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Level	Weight	Analytic conductor	Analytic rank	Dim.

Bad $p$	Char.	Primitive character	Character order	Is maximal/largest

Coefficient field	Self-twists	CM/RM discriminant	Inner twist count	Is self-dual

Coefficient ring index	Coefficient ring gens.	Is twist minimal	Projective image

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Results (1-50 of 254 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
468.1.e.a	$468$	$1$	468.e	52.b	$2$	$1$	$1$	$0.234$	$\Q$	$D_{2}$	$\Q(\sqrt{-39}) $, $\Q(\sqrt{-13}) $	$\Q(\sqrt{3}) $	✓	✓			468.1.e.a	$4$	$0$	$-1$	$0$	$0$	$0$		$1$		$q-q^{2}+q^{4}-q^{8}+2q^{11}-q^{13}+q^{16}+\cdots$
468.1.e.b	$468$	$1$	468.e	52.b	$2$	$1$	$1$	$0.234$	$\Q$	$D_{2}$	$\Q(\sqrt{-39}) $, $\Q(\sqrt{-13}) $	$\Q(\sqrt{3}) $	✓	✓			468.1.e.a	$4$	$0$	$1$	$0$	$0$	$0$		$1$		$q+q^{2}+q^{4}+q^{8}-2q^{11}-q^{13}+q^{16}+\cdots$
468.1.e.c	$468$	$1$	468.e	52.b	$2$	$2$	$2$	$0.234$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-39}) $	$\Q(\sqrt{39}) $		✓	✓		468.1.e.c	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-i q^{2}-q^{4}+2 i q^{5}+i q^{8}+2 q^{10}+\cdots$
468.1.o.a	$468$	$1$	468.o	156.l	$4$	$4$	$2$	$0.234$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	468.1.o.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{8}+q^{13}+\cdots$
468.1.q.a	$468$	$1$	468.q	52.i	$6$	$4$	$2$	$0.234$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	468.1.q.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{3}q^{5}-\zeta_{12}^{3}q^{8}+\cdots$
468.1.r.a	$468$	$1$	468.r	39.i	$6$	$4$	$2$	$0.234$	$\Q(\sqrt{-2}, \sqrt{-3})$	$S_{4}$	None	None		✓	✓	✓	468.1.r.a	$4$	$0$	$0$	$0$	$0$	$-2$		$1$		$q-\beta _{3}q^{5}+(-1+\beta _{2})q^{7}+(\beta _{1}-\beta _{3})q^{11}+\cdots$
468.1.v.a	$468$	$1$	468.v	468.v	$6$	$4$	$2$	$0.234$	$\Q(\zeta_{12})$	$A_{4}$	None	None		✓	✓	✓	468.1.v.a	$4$	$0$	$0$	$0$	$2$	$0$		$1$		$q-\zeta_{12}q^{2}+\zeta_{12}q^{3}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{4}q^{5}+\cdots$
468.1.y.a	$468$	$1$	468.y	468.y	$6$	$4$	$2$	$0.234$	$\Q(\zeta_{12})$	$A_{4}$	None	None		✓	✓	✓	468.1.v.a	$4$	$0$	$0$	$0$	$2$	$0$		$1$		$q-\zeta_{12}^{3}q^{2}+\zeta_{12}^{3}q^{3}-q^{4}-\zeta_{12}^{4}q^{5}+\cdots$
468.1.z.a	$468$	$1$	468.z	117.n	$6$	$2$	$1$	$0.234$	$\Q(\sqrt{-3}) $	$D_{6}$	None	$\Q(\sqrt{13}) $		✓	✓	✓	468.1.z.a	$4$	$0$	$0$	$1$	$0$	$0$		$1$		$q+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{9}+\zeta_{6}q^{13}+(-\zeta_{6}+\cdots)q^{17}+\cdots$
468.1.br.a	$468$	$1$	468.br	52.j	$6$	$2$	$1$	$0.234$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-1}) $	None			✓	✓	52.1.j.a	$4$	$0$	$1$	$0$	$2$	$0$		$1$		$q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+q^{5}-q^{8}+\zeta_{6}q^{10}+\cdots$
468.1.bx.a	$468$	$1$	468.bx	156.v	$12$	$8$	$2$	$0.234$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	468.1.bx.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+(-\zeta_{24}-\zeta_{24}^{5}+\cdots)q^{5}+\cdots$
