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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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Results (1-50 of 1802 matches)

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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
4002.2.a.y	$4002$	$2$	4002.a	1.a	$1$	$3$	$3$	$31.956$	3.3.1772.1	None	✓	$1$	$0$	$-3$	$-3$	$-1$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-\beta _{1}q^{5}+q^{6}+(2+\cdots)q^{7}+\cdots$
4002.2.a.z	$4002$	$2$	4002.a	1.a	$1$	$3$	$3$	$31.956$	3.3.316.1	None	✓	$1$	$1$	$3$	$-3$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-\beta _{2}q^{5}-q^{6}+(-2\beta _{1}+\cdots)q^{7}+\cdots$
4005.2.a.i	$4005$	$2$	4005.a	1.a	$1$	$3$	$3$	$31.980$	$\Q(\zeta_{18})^+$	None	✓	$1$	$0$	$0$	$0$	$-3$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}-q^{5}+(1+\beta _{2})q^{7}+\cdots$
4005.2.a.j	$4005$	$2$	4005.a	1.a	$1$	$3$	$3$	$31.980$	$\Q(\zeta_{14})^+$	None	✓	$1$	$1$	$2$	$0$	$-3$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{4}-q^{5}+\cdots$
4008.2.a.e	$4008$	$2$	4008.a	1.a	$1$	$3$	$3$	$32.004$	3.3.148.1	None	✓	$1$	$1$	$0$	$-3$	$6$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(2-\beta _{2})q^{5}+(-2+2\beta _{1})q^{7}+\cdots$
4009.2.a.b	$4009$	$2$	4009.a	1.a	$1$	$3$	$3$	$32.012$	$\Q(\zeta_{14})^+$	None	✓	$1$	$1$	$2$	$-2$	$-3$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(-1+\beta _{1})q^{3}+(1-2\beta _{1}+\cdots)q^{4}+\cdots$
4011.2.a.e	$4011$	$2$	4011.a	1.a	$1$	$3$	$3$	$32.028$	3.3.229.1	None	✓	$1$	$0$	$0$	$-3$	$2$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{2})q^{5}+\cdots$
4012.2.a.f	$4012$	$2$	4012.a	1.a	$1$	$3$	$3$	$32.036$	3.3.321.1	None	✓	$1$	$1$	$0$	$-3$	$1$	$3$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{3}-\beta _{1}q^{5}+q^{7}-2q^{9}-2q^{11}+\cdots$
4014.2.a.m	$4014$	$2$	4014.a	1.a	$1$	$3$	$3$	$32.052$	$\Q(\zeta_{18})^+$	None	✓	$1$	$1$	$-3$	$0$	$3$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(1+\beta _{1})q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots$
4014.2.a.n	$4014$	$2$	4014.a	1.a	$1$	$3$	$3$	$32.052$	$\Q(\zeta_{14})^+$	None	✓	$1$	$0$	$-3$	$0$	$7$	$-9$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(2+\beta _{1})q^{5}+(-3+\beta _{1}+\cdots)q^{7}+\cdots$
4014.2.a.o	$4014$	$2$	4014.a	1.a	$1$	$3$	$3$	$32.052$	3.3.257.1	None	✓	$1$	$0$	$3$	$0$	$1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+\beta _{1}q^{5}+(\beta _{1}+\beta _{2})q^{7}+\cdots$
4014.2.a.p	$4014$	$2$	4014.a	1.a	$1$	$3$	$3$	$32.052$	3.3.473.1	None	✓	$1$	$0$	$3$	$0$	$1$	$9$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+\beta _{2}q^{5}+(3-\beta _{1})q^{7}+q^{8}+\cdots$
4018.2.a.bd	$4018$	$2$	4018.a	1.a	$1$	$3$	$3$	$32.084$	3.3.404.1	None	✓	$1$	$1$	$-3$	$0$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(\beta _{1}-\beta _{2})q^{3}+q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots$
4018.2.a.be	$4018$	$2$	4018.a	1.a	$1$	$3$	$3$	$32.084$	3.3.404.1	None	✓	$1$	$0$	$-3$	$0$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-\beta _{1}+\beta _{2})q^{3}+q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots$
4018.2.a.bf	$4018$	$2$	4018.a	1.a	$1$	$3$	$3$	$32.084$	3.3.321.1	None	✓	$1$	$1$	$3$	$-3$	$4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+(1-\beta _{2})q^{5}-q^{6}+\cdots$
4018.2.a.bg	$4018$	$2$	4018.a	1.a	$1$	$3$	$3$	$32.084$	3.3.568.1	None	✓	$1$	$0$	$3$	$-1$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{2}q^{3}+q^{4}-\beta _{1}q^{5}+\beta _{2}q^{6}+\cdots$
