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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 315 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
240.1.bm.a	$240$	$1$	240.bm	240.am	$4$	$4$	$2$	$0.120$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-15}) $	None		✓	✓	✓	240.1.bm.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}q^{2}+\zeta_{8}q^{3}+\zeta_{8}^{2}q^{4}+\zeta_{8}^{3}q^{5}+\cdots$
240.2.a.a	$240$	$2$	240.a	1.a	$1$	$1$	$1$	$1.916$	$\Q$	$_{}$	None	None	✓		✓	✓	120.2.a.a	$1$	$1$	$0$	$-1$	$-1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-4q^{7}+q^{9}-6q^{13}+q^{15}+\cdots$
240.2.a.b	$240$	$2$	240.a	1.a	$1$	$1$	$1$	$1.916$	$\Q$	$_{}$	None	None	✓		✓	✓	30.2.a.a	$1$	$0$	$0$	$-1$	$-1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+4q^{7}+q^{9}+2q^{13}+q^{15}+\cdots$
240.2.a.c	$240$	$2$	240.a	1.a	$1$	$1$	$1$	$1.916$	$\Q$	$_{}$	None	None	✓		✓	✓	120.2.a.b	$1$	$0$	$0$	$-1$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+q^{9}+4q^{11}+6q^{13}+\cdots$
240.2.a.d	$240$	$2$	240.a	1.a	$1$	$1$	$1$	$1.916$	$\Q$	$_{}$	None	None	✓		✓	✓	15.2.a.a	$1$	$0$	$0$	$1$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots$
240.2.f.a	$240$	$2$	240.f	5.b	$2$	$2$	$2$	$1.916$	$\Q(\sqrt{-1}) $	$_{}$	None	None					30.2.c.a	$2$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{3}+(i-2)q^{5}+2 i q^{7}-q^{9}+\cdots$
240.2.f.b	$240$	$2$	240.f	5.b	$2$	$2$	$2$	$1.916$	$\Q(\sqrt{-1}) $	$_{}$	None	None					60.2.d.a	$2$	$0$	$0$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{3}+(-2 i+1)q^{5}-4 i q^{7}+\cdots$
240.2.f.c	$240$	$2$	240.f	5.b	$2$	$2$	$2$	$1.916$	$\Q(\sqrt{-1}) $	$_{}$	None	None					120.2.f.a	$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{3}+(i+2)q^{5}+2 i q^{7}-q^{9}+\cdots$
240.2.h.a	$240$	$2$	240.h	12.b	$2$	$4$	$4$	$1.916$	$\Q(i, \sqrt{6})$	$_{}$	None	None		✓			240.2.h.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}-\beta _{2}q^{5}+(\beta _{1}+\beta _{3})q^{7}+3\beta _{2}q^{9}+\cdots$
240.2.h.b	$240$	$2$	240.h	12.b	$2$	$4$	$4$	$1.916$	$\Q(\zeta_{12})$	$_{}$	None	None		✓			240.2.h.b	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta_{3} q^{3}-\beta_1 q^{5}+2\beta_{2} q^{7}+3 q^{9}+\cdots$
240.2.o.a	$240$	$2$	240.o	60.h	$2$	$4$	$4$	$1.916$	$\Q(\sqrt{2}, \sqrt{-5})$	$_{}$	$\Q(\sqrt{-5}) $	None		✓			240.2.o.a	$8$	$0$	$0$	$0$	$0$	$0$		$3$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{3}-\beta _{2}q^{5}+(\beta _{1}-\beta _{3})q^{7}+(-2+\cdots)q^{9}+\cdots$
240.2.o.b	$240$	$2$	240.o	60.h	$2$	$8$	$8$	$1.916$	$\Q(\zeta_{24})$	$_{}$	None	None		✓	✓		240.2.o.b	$8$	$0$	$0$	$0$	$0$	$0$		$2^{10}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta_{2} q^{3}-\beta_1 q^{5}+(\beta_{4}-\beta_1+1)q^{9}+\cdots$
240.2.s.a	$240$	$2$	240.s	16.e	$4$	$4$	$2$	$1.916$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			240.2.s.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-\zeta_{8}+\zeta_{8}^{3})q^{2}+\zeta_{8}^{3}q^{3}+2q^{4}+\cdots$
240.2.s.b	$240$	$2$	240.s	16.e	$4$	$8$	$4$	$1.916$	8.0.18939904.2	$_{}$	None	None		✓			240.2.s.b	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+(-\beta _{4}+\beta _{5})q^{2}-\beta _{6}q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots$
240.2.s.c	$240$	$2$	240.s	16.e	$4$	$20$	$10$	$1.916$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None		✓	✓		240.2.s.c	$2$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{2}-\beta _{4}q^{3}+\beta _{2}q^{4}+\beta _{5}q^{5}+\cdots$