468.1.cd.a	$468$	$1$	468.cd	13.f	$12$	$4$	$1$	$0.234$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	468.1.cd.a	$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q+(\zeta_{12}^{2}+\zeta_{12}^{3})q^{7}-\zeta_{12}q^{13}+(\zeta_{12}+\cdots)q^{19}+\cdots$
468.2.a.a	$468$	$2$	468.a	1.a	$1$	$1$	$1$	$3.737$	$\Q$	$_{}$	None	None	✓	✓			468.2.a.a	$1$	$0$	$0$	$0$	$-4$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-4q^{5}+4q^{7}+4q^{11}-q^{13}+8q^{23}+\cdots$
468.2.a.b	$468$	$2$	468.a	1.a	$1$	$1$	$1$	$3.737$	$\Q$	$_{}$	None	None	✓		✓	✓	52.2.a.a	$1$	$1$	$0$	$0$	$-2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-2q^{7}+2q^{11}-q^{13}-6q^{17}+\cdots$
468.2.a.c	$468$	$2$	468.a	1.a	$1$	$1$	$1$	$3.737$	$\Q$	$_{}$	None	None	✓				156.2.a.b	$1$	$0$	$0$	$0$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{7}+q^{13}+6q^{17}+2q^{19}-5q^{25}+\cdots$
468.2.a.d	$468$	$2$	468.a	1.a	$1$	$1$	$1$	$3.737$	$\Q$	$_{}$	None	None	✓				156.2.a.a	$1$	$0$	$0$	$0$	$4$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{5}-2q^{7}+4q^{11}+q^{13}-2q^{17}+\cdots$
468.2.a.e	$468$	$2$	468.a	1.a	$1$	$1$	$1$	$3.737$	$\Q$	$_{}$	None	None	✓	✓			468.2.a.a	$1$	$0$	$0$	$0$	$4$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{5}+4q^{7}-4q^{11}-q^{13}-8q^{23}+\cdots$
468.2.b.a	$468$	$2$	468.b	13.b	$2$	$2$	$2$	$3.737$	$\Q(\sqrt{-3}) $	$_{}$	None	None					156.2.b.a	$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta q^{5}-\beta q^{11}+(\beta-1)q^{13}-6 q^{17}+\cdots$
468.2.b.b	$468$	$2$	468.b	13.b	$2$	$2$	$2$	$3.737$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		✓			468.2.b.b	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta q^{7}+(-\beta-1)q^{13}-\beta q^{19}+5 q^{25}+\cdots$
468.2.b.c	$468$	$2$	468.b	13.b	$2$	$2$	$2$	$3.737$	$\Q(\sqrt{-1}) $	$_{}$	None	None					156.2.b.b	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{5}-2\beta q^{7}-3\beta q^{11}+(\beta+3)q^{13}+\cdots$
468.2.c.a	$468$	$2$	468.c	12.b	$2$	$4$	$4$	$3.737$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			468.2.c.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta_{3} q^{2}+2 q^{4}-2\beta_{2} q^{5}+\beta_1 q^{7}+\cdots$
468.2.c.b	$468$	$2$	468.c	12.b	$2$	$8$	$8$	$3.737$	8.0.157351936.1	$_{}$	None	None		✓			468.2.c.b	$4$	$0$	$0$	$0$	$0$	$0$		$2\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-\beta _{2}+\beta _{4})q^{4}-\beta _{5}q^{5}+\cdots$
468.2.c.c	$468$	$2$	468.c	12.b	$2$	$12$	$12$	$3.737$	12.0.$\cdots$.1	$_{}$	None	None		✓	✓		468.2.c.c	$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{3}+\beta _{10})q^{5}+(\beta _{6}+\cdots)q^{7}+\cdots$
468.2.h.a	$468$	$2$	468.h	156.h	$2$	$4$	$4$	$3.737$	$\Q(\sqrt{-2}, \sqrt{13})$	$_{}$	$\Q(\sqrt{-13}) $	None		✓			468.2.h.a	$4$	$0$	$0$	$0$	$0$	$-4$		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{2}q^{2}-2q^{4}+(-1-\beta _{3})q^{7}+2\beta _{2}q^{8}+\cdots$
468.2.h.b	$468$	$2$	468.h	156.h	$2$	$4$	$4$	$3.737$	$\Q(\sqrt{-2}, \sqrt{13})$	$_{}$	$\Q(\sqrt{-13}) $	None		✓			468.2.h.a	$4$	$0$	$0$	$0$	$0$	$4$		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{2}q^{2}-2q^{4}+(1+\beta _{3})q^{7}+2\beta _{2}q^{8}+\cdots$
