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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 181 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
324.1.d.a	$324$	$1$	324.d	4.b	$2$	$1$	$1$	$0.162$	$\Q$	$D_{3}$	$\Q(\sqrt{-1})$	None	✓	✓			324.1.d.a	$2$	$0$	$-1$	$0$	$1$	$0$		$1$		$q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}-q^{13}+\cdots$
324.1.d.b	$324$	$1$	324.d	4.b	$2$	$1$	$1$	$0.162$	$\Q$	$D_{3}$	$\Q(\sqrt{-1})$	None	✓	✓			324.1.d.a	$2$	$0$	$1$	$0$	$-1$	$0$		$1$		$q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}-q^{13}+\cdots$
324.1.f.a	$324$	$1$	324.f	36.f	$6$	$2$	$1$	$0.162$	$\Q(\sqrt{-3})$	$D_{3}$	$\Q(\sqrt{-1})$	None		✓			324.1.d.a	$4$	$0$	$-1$	$0$	$1$	$0$		$1$		$q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+q^{8}-q^{10}+\cdots$
324.1.f.b	$324$	$1$	324.f	36.f	$6$	$2$	$1$	$0.162$	$\Q(\sqrt{-3})$	$D_{3}$	$\Q(\sqrt{-1})$	None		✓			324.1.d.a	$4$	$0$	$1$	$0$	$-1$	$0$		$1$		$q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-\zeta_{6}q^{5}-q^{8}-q^{10}+\cdots$
324.1.g.a	$324$	$1$	324.g	9.d	$6$	$2$	$1$	$0.162$	$\Q(\sqrt{-3})$	$D_{3}$	$\Q(\sqrt{-3})$	None			✓	✓	108.1.c.a	$4$	$0$	$0$	$0$	$0$	$1$		$1$		$q-\zeta_{6}^{2}q^{7}+\zeta_{6}q^{13}-q^{19}+\zeta_{6}^{2}q^{25}+\cdots$
324.2.a.a	$324$	$2$	324.a	1.a	$1$	$1$	$1$	$2.587$	$\Q$	$_{}$	None	None	✓		✓	✓	36.2.e.a	$1$	$1$	$0$	$0$	$-3$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{5}-q^{7}-3q^{11}-q^{13}-6q^{17}+\cdots$
324.2.a.b	$324$	$2$	324.a	1.a	$1$	$1$	$1$	$2.587$	$\Q$	$_{}$	None	None	✓	✓			324.2.a.b	$1$	$0$	$0$	$0$	$-3$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{5}+2q^{7}+6q^{11}+5q^{13}+3q^{17}+\cdots$
324.2.a.c	$324$	$2$	324.a	1.a	$1$	$1$	$1$	$2.587$	$\Q$	$_{}$	None	None	✓				36.2.e.a	$1$	$0$	$0$	$0$	$3$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{5}-q^{7}+3q^{11}-q^{13}+6q^{17}+\cdots$
324.2.a.d	$324$	$2$	324.a	1.a	$1$	$1$	$1$	$2.587$	$\Q$	$_{}$	None	None	✓	✓			324.2.a.b	$1$	$0$	$0$	$0$	$3$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{5}+2q^{7}-6q^{11}+5q^{13}-3q^{17}+\cdots$
324.2.b.a	$324$	$2$	324.b	12.b	$2$	$4$	$4$	$2.587$	$\Q(\sqrt{-2}, \sqrt{3})$	$_{}$	$\Q(\sqrt{-1})$	None		✓			324.2.b.a	$4$	$0$	$0$	$0$	$0$	$0$		$3^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{2}-2q^{4}-\beta _{2}q^{5}-2\beta _{1}q^{8}+\cdots$
324.2.b.b	$324$	$2$	324.b	12.b	$2$	$8$	$8$	$2.587$	8.0.170772624.1	$_{}$	None	None					36.2.h.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{2}-\beta _{2}q^{4}+(\beta _{3}-\beta _{4}+\beta _{7})q^{5}+\cdots$
324.2.b.c	$324$	$2$	324.b	12.b	$2$	$8$	$8$	$2.587$	8.0.5780865024.3	$_{}$	None	None		✓			324.2.b.c	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(\beta _{3}+\beta _{5})q^{5}+\cdots$
324.2.e.a	$324$	$2$	324.e	9.c	$3$	$2$	$1$	$2.587$	$\Q(\sqrt{-3})$	$_{}$	None	None		✓			324.2.a.b	$2$	$0$	$0$	$0$	$-3$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-3\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}+(6-6\zeta_{6})q^{11}+\cdots$
