.a.g	$6016$	$2$	6016.a	1.a	$1$	$8$	$8$	$48.038$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$1$	$0$	$2$	$-4$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(-1-\beta _{2})q^{5}+(-1-\beta _{6}+\cdots)q^{7}+\cdots$
6016.2.a.h	$6016$	$2$	6016.a	1.a	$1$	$8$	$8$	$48.038$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$0$	$0$	$2$	$4$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(1+\beta _{2})q^{5}+(1+\beta _{6})q^{7}+\cdots$
6016.2.a.i	$6016$	$2$	6016.a	1.a	$1$	$10$	$10$	$48.038$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$1$	$0$	$-2$	$-4$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+\beta _{6}q^{5}-\beta _{4}q^{7}+\beta _{2}q^{9}+\cdots$
6016.2.a.j	$6016$	$2$	6016.a	1.a	$1$	$10$	$10$	$48.038$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$1$	$0$	$-2$	$4$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}-\beta _{6}q^{5}+\beta _{4}q^{7}+\beta _{2}q^{9}+\cdots$
6016.2.a.k	$6016$	$2$	6016.a	1.a	$1$	$10$	$10$	$48.038$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$1$	$0$	$2$	$-4$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+\beta _{6}q^{5}+\beta _{4}q^{7}+\beta _{2}q^{9}+\cdots$
6016.2.a.l	$6016$	$2$	6016.a	1.a	$1$	$10$	$10$	$48.038$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$0$	$0$	$2$	$4$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}-\beta _{6}q^{5}-\beta _{4}q^{7}+\beta _{2}q^{9}+\cdots$
6018.2.a.q	$6018$	$2$	6018.a	1.a	$1$	$6$	$6$	$48.054$	6.6.5173625.1	None	✓	$1$	$1$	$6$	$-6$	$-5$	$-1$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+(-1+\beta _{1})q^{5}-q^{6}+\cdots$
6018.2.a.r	$6018$	$2$	6018.a	1.a	$1$	$6$	$6$	$48.054$	6.6.18461324.1	None	✓	$1$	$1$	$6$	$6$	$-3$	$-7$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-\beta _{1}q^{5}+q^{6}+(-2+\cdots)q^{7}+\cdots$
6018.2.a.s	$6018$	$2$	6018.a	1.a	$1$	$8$	$8$	$48.054$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$0$	$-8$	$-8$	$-1$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+\beta _{4}q^{5}+q^{6}+(1+\cdots)q^{7}+\cdots$
6018.2.a.t	$6018$	$2$	6018.a	1.a	$1$	$8$	$8$	$48.054$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$1$	$-8$	$8$	$-6$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+(-1-\beta _{4})q^{5}-q^{6}+\cdots$
6018.2.a.u	$6018$	$2$	6018.a	1.a	$1$	$9$	$9$	$48.054$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$1$	$-9$	$-9$	$2$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-\beta _{6}q^{5}+q^{6}+(-1+\cdots)q^{7}+\cdots$
6018.2.a.v	$6018$	$2$	6018.a	1.a	$1$	$9$	$9$	$48.054$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$1$	$-9$	$-9$	$6$	$-11$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+(1-\beta _{1})q^{5}+q^{6}+\cdots$
6018.2.a.w	$6018$	$2$	6018.a	1.a	$1$	$9$	$9$	$48.054$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$0$	$-9$	$9$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+\beta _{1}q^{5}-q^{6}-\beta _{4}q^{7}+\cdots$
6018.2.a.x	$6018$	$2$	6018.a	1.a	$1$	$10$	$10$	$48.054$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$0$	$-10$	$-10$	$1$	$10$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+\beta _{1}q^{5}+q^{6}+(1+\cdots)q^{7}+\cdots$
6018.2.a.y	$6018$	$2$	6018.a	1.a	$1$	$10$	$10$	$48.054$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$1$	$-10$	$10$	$-2$	$-6$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-\beta _{1}q^{5}-q^{6}+(-1+\cdots)q^{7}+\cdots$
6020.2.a.d	$6020$	$2$	6020.a	1.a	$1$	$7$	$7$	$48.070$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$1$	$0$	$-3$	$7$	$7$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{4}q^{3}+q^{5}+q^{7}+(-1-\beta _{2}+\beta _{3}+\cdots)q^{9}+\cdots$
6020.2.a.e	$6020$	$2$	6020.a	1.a	$1$	$7$	$7$	$48.070$	7.7.187391161.1	None	✓	$1$	$1$	$0$	$-1$	$-7$	$-7$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{5}q^{3}-q^{5}-q^{7}+(-1+\beta _{1}-\beta _{3}+\cdots)q^{9}+\cdots$
6020.2.a.f	$6020$	$2$	6020.a	1.a	$1$	$8$	$8$	$48.070$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$1$	$0$	$-5$	$-8$	$8$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}-q^{5}+q^{7}+(2-\beta _{1}+\cdots)q^{9}+\cdots$