468.2.h.c	$468$	$2$	468.h	156.h	$2$	$4$	$4$	$3.737$	$\Q(\zeta_{8})$	$_{}$	$\Q(\sqrt{-1}) $	None		✓			468.2.h.c	$8$	$0$	$0$	$0$	$0$	$0$		$2\cdot 3^{2}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta_{2} q^{2}+2 q^{4}-\beta_{2} q^{5}-2\beta_{2} q^{8}+\cdots$
468.2.h.d	$468$	$2$	468.h	156.h	$2$	$16$	$16$	$3.737$	16.0.$\cdots$.1	$_{}$	None	None		✓	✓		468.2.h.d	$8$	$0$	$0$	$0$	$0$	$0$		$2^{11}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{7}q^{2}+(-\beta _{3}-\beta _{8})q^{4}+(-\beta _{6}-\beta _{12}+\cdots)q^{5}+\cdots$
468.2.i.a	$468$	$2$	468.i	9.c	$3$	$2$	$1$	$3.737$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			468.2.i.a	$2$	$0$	$0$	$3$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{7}+(3-3\zeta_{6})q^{9}+\cdots$
468.2.i.b	$468$	$2$	468.i	9.c	$3$	$10$	$5$	$3.737$	10.0.$\cdots$.1	$_{}$	None	None		✓			468.2.i.b	$2$	$0$	$0$	$-3$	$7$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{3}+(2-\beta _{1}-\beta _{2}+2\beta _{4}-\beta _{5}+\cdots)q^{5}+\cdots$
468.2.i.c	$468$	$2$	468.i	9.c	$3$	$12$	$6$	$3.737$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		✓	✓		468.2.i.c	$2$	$0$	$0$	$0$	$-1$	$0$		$3^{3}$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{5}-\beta _{7})q^{3}+\beta _{1}q^{5}+(\beta _{2}+\beta _{4}+\cdots)q^{7}+\cdots$
468.2.j.a	$468$	$2$	468.j	117.h	$3$	$28$	$14$	$3.737$		$_{}$	None	None		✓	✓	✓	468.2.j.a	$2$	$0$	$0$	$0$	$0$	$2$			$\mathrm{SU}(2)[C_{3}]$
468.2.k.a	$468$	$2$	468.k	117.f	$3$	$28$	$14$	$3.737$		$_{}$	None	None		✓	✓	✓	468.2.j.a	$2$	$0$	$0$	$0$	$0$	$-4$			$\mathrm{SU}(2)[C_{3}]$
468.2.l.a	$468$	$2$	468.l	13.c	$3$	$2$	$1$	$3.737$	$\Q(\sqrt{-3}) $	$_{}$	None	None					52.2.e.a	$2$	$0$	$0$	$0$	$-4$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-2q^{5}-\zeta_{6}q^{7}+(-5+5\zeta_{6})q^{11}+\cdots$
468.2.l.b	$468$	$2$	468.l	13.c	$3$	$2$	$1$	$3.737$	$\Q(\sqrt{-3}) $	$_{}$	None	None					156.2.i.a	$2$	$0$	$0$	$0$	$-4$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-2q^{5}-\zeta_{6}q^{7}+(2-2\zeta_{6})q^{11}+(4+\cdots)q^{13}+\cdots$
468.2.l.c	$468$	$2$	468.l	13.c	$3$	$2$	$1$	$3.737$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		✓			468.2.l.c	$4$	$0$	$0$	$0$	$0$	$-5$		$1$	$\mathrm{U}(1)[D_{3}]$	$q-5\zeta_{6}q^{7}+(-4+\zeta_{6})q^{13}-8\zeta_{6}q^{19}+\cdots$
468.2.l.d	$468$	$2$	468.l	13.c	$3$	$2$	$1$	$3.737$	$\Q(\sqrt{-3}) $	$_{}$	None	None					52.2.e.b	$2$	$0$	$0$	$0$	$6$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+3q^{5}+4\zeta_{6}q^{7}+(-3-\zeta_{6})q^{13}+\cdots$
468.2.l.e	$468$	$2$	468.l	13.c	$3$	$4$	$2$	$3.737$	$\Q(\sqrt{-3}, \sqrt{7})$	$_{}$	None	None		✓	✓		468.2.l.e	$4$	$0$	$0$	$0$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{3}q^{5}+(2+2\beta _{2})q^{7}+(-2\beta _{1}-2\beta _{3})q^{11}+\cdots$
468.2.n.a	$468$	$2$	468.n	52.f	$4$	$2$	$1$	$3.737$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None		✓			468.2.n.a	$4$	$1$	$-2$	$0$	$-6$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(-i-1)q^{2}+2 i q^{4}+(-3 i-3)q^{5}+\cdots$