324.2.e.b	$324$	$2$	324.e	9.c	$3$	$2$	$1$	$2.587$	$\Q(\sqrt{-3})$	$_{}$	$\Q(\sqrt{-3})$	None					108.2.a.a	$4$	$0$	$0$	$0$	$0$	$-5$		$1$	$\mathrm{U}(1)[D_{3}]$	$q+(-5+5\zeta_{6})q^{7}+7\zeta_{6}q^{13}-q^{19}+\cdots$
324.2.e.c	$324$	$2$	324.e	9.c	$3$	$2$	$1$	$2.587$	$\Q(\sqrt{-3})$	$_{}$	$\Q(\sqrt{-3})$	None					36.2.a.a	$4$	$0$	$0$	$0$	$0$	$4$		$1$	$\mathrm{U}(1)[D_{3}]$	$q+(4-4\zeta_{6})q^{7}-2\zeta_{6}q^{13}+8q^{19}+\cdots$
324.2.e.d	$324$	$2$	324.e	9.c	$3$	$2$	$1$	$2.587$	$\Q(\sqrt{-3})$	$_{}$	None	None		✓			324.2.a.b	$2$	$0$	$0$	$0$	$3$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+3\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}+(-6+6\zeta_{6})q^{11}+\cdots$
324.2.h.a	$324$	$2$	324.h	36.h	$6$	$4$	$2$	$2.587$	$\Q(\sqrt{-2}, \sqrt{-3})$	$_{}$	None	None					108.2.b.b	$4$	$0$	$0$	$0$	$0$	$6$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{3}q^{2}-2q^{4}+2\beta _{1}q^{5}+(2-\beta _{2}+\cdots)q^{7}+\cdots$
324.2.h.b	$324$	$2$	324.h	36.h	$6$	$4$	$2$	$2.587$	$\Q(\sqrt{-2}, \sqrt{-3})$	$_{}$	None	None					108.2.b.b	$4$	$0$	$0$	$0$	$0$	$-6$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{2}+2\beta _{2}q^{4}+2\beta _{1}q^{5}+(-2+\cdots)q^{7}+\cdots$
324.2.h.c	$324$	$2$	324.h	36.h	$6$	$4$	$2$	$2.587$	$\Q(\sqrt{-2}, \sqrt{-3})$	$_{}$	$\Q(\sqrt{-1})$	None					36.2.b.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+(\beta _{1}-\beta _{3})q^{2}+(2-2\beta _{2})q^{4}+\beta _{1}q^{5}+\cdots$
324.2.h.d	$324$	$2$	324.h	36.h	$6$	$8$	$4$	$2.587$	8.0.12960000.1	$_{}$	None	None					108.2.b.a	$8$	$0$	$0$	$0$	$0$	$0$		$3^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\beta _{3}+\beta _{7})q^{2}+(-\beta _{1}-\beta _{2})q^{4}+\cdots$
324.2.h.e	$324$	$2$	324.h	36.h	$6$	$8$	$4$	$2.587$	$\Q(\zeta_{24})$	$_{}$	$\Q(\sqrt{-1})$	None		✓			324.2.b.a	$8$	$0$	$0$	$0$	$0$	$0$		$3^{6}$	$\mathrm{U}(1)[D_{6}]$	$q-\beta_{3} q^{2}+(-2\beta_1+2)q^{4}+(-\beta_{6}+\beta_{5})q^{5}+\cdots$
324.2.h.f	$324$	$2$	324.h	36.h	$6$	$16$	$8$	$2.587$	16.0. $\cdots$ .1	$_{}$	None	None		✓	✓		324.2.b.c	$8$	$0$	$0$	$0$	$0$	$0$		$3^{4}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{15}q^{2}+(-1+\beta _{8}-\beta _{9}-\beta _{11}+\cdots)q^{4}+\cdots$
324.2.i.a	$324$	$2$	324.i	27.e	$9$	$18$	$3$	$2.587$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	$_{}$	None	None			✓	✓	108.2.i.a	$2$	$0$	$0$	$0$	$-3$	$0$		$3^{5}$	$\mathrm{SU}(2)[C_{9}]$	$q+(-\beta _{1}-\beta _{3})q^{5}+(-\beta _{8}-\beta _{9}-\beta _{10}+\cdots)q^{7}+\cdots$
324.2.l.a	$324$	$2$	324.l	108.l	$18$	$96$	$16$	$2.587$		$_{}$	None	None			✓	✓	108.2.l.a	$4$	$0$	$6$	$0$	$12$	$0$			$\mathrm{SU}(2)[C_{18}]$
324.2.m.a	$324$	$2$	324.m	81.g	$27$	$162$	$9$	$2.587$		$_{}$	None	None		✓	✓	✓	324.2.m.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{27}]$
324.2.p.a	$324$	$2$	324.p	324.p	$54$	$936$	$52$	$2.587$		$_{}$	None	None		✓	✓	✓	324.2.p.a	$4$	$0$	$-18$	$0$	$-36$	$0$			$\mathrm{SU}(2)[C_{54}]$
