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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 259 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
252.1.h.a	$252$	$1$	252.h	84.h	$2$	$4$	$4$	$0.126$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-7}) $	None		✓	✓	✓	252.1.h.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{2}q^{7}-\zeta_{8}^{3}q^{8}+\cdots$
252.1.z.a	$252$	$1$	252.z	7.d	$6$	$2$	$1$	$0.126$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	252.1.z.a	$4$	$0$	$0$	$0$	$0$	$1$		$1$		$q-\zeta_{6}^{2}q^{7}+(\zeta_{6}+\zeta_{6}^{2})q^{13}+(-1-\zeta_{6}+\cdots)q^{19}+\cdots$
252.2.a.a	$252$	$2$	252.a	1.a	$1$	$1$	$1$	$2.012$	$\Q$	$_{}$	None	None	✓		✓	✓	84.2.a.a	$1$	$1$	$0$	$0$	$-4$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-4q^{5}-q^{7}-2q^{11}-6q^{13}+4q^{17}+\cdots$
252.2.a.b	$252$	$2$	252.a	1.a	$1$	$1$	$1$	$2.012$	$\Q$	$_{}$	None	None	✓		✓	✓	84.2.a.b	$1$	$0$	$0$	$0$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{7}+6q^{11}+2q^{13}-4q^{19}+6q^{23}+\cdots$
252.2.b.a	$252$	$2$	252.b	28.d	$2$	$2$	$2$	$2.012$	$\Q(\sqrt{-7}) $	$_{}$	$\Q(\sqrt{-7}) $	None					28.2.d.a	$4$	$0$	$1$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+\beta q^{2}+(-2+\beta )q^{4}+(-1+2\beta )q^{7}+\cdots$
252.2.b.b	$252$	$2$	252.b	28.d	$2$	$4$	$4$	$2.012$	$\Q(\sqrt{-2}, \sqrt{7})$	$_{}$	$\Q(\sqrt{-21}) $	None		✓			252.2.b.b	$8$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{2}-2q^{4}-\beta _{2}q^{5}+\beta _{3}q^{7}-2\beta _{1}q^{8}+\cdots$
252.2.b.c	$252$	$2$	252.b	28.d	$2$	$4$	$4$	$2.012$	$\Q(i, \sqrt{7})$	$_{}$	$\Q(\sqrt{-7}) $	None		✓			252.2.b.c	$8$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1+2\beta _{2}+\cdots)q^{7}+\cdots$
252.2.b.d	$252$	$2$	252.b	28.d	$2$	$4$	$4$	$2.012$	4.0.2312.1	$_{}$	None	None					84.2.b.a	$2$	$0$	$1$	$0$	$0$	$-2$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(-\beta _{1}-\beta _{3})q^{5}+\cdots$
252.2.b.e	$252$	$2$	252.b	28.d	$2$	$4$	$4$	$2.012$	4.0.2312.1	$_{}$	None	None					84.2.b.a	$2$	$0$	$1$	$0$	$0$	$2$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{1}+\beta _{3})q^{5}+(1+\cdots)q^{7}+\cdots$
252.2.e.a	$252$	$2$	252.e	12.b	$2$	$12$	$12$	$2.012$	12.0.$\cdots$.1	$_{}$	None	None		✓	✓	✓	252.2.e.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(\beta _{7}-\beta _{9}-\beta _{10}+\cdots)q^{5}+\cdots$
252.2.f.a	$252$	$2$	252.f	21.c	$2$	$4$	$4$	$2.012$	$\Q(\sqrt{-2}, \sqrt{3})$	$_{}$	None	None		✓	✓	✓	252.2.f.a	$4$	$0$	$0$	$0$	$0$	$-4$		$2^{2}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{5}+(-1-\beta _{1})q^{7}-\beta _{2}q^{11}+\cdots$
252.2.i.a	$252$	$2$	252.i	63.h	$3$	$2$	$1$	$2.012$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			252.2.i.a	$2$	$1$	$0$	$-3$	$-2$	$-5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1-\zeta_{6})q^{3}-2\zeta_{6}q^{5}+(-3+\zeta_{6})q^{7}+\cdots$