240.2.t.a	$240$	$2$	240.t	240.t	$4$	$8$	$4$	$1.916$	$\Q(i, \sqrt{6}, \sqrt{10})$	$_{}$	$\Q(\sqrt{-15}) $	None		✓			240.2.t.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+\beta _{1}q^{2}+(\beta _{1}-\beta _{5})q^{3}+\beta _{2}q^{4}+(-\beta _{4}+\cdots)q^{5}+\cdots$
240.2.t.b	$240$	$2$	240.t	240.t	$4$	$80$	$40$	$1.916$		$_{}$	None	None		✓	✓		240.2.t.b	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
240.2.v.a	$240$	$2$	240.v	15.e	$4$	$4$	$2$	$1.916$	$\Q(\zeta_{8})$	$_{}$	None	None					120.2.r.b	$2$	$0$	$0$	$-4$	$4$	$4$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+(\beta_{2}-1)q^{3}+(2\beta_1+1)q^{5}+(-\beta_{3}-\beta_{2}+\beta_1+1)q^{7}+\cdots$
240.2.v.b	$240$	$2$	240.v	15.e	$4$	$4$	$2$	$1.916$	$\Q(i, \sqrt{5})$	$_{}$	None	None					60.2.i.a	$4$	$0$	$0$	$-2$	$0$	$4$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1+\beta _{3})q^{3}+(-1-\beta _{1}+\beta _{3})q^{5}+\cdots$
240.2.v.c	$240$	$2$	240.v	15.e	$4$	$4$	$2$	$1.916$	$\Q(\zeta_{8})$	$_{}$	None	None					120.2.r.b	$2$	$0$	$0$	$0$	$-4$	$4$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+(-\beta_{3}+\beta_1)q^{3}+(-2\beta_1-1)q^{5}+\cdots$
240.2.v.d	$240$	$2$	240.v	15.e	$4$	$4$	$2$	$1.916$	$\Q(\zeta_{8})$	$_{}$	None	None					120.2.r.a	$4$	$0$	$0$	$4$	$0$	$-12$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+(2\zeta_{8}-\zeta_{8}^{3})q^{5}+\cdots$
240.2.v.e	$240$	$2$	240.v	15.e	$4$	$4$	$2$	$1.916$	$\Q(\zeta_{8})$	$_{}$	None	None					30.2.e.a	$4$	$0$	$0$	$4$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+(-2\zeta_{8}-\zeta_{8}^{3})q^{5}+\cdots$
240.2.w.a	$240$	$2$	240.w	20.e	$4$	$4$	$2$	$1.916$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			240.2.w.a	$4$	$0$	$0$	$0$	$-8$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\zeta_{8}q^{3}+(-2+\zeta_{8}^{2})q^{5}+4\zeta_{8}^{3}q^{7}+\cdots$
240.2.w.b	$240$	$2$	240.w	20.e	$4$	$8$	$4$	$1.916$	$\Q(\zeta_{24})$	$_{}$	None	None		✓	✓		240.2.w.b	$4$	$0$	$0$	$0$	$8$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta_{5} q^{3}+(-\beta_{3}+\beta_{2}+1)q^{5}+(-\beta_{6}-\beta_{4}+2\beta_1)q^{7}+\cdots$
240.2.y.a	$240$	$2$	240.y	80.s	$4$	$2$	$1$	$1.916$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			240.2.y.a	$2$	$1$	$-2$	$-2$	$-2$	$-2$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-i-1)q^{2}-q^{3}+2 i q^{4}+(-2 i-1)q^{5}+\cdots$
240.2.y.b	$240$	$2$	240.y	80.s	$4$	$2$	$1$	$1.916$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			240.2.y.b	$2$	$0$	$-2$	$2$	$-2$	$6$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-i-1)q^{2}+q^{3}+2 i q^{4}+(-2 i-1)q^{5}+\cdots$
240.2.y.c	$240$	$2$	240.y	80.s	$4$	$2$	$1$	$1.916$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			240.2.y.c	$2$	$0$	$2$	$-2$	$2$	$6$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(i+1)q^{2}-q^{3}+2 i q^{4}+(-2 i+1)q^{5}+\cdots$
240.2.y.d	$240$	$2$	240.y	80.s	$4$	$6$	$3$	$1.916$	6.0.399424.1	$_{}$	None	None		✓			240.2.y.d	$2$	$0$	$0$	$6$	$6$	$-2$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{3}q^{2}+q^{3}+(-\beta _{1}-\beta _{5})q^{4}+(1+\cdots)q^{5}+\cdots$
240.2.y.e	$240$	$2$	240.y	80.s	$4$	$16$	$8$	$1.916$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓			240.2.y.e	$2$	$0$	$2$	$16$	$-4$	$-4$		$2^{5}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{7}q^{2}+q^{3}+(-1+\beta _{2}-\beta _{3}-\beta _{4}+\cdots)q^{4}+\cdots$
240.2.y.f	$240$	$2$	240.y	80.s	$4$	$20$	$10$	$1.916$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None		✓	✓		240.2.y.f	$2$	$0$	$0$	$-20$	$0$	$-4$		$2^{6}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{13}q^{2}-q^{3}-\beta _{3}q^{4}+\beta _{7}q^{5}-\beta _{13}q^{6}+\cdots$