324.3.c.a	$324$	$3$	324.c	3.b	$2$	$4$	$4$	$8.828$	$\Q(\sqrt{-2}, \sqrt{3})$	$_{}$	None	None		✓			324.3.c.a	$2$	$0$	$0$	$0$	$0$	$-4$		$3^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{5}+(-1+\beta _{2})q^{7}-\beta _{3}q^{11}+\cdots$
324.3.c.b	$324$	$3$	324.c	3.b	$2$	$4$	$4$	$8.828$	$\Q(\sqrt{-3}, \sqrt{-11})$	$_{}$	None	None					36.3.g.a	$2$	$0$	$0$	$0$	$0$	$2$		$2^{2}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{5}+(1-\beta _{2})q^{7}+(-\beta _{1}+\beta _{3})q^{11}+\cdots$
324.3.d.a	$324$	$3$	324.d	4.b	$2$	$2$	$2$	$8.828$	$\Q(\sqrt{3})$	$_{}$	$\Q(\sqrt{-1})$	None	✓	✓			324.3.d.a	$2$	$0$	$-4$	$0$	$-8$	$0$		$3$	$\mathrm{U}(1)[D_{2}]$	$q-2q^{2}+4q^{4}+(-4+\beta )q^{5}-8q^{8}+\cdots$
324.3.d.b	$324$	$3$	324.d	4.b	$2$	$2$	$2$	$8.828$	$\Q(\sqrt{-3})$	$_{}$	None	None					36.3.f.a	$2$	$0$	$-2$	$0$	$8$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta-1)q^{2}+(2\beta-2)q^{4}+4 q^{5}+\cdots$
324.3.d.c	$324$	$3$	324.d	4.b	$2$	$2$	$2$	$8.828$	$\Q(\sqrt{-3})$	$_{}$	None	None					36.3.f.a	$2$	$0$	$2$	$0$	$-8$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta+1)q^{2}+(2\beta-2)q^{4}-4 q^{5}+\cdots$
324.3.d.d	$324$	$3$	324.d	4.b	$2$	$2$	$2$	$8.828$	$\Q(\sqrt{3})$	$_{}$	$\Q(\sqrt{-1})$	None	✓	✓			324.3.d.a	$2$	$0$	$4$	$0$	$8$	$0$		$3$	$\mathrm{U}(1)[D_{2}]$	$q+2q^{2}+4q^{4}+(4+\beta )q^{5}+8q^{8}+(8+\cdots)q^{10}+\cdots$
324.3.d.e	$324$	$3$	324.d	4.b	$2$	$6$	$6$	$8.828$	6.0.3636603.2	$_{}$	None	None		✓			324.3.d.e	$2$	$0$	$-1$	$0$	$-2$	$0$		$2^{6}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{2}-\beta _{1}q^{4}+(-\beta _{1}+\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots$
324.3.d.f	$324$	$3$	324.d	4.b	$2$	$6$	$6$	$8.828$	6.0.3636603.2	$_{}$	None	None		✓			324.3.d.e	$2$	$0$	$1$	$0$	$2$	$0$		$2^{6}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}-\beta _{2}q^{4}+(-\beta _{1}+\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots$
324.3.d.g	$324$	$3$	324.d	4.b	$2$	$8$	$8$	$8.828$	8.0. $\cdots$ .1	$_{}$	None	None					36.3.f.c	$2$	$0$	$-3$	$0$	$6$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2}+\beta _{5}-\beta _{6})q^{4}+\cdots$
324.3.d.h	$324$	$3$	324.d	4.b	$2$	$8$	$8$	$8.828$	8.0. $\cdots$ .4	$_{}$	None	None		✓			324.3.d.h	$4$	$0$	$0$	$0$	$0$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{2}+(-1-\beta _{6})q^{4}+(-2\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$
324.3.d.i	$324$	$3$	324.d	4.b	$2$	$8$	$8$	$8.828$	8.0. $\cdots$ .1	$_{}$	None	None					36.3.f.c	$2$	$0$	$3$	$0$	$-6$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{6}q^{2}+(-\beta _{1}+\beta _{2}+\beta _{4}+\beta _{6})q^{4}+\cdots$
324.3.f.a	$324$	$3$	324.f	36.f	$6$	$2$	$1$	$8.828$	$\Q(\sqrt{-3})$	$_{}$	None	None					12.3.d.a	$2$	$0$	$-4$	$0$	$-2$	$12$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q-2q^{2}+4q^{4}+(-2+2\zeta_{6})q^{5}+(8+\cdots)q^{7}+\cdots$