252.2.i.b	$252$	$2$	252.i	63.h	$3$	$14$	$7$	$2.012$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None		✓	✓		252.2.i.b	$2$	$0$	$0$	$3$	$-2$	$6$		$3^{4}$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}+\beta _{3})q^{3}-\beta _{9}q^{5}+\beta _{10}q^{7}+\cdots$
252.2.j.a	$252$	$2$	252.j	9.c	$3$	$6$	$3$	$2.012$	6.0.309123.1	$_{}$	None	None		✓			252.2.j.a	$2$	$0$	$0$	$-2$	$-1$	$3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{2}+\beta _{4})q^{3}+(-\beta _{1}+\beta _{5})q^{5}+(1+\cdots)q^{7}+\cdots$
252.2.j.b	$252$	$2$	252.j	9.c	$3$	$6$	$3$	$2.012$	6.0.309123.1	$_{}$	None	None		✓			252.2.j.b	$2$	$0$	$0$	$2$	$3$	$-3$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\beta _{3}+\beta _{4})q^{3}+(-\beta _{1}-\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots$
252.2.k.a	$252$	$2$	252.k	7.c	$3$	$2$	$1$	$2.012$	$\Q(\sqrt{-3}) $	$_{}$	None	None					84.2.i.a	$2$	$0$	$0$	$0$	$-2$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2+2\zeta_{6})q^{5}+(-1+3\zeta_{6})q^{7}+\cdots$
252.2.k.b	$252$	$2$	252.k	7.c	$3$	$2$	$1$	$2.012$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		✓			252.2.k.b	$4$	$0$	$0$	$0$	$0$	$5$		$1$	$\mathrm{U}(1)[D_{3}]$	$q+(3-\zeta_{6})q^{7}+5q^{13}+(1-\zeta_{6})q^{19}+\cdots$
252.2.k.c	$252$	$2$	252.k	7.c	$3$	$2$	$1$	$2.012$	$\Q(\sqrt{-3}) $	$_{}$	None	None					28.2.e.a	$2$	$0$	$0$	$0$	$3$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(3-3\zeta_{6})q^{5}+(-1-2\zeta_{6})q^{7}-3\zeta_{6}q^{11}+\cdots$
252.2.l.a	$252$	$2$	252.l	63.g	$3$	$2$	$1$	$2.012$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			252.2.i.a	$2$	$0$	$0$	$0$	$4$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-2\zeta_{6})q^{3}+2q^{5}+(1+2\zeta_{6})q^{7}+\cdots$
252.2.l.b	$252$	$2$	252.l	63.g	$3$	$14$	$7$	$2.012$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None		✓	✓		252.2.i.b	$2$	$0$	$0$	$0$	$4$	$-3$		$3^{4}$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{3}+(-\beta _{5}+\beta _{9})q^{5}+\beta _{6}q^{7}+\cdots$
252.2.n.a	$252$	$2$	252.n	252.n	$6$	$4$	$2$	$2.012$	$\Q(\zeta_{12})$	$_{}$	None	None		✓			252.2.n.a	$4$	$0$	$2$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(-2\zeta_{12}+\cdots)q^{3}+\cdots$
252.2.n.b	$252$	$2$	252.n	252.n	$6$	$84$	$42$	$2.012$		$_{}$	None	None		✓	✓		252.2.n.b	$4$	$0$	$-1$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
252.2.o.a	$252$	$2$	252.o	252.o	$6$	$88$	$44$	$2.012$		$_{}$	None	None		✓	✓	✓	252.2.o.a	$4$	$0$	$-3$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
252.2.t.a	$252$	$2$	252.t	21.g	$6$	$4$	$2$	$2.012$	$\Q(\sqrt{-2}, \sqrt{-3})$	$_{}$	None	None		✓	✓	✓	252.2.t.a	$4$	$0$	$0$	$0$	$0$	$2$		$3$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{2}q^{5}+(2-3\beta _{1})q^{7}+(-\beta _{2}-\beta _{3})q^{11}+\cdots$
252.2.w.a	$252$	$2$	252.w	63.i	$6$	$16$	$8$	$2.012$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓	✓	✓	252.2.w.a	$2$	$0$	$0$	$0$	$0$	$-1$		$3^{4}$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{10}q^{3}+\beta _{7}q^{5}+(\beta _{3}-\beta _{8})q^{7}-\beta _{4}q^{9}+\cdots$