6020.2.a.g	$6020$	$2$	6020.a	1.a	$1$	$9$	$9$	$48.070$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$1$	$0$	$0$	$9$	$-9$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+q^{5}-q^{7}+(1+\beta _{2})q^{9}+(-\beta _{3}+\cdots)q^{11}+\cdots$
6021.2.a.l	$6021$	$2$	6021.a	1.a	$1$	$10$	$10$	$48.078$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$2$	$0$	$0$	$0$	$0$	$2$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(2+\beta _{3}+\beta _{6}+\beta _{8})q^{4}+(\beta _{4}+\cdots)q^{5}+\cdots$
6024.2.a.k	$6024$	$2$	6024.a	1.a	$1$	$8$	$8$	$48.102$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$1$	$0$	$8$	$-5$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-\beta _{1}-\beta _{2})q^{5}+(-\beta _{3}-\beta _{7})q^{7}+\cdots$
6025.2.a.f	$6025$	$2$	6025.a	1.a	$1$	$7$	$7$	$48.110$	7.7.31056073.1	None	✓	$1$	$1$	$4$	$3$	$0$	$7$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}-\beta _{6}q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
6027.2.a.y	$6027$	$2$	6027.a	1.a	$1$	$7$	$7$	$48.126$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$0$	$4$	$-7$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}-q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots$
6027.2.a.z	$6027$	$2$	6027.a	1.a	$1$	$8$	$8$	$48.126$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$1$	$-2$	$-8$	$2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{5}q^{5}+\cdots$
6027.2.a.ba	$6027$	$2$	6027.a	1.a	$1$	$8$	$8$	$48.126$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$1$	$-2$	$8$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{5}q^{5}+\cdots$
6027.2.a.bb	$6027$	$2$	6027.a	1.a	$1$	$8$	$8$	$48.126$	8.8.7457527933.1	None	✓	$1$	$1$	$1$	$-8$	$-7$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1}-\beta _{2})q^{2}-q^{3}+(2+\beta _{6})q^{4}+\cdots$
6027.2.a.bc	$6027$	$2$	6027.a	1.a	$1$	$8$	$8$	$48.126$	8.8.7457527933.1	None	✓	$1$	$0$	$1$	$8$	$7$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1}-\beta _{2})q^{2}+q^{3}+(2+\beta _{6})q^{4}+\cdots$
6027.2.a.bd	$6027$	$2$	6027.a	1.a	$1$	$10$	$10$	$48.126$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$0$	$4$	$-10$	$-6$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+(-1-\beta _{4}+\cdots)q^{5}+\cdots$
6027.2.a.be	$6027$	$2$	6027.a	1.a	$1$	$10$	$10$	$48.126$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$0$	$4$	$10$	$6$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+(1+\beta _{4}+\cdots)q^{5}+\cdots$
6030.2.a.bx	$6030$	$2$	6030.a	1.a	$1$	$8$	$8$	$48.150$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$0$	$-8$	$0$	$-8$	$4$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}+(1-\beta _{6})q^{7}-q^{8}+\cdots$
6030.2.a.by	$6030$	$2$	6030.a	1.a	$1$	$8$	$8$	$48.150$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$0$	$8$	$0$	$8$	$4$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+(1-\beta _{6})q^{7}+q^{8}+\cdots$
6032.2.a.s	$6032$	$2$	6032.a	1.a	$1$	$6$	$6$	$48.166$	6.6.226964648.1	None	✓	$1$	$0$	$0$	$-2$	$3$	$1$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{4}q^{3}+(1+\beta _{3})q^{5}+\beta _{1}q^{7}+(1-\beta _{5})q^{9}+\cdots$
6032.2.a.t	$6032$	$2$	6032.a	1.a	$1$	$6$	$6$	$48.166$	6.6.11341289.1	None	✓	$1$	$1$	$0$	$3$	$-5$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(-\beta _{1}+\beta _{5})q^{5}+(1-\beta _{1}+\cdots)q^{7}+\cdots$
6032.2.a.u	$6032$	$2$	6032.a	1.a	$1$	$7$	$7$	$48.166$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$1$	$0$	$-2$	$-2$	$-7$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{3}+(-1+\beta _{2}-\beta _{6})q^{5}+(-1+\cdots)q^{7}+\cdots$
6032.2.a.v	$6032$	$2$	6032.a	1.a	$1$	$9$	$9$	$48.166$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$1$	$0$	$-2$	$-4$	$3$	$+$	$3$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+\beta _{6}q^{5}+\beta _{3}q^{7}+(\beta _{3}-\beta _{7}+\cdots)q^{9}+\cdots$
6032.2.a.w	$6032$	$2$	6032.a	1.a	$1$	$9$	$9$	$48.166$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$0$	$0$	$-2$	$-2$	$1$	$-$	$2^{5}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}-\beta _{5}q^{5}-\beta _{4}q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots$

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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.