4018.2.a.bh	$4018$	$2$	4018.a	1.a	$1$	$3$	$3$	$32.084$	3.3.321.1	None	✓	$1$	$1$	$3$	$3$	$-4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+(-1+\beta _{2})q^{5}+q^{6}+\cdots$
4022.2.a.b	$4022$	$2$	4022.a	1.a	$1$	$3$	$3$	$32.116$	3.3.169.1	None	✓	$1$	$1$	$3$	$-3$	$1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+\beta _{1}q^{5}-q^{6}+(-1+\cdots)q^{7}+\cdots$
4025.2.a.j	$4025$	$2$	4025.a	1.a	$1$	$3$	$3$	$32.140$	3.3.148.1	None	✓	$1$	$0$	$1$	$-2$	$0$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+(\beta _{1}+\beta _{2})q^{2}+(-1+\beta _{1})q^{3}+(1+2\beta _{1}+\cdots)q^{4}+\cdots$
4025.2.a.k	$4025$	$2$	4025.a	1.a	$1$	$3$	$3$	$32.140$	$\Q(\zeta_{14})^+$	None	✓	$1$	$1$	$2$	$0$	$0$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(-1+\beta _{1}-2\beta _{2})q^{3}+\cdots$
4026.2.a.n	$4026$	$2$	4026.a	1.a	$1$	$3$	$3$	$32.148$	$\Q(\zeta_{18})^+$	None	✓	$1$	$1$	$-3$	$3$	$-3$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+(-1-\beta _{1})q^{5}-q^{6}+\cdots$
4026.2.a.o	$4026$	$2$	4026.a	1.a	$1$	$3$	$3$	$32.148$	3.3.1129.1	None	✓	$1$	$1$	$3$	$-3$	$-3$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+(-1+\beta _{1})q^{5}-q^{6}+\cdots$
4026.2.a.p	$4026$	$2$	4026.a	1.a	$1$	$3$	$3$	$32.148$	$\Q(\zeta_{14})^+$	None	✓	$1$	$1$	$3$	$3$	$-5$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+(-2-\beta _{2})q^{5}+q^{6}+\cdots$
4029.2.a.d	$4029$	$2$	4029.a	1.a	$1$	$3$	$3$	$32.172$	3.3.148.1	None	✓	$1$	$1$	$0$	$-3$	$-5$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}-q^{3}+(1-\beta _{1}-\beta _{2})q^{4}+(-2+\cdots)q^{5}+\cdots$
4038.2.a.f	$4038$	$2$	4038.a	1.a	$1$	$3$	$3$	$32.244$	3.3.169.1	None	✓	$1$	$1$	$-3$	$-3$	$-1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+(1-2\beta _{1}+2\beta _{2})q^{5}+\cdots$
4038.2.a.g	$4038$	$2$	4038.a	1.a	$1$	$3$	$3$	$32.244$	3.3.148.1	None	✓	$1$	$1$	$-3$	$-3$	$0$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-\beta _{2}q^{5}+q^{6}+(1+\cdots)q^{7}+\cdots$
4038.2.a.h	$4038$	$2$	4038.a	1.a	$1$	$3$	$3$	$32.244$	3.3.169.1	None	✓	$1$	$1$	$-3$	$-3$	$3$	$-7$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+(-3+\cdots)q^{7}+\cdots$
4038.2.a.i	$4038$	$2$	4038.a	1.a	$1$	$3$	$3$	$32.244$	3.3.148.1	None	✓	$1$	$1$	$-3$	$3$	$-6$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+(-2-\beta _{2})q^{5}-q^{6}+\cdots$
4038.2.a.j	$4038$	$2$	4038.a	1.a	$1$	$3$	$3$	$32.244$	$\Q(\zeta_{18})^+$	None	✓	$1$	$1$	$3$	$3$	$-3$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+(-1+\cdots)q^{7}+\cdots$
4038.2.a.k	$4038$	$2$	4038.a	1.a	$1$	$3$	$3$	$32.244$	3.3.473.1	None	✓	$1$	$1$	$3$	$3$	$-3$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+(-1+\cdots)q^{7}+\cdots$
4041.2.a.c	$4041$	$2$	4041.a	1.a	$1$	$3$	$3$	$32.268$	$\Q(\zeta_{14})^+$	None	✓	$1$	$0$	$1$	$0$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(-\beta _{1}-\beta _{2})q^{5}+\cdots$
4042.2.a.d	$4042$	$2$	4042.a	1.a	$1$	$3$	$3$	$32.276$	3.3.257.1	None	✓	$1$	$1$	$3$	$0$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-1+\beta _{1}+\beta _{2})q^{7}+q^{8}+\cdots$
4046.2.a.x	$4046$	$2$	4046.a	1.a	$1$	$3$	$3$	$32.307$	3.3.148.1	None	✓	$1$	$1$	$-3$	$-2$	$2$	$-3$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(1-\beta _{2})q^{5}+\cdots$
4046.2.a.y	$4046$	$2$	4046.a	1.a	$1$	$3$	$3$	$32.307$	$\Q(\zeta_{18})^+$	None	✓	$1$	$1$	$-3$	$0$	$0$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{2}q^{5}-\beta _{1}q^{6}+\cdots$