252.2.x.a	$252$	$2$	252.x	63.o	$6$	$16$	$8$	$2.012$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓	✓	✓	252.2.x.a	$4$	$0$	$0$	$0$	$0$	$-1$		$3^{4}$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\beta _{1}-\beta _{8})q^{3}+\beta _{15}q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$
252.2.ba.a	$252$	$2$	252.ba	36.h	$6$	$72$	$36$	$2.012$		$_{}$	None	None		✓	✓	✓	252.2.ba.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
252.2.bb.a	$252$	$2$	252.bb	252.ab	$6$	$88$	$44$	$2.012$		$_{}$	None	None		✓	✓	✓	252.2.o.a	$4$	$0$	$0$	$0$	$-6$	$0$			$\mathrm{SU}(2)[C_{6}]$
252.2.be.a	$252$	$2$	252.be	84.n	$6$	$32$	$16$	$2.012$		$_{}$	None	None		✓	✓	✓	252.2.be.a	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
252.2.bf.a	$252$	$2$	252.bf	28.f	$6$	$4$	$2$	$2.012$	$\Q(\sqrt{-3}, \sqrt{-7})$	$_{}$	None	None		✓			252.2.bf.a	$4$	$0$	$-1$	$0$	$6$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{3}q^{2}+(1+\beta _{1}-\beta _{2})q^{4}+(2-\beta _{2}+\cdots)q^{5}+\cdots$
252.2.bf.b	$252$	$2$	252.bf	28.f	$6$	$4$	$2$	$2.012$	$\Q(\sqrt{-2}, \sqrt{-3})$	$_{}$	None	None		✓			252.2.bf.b	$4$	$0$	$0$	$0$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{3}q^{2}-2q^{4}-2\beta _{1}q^{5}+(1-3\beta _{2}+\cdots)q^{7}+\cdots$
252.2.bf.c	$252$	$2$	252.bf	28.f	$6$	$4$	$2$	$2.012$	$\Q(\sqrt{-2}, \sqrt{-3})$	$_{}$	None	None		✓			252.2.bf.b	$4$	$0$	$0$	$0$	$0$	$2$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{2}+2\beta _{2}q^{4}+(2\beta _{1}-2\beta _{3})q^{5}+\cdots$
252.2.bf.d	$252$	$2$	252.bf	28.f	$6$	$4$	$2$	$2.012$	$\Q(\sqrt{-3}, \sqrt{-7})$	$_{}$	None	None		✓			252.2.bf.a	$4$	$0$	$1$	$0$	$-6$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{3}q^{2}+(1+\beta _{1}-\beta _{2})q^{4}+(-2+\beta _{2}+\cdots)q^{5}+\cdots$
252.2.bf.e	$252$	$2$	252.bf	28.f	$6$	$4$	$2$	$2.012$	$\Q(\zeta_{12})$	$_{}$	None	None					28.2.f.a	$4$	$0$	$2$	$0$	$6$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+2\zeta_{12}q^{4}+\cdots$
252.2.bf.f	$252$	$2$	252.bf	28.f	$6$	$8$	$4$	$2.012$	8.0.562828176.1	$_{}$	None	None					84.2.o.a	$2$	$0$	$-1$	$0$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{5}q^{2}+(-\beta _{4}+\beta _{6}-\beta _{7})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots$
252.2.bf.g	$252$	$2$	252.bf	28.f	$6$	$8$	$4$	$2.012$	8.0.562828176.1	$_{}$	None	None					84.2.o.a	$2$	$0$	$-1$	$0$	$0$	$2$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\beta _{1}-\beta _{5})q^{2}+(-\beta _{2}-\beta _{6}+\beta _{7})q^{4}+\cdots$
252.2.bi.a	$252$	$2$	252.bi	252.ai	$6$	$4$	$2$	$2.012$	$\Q(\zeta_{12})$	$_{}$	None	None		✓			252.2.bi.a	$4$	$0$	$2$	$0$	$-6$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(2\zeta_{12}+\cdots)q^{3}+\cdots$
252.2.bi.b	$252$	$2$	252.bi	252.ai	$6$	$4$	$2$	$2.012$	$\Q(\zeta_{12})$	$_{}$	None	None		✓			252.2.bi.a	$4$	$0$	$2$	$0$	$6$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(-2\zeta_{12}+\cdots)q^{3}+\cdots$