324.3.f.b	$324$	$3$	324.f	36.f	$6$	$2$	$1$	$8.828$	$\Q(\sqrt{-3})$	$_{}$	None	None					108.3.d.a	$2$	$0$	$-4$	$0$	$7$	$-15$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q-2q^{2}+4q^{4}+(7-7\zeta_{6})q^{5}+(-10+\cdots)q^{7}+\cdots$
324.3.f.c	$324$	$3$	324.f	36.f	$6$	$2$	$1$	$8.828$	$\Q(\sqrt{-3})$	$_{}$	None	None					108.3.d.a	$2$	$0$	$-2$	$0$	$-7$	$15$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-2+2\zeta_{6})q^{2}-4\zeta_{6}q^{4}+(-7+7\zeta_{6})q^{5}+\cdots$
324.3.f.d	$324$	$3$	324.f	36.f	$6$	$2$	$1$	$8.828$	$\Q(\sqrt{-3})$	$_{}$	None	None					12.3.d.a	$2$	$0$	$-2$	$0$	$2$	$-12$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-2+2\zeta_{6})q^{2}-4\zeta_{6}q^{4}+(2-2\zeta_{6})q^{5}+\cdots$
324.3.f.e	$324$	$3$	324.f	36.f	$6$	$2$	$1$	$8.828$	$\Q(\sqrt{-3})$	$_{}$	$\Q(\sqrt{-1})$	None					36.3.d.a	$4$	$0$	$-2$	$0$	$8$	$0$		$1$	$\mathrm{U}(1)[D_{6}]$	$q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+(8-8\zeta_{6})q^{5}+\cdots$
324.3.f.f	$324$	$3$	324.f	36.f	$6$	$2$	$1$	$8.828$	$\Q(\sqrt{-3})$	$_{}$	$\Q(\sqrt{-1})$	None					36.3.d.a	$4$	$0$	$2$	$0$	$-8$	$0$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+(-8+8\zeta_{6})q^{5}+\cdots$
324.3.f.g	$324$	$3$	324.f	36.f	$6$	$2$	$1$	$8.828$	$\Q(\sqrt{-3})$	$_{}$	None	None					12.3.d.a	$2$	$0$	$2$	$0$	$-2$	$-12$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(2-2\zeta_{6})q^{2}-4\zeta_{6}q^{4}+(-2+2\zeta_{6})q^{5}+\cdots$
324.3.f.h	$324$	$3$	324.f	36.f	$6$	$2$	$1$	$8.828$	$\Q(\sqrt{-3})$	$_{}$	None	None					108.3.d.a	$2$	$0$	$2$	$0$	$7$	$15$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(2-2\zeta_{6})q^{2}-4\zeta_{6}q^{4}+(7-7\zeta_{6})q^{5}+\cdots$
324.3.f.i	$324$	$3$	324.f	36.f	$6$	$2$	$1$	$8.828$	$\Q(\sqrt{-3})$	$_{}$	None	None					108.3.d.a	$2$	$0$	$4$	$0$	$-7$	$-15$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+2q^{2}+4q^{4}+(-7+7\zeta_{6})q^{5}+(-10+\cdots)q^{7}+\cdots$
324.3.f.j	$324$	$3$	324.f	36.f	$6$	$2$	$1$	$8.828$	$\Q(\sqrt{-3})$	$_{}$	None	None					12.3.d.a	$2$	$0$	$4$	$0$	$2$	$12$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+2q^{2}+4q^{4}+(2-2\zeta_{6})q^{5}+(8-4\zeta_{6})q^{7}+\cdots$
324.3.f.k	$324$	$3$	324.f	36.f	$6$	$4$	$2$	$8.828$	$\Q(\zeta_{12})$	$_{}$	$\Q(\sqrt{-1})$	None		✓			324.3.d.a	$4$	$0$	$-4$	$0$	$-8$	$0$		$3^{3}$	$\mathrm{U}(1)[D_{6}]$	$q+(2\beta_1-2)q^{2}-4\beta_1 q^{4}+(-\beta_{2}-4\beta_1)q^{5}+\cdots$
324.3.f.l	$324$	$3$	324.f	36.f	$6$	$4$	$2$	$8.828$	$\Q(\sqrt{-3}, \sqrt{13})$	$_{}$	None	None					108.3.d.c	$4$	$0$	$-3$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1+\beta _{1})q^{2}+(-\beta _{1}+3\beta _{2}+\beta _{3})q^{4}+\cdots$
324.3.f.m	$324$	$3$	324.f	36.f	$6$	$4$	$2$	$8.828$	$\Q(\sqrt{-3}, \sqrt{13})$	$_{}$	None	None					108.3.d.c	$4$	$0$	$3$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(1-\beta _{1})q^{2}+(-\beta _{1}+3\beta _{2}+\beta _{3})q^{4}+\cdots$

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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.