4046.2.a.z	$4046$	$2$	4046.a	1.a	$1$	$3$	$3$	$32.307$	$\Q(\zeta_{18})^+$	None	✓	$1$	$1$	$-3$	$0$	$0$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{2}q^{5}+\beta _{1}q^{6}+\cdots$
4046.2.a.ba	$4046$	$2$	4046.a	1.a	$1$	$3$	$3$	$32.307$	3.3.148.1	None	✓	$1$	$0$	$-3$	$2$	$-2$	$3$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+(1-\beta _{1})q^{3}+q^{4}+(-1+\beta _{2})q^{5}+\cdots$
4046.2.a.bb	$4046$	$2$	4046.a	1.a	$1$	$3$	$3$	$32.307$	$\Q(\zeta_{18})^+$	None	✓	$1$	$1$	$3$	$0$	$0$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta _{1}q^{3}+q^{4}+(2\beta _{1}-\beta _{2})q^{5}+\cdots$
4046.2.a.bc	$4046$	$2$	4046.a	1.a	$1$	$3$	$3$	$32.307$	$\Q(\zeta_{18})^+$	None	✓	$1$	$1$	$3$	$0$	$0$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{1}q^{3}+q^{4}+(-2\beta _{1}+\beta _{2})q^{5}+\cdots$
4047.2.a.c	$4047$	$2$	4047.a	1.a	$1$	$3$	$3$	$32.315$	3.3.148.1	None	✓	$1$	$1$	$2$	$-3$	$-1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}-q^{3}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots$
4048.2.a.n	$4048$	$2$	4048.a	1.a	$1$	$3$	$3$	$32.323$	3.3.473.1	None	✓	$1$	$1$	$0$	$-3$	$-7$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+(-2-\beta _{2})q^{5}+2\beta _{1}q^{7}+\cdots$
4048.2.a.o	$4048$	$2$	4048.a	1.a	$1$	$3$	$3$	$32.323$	$\Q(\zeta_{18})^+$	None	✓	$1$	$1$	$0$	$-3$	$3$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+(1+\beta _{1}-\beta _{2})q^{5}+\cdots$
4048.2.a.p	$4048$	$2$	4048.a	1.a	$1$	$3$	$3$	$32.323$	$\Q(\zeta_{18})^+$	None	✓	$1$	$1$	$0$	$-3$	$3$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-2\beta _{1}+\beta _{2})q^{3}+(1+\beta _{1}-\beta _{2})q^{5}+\cdots$
4048.2.a.q	$4048$	$2$	4048.a	1.a	$1$	$3$	$3$	$32.323$	3.3.321.1	None	✓	$1$	$1$	$0$	$-1$	$-3$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{3}+(-1+\beta _{1}+\beta _{2})q^{5}-\beta _{2}q^{7}+\cdots$
4048.2.a.r	$4048$	$2$	4048.a	1.a	$1$	$3$	$3$	$32.323$	3.3.257.1	None	✓	$1$	$1$	$0$	$1$	$-1$	$5$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{2})q^{5}+(2-\beta _{1}+\cdots)q^{7}+\cdots$
4048.2.a.s	$4048$	$2$	4048.a	1.a	$1$	$3$	$3$	$32.323$	3.3.169.1	None	✓	$1$	$1$	$0$	$1$	$1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1}+\beta _{2})q^{3}+\beta _{1}q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots$
4048.2.a.t	$4048$	$2$	4048.a	1.a	$1$	$3$	$3$	$32.323$	3.3.257.1	None	✓	$1$	$1$	$0$	$3$	$-1$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{3}-\beta _{1}q^{5}+(1-\beta _{2})q^{7}+\cdots$
4048.2.a.u	$4048$	$2$	4048.a	1.a	$1$	$3$	$3$	$32.323$	3.3.169.1	None	✓	$1$	$0$	$0$	$5$	$-5$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+(2-\beta _{1})q^{3}+(-2-\beta _{2})q^{5}+(\beta _{1}-2\beta _{2})q^{7}+\cdots$
4055.2.a.a	$4055$	$2$	4055.a	1.a	$1$	$3$	$3$	$32.379$	$\Q(\zeta_{14})^+$	None	✓	$1$	$1$	$1$	$-1$	$3$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{2}q^{3}+\beta _{2}q^{4}+q^{5}+(1+\cdots)q^{6}+\cdots$
4056.2.a.x	$4056$	$2$	4056.a	1.a	$1$	$3$	$3$	$32.387$	$\Q(\zeta_{14})^+$	None	✓	$1$	$1$	$0$	$-3$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(-1-\beta _{2})q^{5}+(-1+2\beta _{1}+\cdots)q^{7}+\cdots$
4056.2.a.y	$4056$	$2$	4056.a	1.a	$1$	$3$	$3$	$32.387$	3.3.837.1	None	✓	$1$	$1$	$0$	$-3$	$0$	$-3$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{3}+\beta _{2}q^{5}+(-1+\beta _{1})q^{7}+q^{9}+\cdots$

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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.