252.2.bi.c	$252$	$2$	252.bi	252.ai	$6$	$80$	$40$	$2.012$		$_{}$	None	None		✓	✓		252.2.bi.c	$8$	$0$	$-6$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
252.2.bj.a	$252$	$2$	252.bj	252.aj	$6$	$4$	$2$	$2.012$	$\Q(\zeta_{12})$	$_{}$	None	None		✓			252.2.n.a	$4$	$1$	$-4$	$0$	$-12$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1+\zeta_{12}^{3})q^{2}+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+\cdots$
252.2.bj.b	$252$	$2$	252.bj	252.aj	$6$	$84$	$42$	$2.012$		$_{}$	None	None		✓	✓		252.2.n.b	$4$	$0$	$2$	$0$	$6$	$0$			$\mathrm{SU}(2)[C_{6}]$
252.2.bm.a	$252$	$2$	252.bm	63.s	$6$	$16$	$8$	$2.012$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓	✓	✓	252.2.w.a	$2$	$0$	$0$	$0$	$0$	$-1$		$3^{4}$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\beta _{5}-\beta _{10})q^{3}+(\beta _{7}-\beta _{11})q^{5}+\cdots$
252.3.c.a	$252$	$3$	252.c	3.b	$2$	$4$	$4$	$6.867$	$\Q(\sqrt{-2}, \sqrt{7})$	$_{}$	None	None		✓	✓	✓	252.3.c.a	$2$	$0$	$0$	$0$	$0$	$0$		$2\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{5}+\beta _{3}q^{7}+(2\beta _{1}+\beta _{2})q^{11}+\cdots$
252.3.d.a	$252$	$3$	252.d	7.b	$2$	$2$	$2$	$6.867$	$\Q(\sqrt{-3}) $	$_{}$	None	None					84.3.d.a	$2$	$0$	$0$	$0$	$0$	$-14$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta q^{5}-7 q^{7}-18 q^{11}+3\beta q^{13}+\cdots$
252.3.d.b	$252$	$3$	252.d	7.b	$2$	$2$	$2$	$6.867$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		✓			252.3.d.b	$4$	$0$	$0$	$0$	$0$	$-2$		$2^{3}$	$\mathrm{U}(1)[D_{2}]$	$q+(-\beta-1)q^{7}-2\beta q^{13}-4\beta q^{19}+\cdots$
252.3.d.c	$252$	$3$	252.d	7.b	$2$	$2$	$2$	$6.867$	$\Q(\sqrt{-6}) $	$_{}$	None	None					28.3.b.a	$2$	$0$	$0$	$0$	$0$	$10$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{5}+(5-\beta )q^{7}+6q^{11}+\beta q^{13}+\cdots$
252.3.g.a	$252$	$3$	252.g	4.b	$2$	$6$	$6$	$6.867$	6.0.1539727.2	$_{}$	None	None					28.3.c.a	$2$	$0$	$1$	$0$	$4$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}+(-\beta _{1}-\beta _{4})q^{4}+(1-\beta _{2}+\cdots)q^{5}+\cdots$
252.3.g.b	$252$	$3$	252.g	4.b	$2$	$12$	$12$	$6.867$	12.0.$\cdots$.1	$_{}$	None	None					84.3.g.a	$2$	$0$	$-2$	$0$	$-8$	$0$		$2^{19}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{2}-\beta _{5}q^{4}+(-\beta _{3}+\beta _{8})q^{5}+\cdots$
252.3.g.c	$252$	$3$	252.g	4.b	$2$	$12$	$12$	$6.867$	12.0.$\cdots$.1	$_{}$	None	None		✓			252.3.g.c	$4$	$0$	$0$	$0$	$0$	$0$		$2^{16}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}+(-1-\beta _{6})q^{4}+(-\beta _{2}+\beta _{7}+\cdots)q^{5}+\cdots$
252.3.h.a	$252$	$3$	252.h	84.h	$2$	$8$	$8$	$6.867$	8.0.157351936.1	$_{}$	$\Q(\sqrt{-7}) $	None		✓			252.3.h.a	$8$	$0$	$0$	$0$	$0$	$0$		$2\cdot 3^{4}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{7}q^{2}+(\beta _{3}+\beta _{6})q^{4}+7\beta _{3}q^{7}+(\beta _{2}+\cdots)q^{8}+\cdots$

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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.