468.2.n.b	$468$	$2$	468.n	52.f	$4$	$2$	$1$	$3.737$	$\Q(\sqrt{-1}) $	$_{}$	None	None					156.2.k.c	$2$	$1$	$-2$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(i-1)q^{2}-2 i q^{4}+(-2 i-2)q^{5}+\cdots$
468.2.n.c	$468$	$2$	468.n	52.f	$4$	$2$	$1$	$3.737$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None					52.2.f.a	$4$	$0$	$-2$	$0$	$6$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(-i-1)q^{2}+2 i q^{4}+(3 i+3)q^{5}+\cdots$
468.2.n.d	$468$	$2$	468.n	52.f	$4$	$2$	$1$	$3.737$	$\Q(\sqrt{-1}) $	$_{}$	None	None					156.2.k.c	$2$	$0$	$2$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-i+1)q^{2}-2 i q^{4}+(-2 i-2)q^{5}+\cdots$
468.2.n.e	$468$	$2$	468.n	52.f	$4$	$2$	$1$	$3.737$	$\Q(\sqrt{-1}) $	$_{}$	None	None					156.2.k.a	$2$	$0$	$2$	$0$	$2$	$-4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(i+1)q^{2}+2 i q^{4}+(i+1)q^{5}+\cdots$
468.2.n.f	$468$	$2$	468.n	52.f	$4$	$2$	$1$	$3.737$	$\Q(\sqrt{-1}) $	$_{}$	None	None					156.2.k.a	$2$	$0$	$2$	$0$	$2$	$4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(i+1)q^{2}+2 i q^{4}+(i+1)q^{5}+\cdots$
468.2.n.g	$468$	$2$	468.n	52.f	$4$	$2$	$1$	$3.737$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None		✓			468.2.n.a	$4$	$0$	$2$	$0$	$6$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(i+1)q^{2}+2 i q^{4}+(3 i+3)q^{5}+\cdots$
468.2.n.h	$468$	$2$	468.n	52.f	$4$	$8$	$4$	$3.737$	8.0.157351936.1	$_{}$	None	None		✓			468.2.n.h	$8$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{1}q^{2}+(\beta _{4}+\beta _{6})q^{4}+(\beta _{1}-\beta _{3})q^{5}+\cdots$
468.2.n.i	$468$	$2$	468.n	52.f	$4$	$8$	$4$	$3.737$	8.0.18939904.2	$_{}$	None	None					52.2.f.b	$4$	$0$	$4$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(1-\beta _{2}+\beta _{5}-\beta _{7})q^{2}+(-\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots$
468.2.n.j	$468$	$2$	468.n	52.f	$4$	$10$	$5$	$3.737$	10.0.$\cdots$.1	$_{}$	None	None					156.2.k.e	$2$	$0$	$-4$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{3}q^{2}+(-\beta _{5}-\beta _{7})q^{4}+(-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$
468.2.n.k	$468$	$2$	468.n	52.f	$4$	$10$	$5$	$3.737$	10.0.$\cdots$.1	$_{}$	None	None					156.2.k.e	$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{1}q^{2}+(\beta _{7}+\beta _{8})q^{4}+(-\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots$
468.2.n.l	$468$	$2$	468.n	52.f	$4$	$16$	$8$	$3.737$	16.0.$\cdots$.7	$_{}$	None	None		✓	✓		468.2.n.l	$8$	$0$	$0$	$0$	$0$	$0$		$2^{12}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{11}q^{2}+\beta _{7}q^{4}-\beta _{2}q^{5}+(\beta _{7}-\beta _{9}+\cdots)q^{7}+\cdots$
468.2.p.a	$468$	$2$	468.p	39.f	$4$	$12$	$6$	$3.737$	12.0.$\cdots$.1	$_{}$	None	None		✓	✓	✓	468.2.p.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{7}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{8}q^{5}-\beta _{4}q^{7}+(\beta _{6}+\beta _{9})q^{11}+(-1+\cdots)q^{13}+\cdots$

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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.