240.2.bb.a	$240$	$2$	240.bb	240.ab	$4$	$88$	$44$	$1.916$		$_{}$	None	None		✓	✓	✓	240.2.bb.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
240.2.bc.a	$240$	$2$	240.bc	80.j	$4$	$2$	$1$	$1.916$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			240.2.y.b	$2$	$0$	$-2$	$0$	$-4$	$6$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-i-1)q^{2}-i q^{3}+2 i q^{4}+(i-2)q^{5}+\cdots$
240.2.bc.b	$240$	$2$	240.bc	80.j	$4$	$2$	$1$	$1.916$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			240.2.y.a	$2$	$1$	$-2$	$0$	$-4$	$-2$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-i-1)q^{2}+i q^{3}+2 i q^{4}+(i-2)q^{5}+\cdots$
240.2.bc.c	$240$	$2$	240.bc	80.j	$4$	$2$	$1$	$1.916$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			240.2.y.c	$2$	$0$	$2$	$0$	$-4$	$6$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(i+1)q^{2}+i q^{3}+2 i q^{4}+(-i-2)q^{5}+\cdots$
240.2.bc.d	$240$	$2$	240.bc	80.j	$4$	$6$	$3$	$1.916$	6.0.399424.1	$_{}$	None	None		✓			240.2.y.d	$2$	$0$	$-2$	$0$	$12$	$-2$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{1}q^{2}-\beta _{3}q^{3}+(\beta _{2}-\beta _{3})q^{4}+(2+\cdots)q^{5}+\cdots$
240.2.bc.e	$240$	$2$	240.bc	80.j	$4$	$16$	$8$	$1.916$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓			240.2.y.e	$2$	$0$	$2$	$0$	$-8$	$-4$		$2^{5}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{2}q^{2}-\beta _{5}q^{3}+(-\beta _{1}+2\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots$
240.2.bc.f	$240$	$2$	240.bc	80.j	$4$	$20$	$10$	$1.916$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None		✓	✓		240.2.y.f	$2$	$0$	$2$	$0$	$8$	$-4$		$2^{6}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{2}-\beta _{5}q^{3}+\beta _{2}q^{4}-\beta _{15}q^{5}+\cdots$
240.2.bf.a	$240$	$2$	240.bf	240.af	$4$	$88$	$44$	$1.916$		$_{}$	None	None		✓	✓	✓	240.2.bb.a	$4$	$0$	$0$	$-4$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
240.2.bk.a	$240$	$2$	240.bk	48.k	$4$	$4$	$2$	$1.916$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			240.2.bk.a	$4$	$1$	$0$	$-4$	$0$	$-16$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(\zeta_{8}+\zeta_{8}^{3})q^{2}+(-1-\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+\cdots$
240.2.bk.b	$240$	$2$	240.bk	48.k	$4$	$60$	$30$	$1.916$		$_{}$	None	None		✓	✓		240.2.bk.b	$4$	$0$	$0$	$4$	$0$	$16$			$\mathrm{SU}(2)[C_{4}]$
240.2.bl.a	$240$	$2$	240.bl	80.q	$4$	$48$	$24$	$1.916$		$_{}$	None	None		✓	✓	✓	240.2.bl.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
240.3.c.a	$240$	$3$	240.c	15.d	$2$	$1$	$1$	$6.540$	$\Q$	$_{}$	$\Q(\sqrt{-15}) $	None	✓				15.3.d.a	$2$	$0$	$0$	$-3$	$-5$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-3q^{3}-5q^{5}+9q^{9}+15q^{15}+14q^{17}+\cdots$
240.3.c.b	$240$	$3$	240.c	15.d	$2$	$1$	$1$	$6.540$	$\Q$	$_{}$	$\Q(\sqrt{-15}) $	None	✓				15.3.d.a	$2$	$0$	$0$	$3$	$5$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+3q^{3}+5q^{5}+9q^{9}+15q^{15}-14q^{17}+\cdots$
240.3.c.c	$240$	$3$	240.c	15.d	$2$	$4$	$4$	$6.540$	$\Q(\sqrt{2}, \sqrt{-17})$	$_{}$	None	None					30.3.b.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+(2\beta _{2}+\beta _{3})q^{5}+(-2\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots$
240.3.c.d	$240$	$3$	240.c	15.d	$2$	$4$	$4$	$6.540$	$\Q(i, \sqrt{5})$	$_{}$	None	None					60.3.b.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{3}+(\beta _{1}-\beta _{3})q^{5}+(-2\beta _{2}+2\beta _{3})q^{7}+\cdots$
240.3.c.e	$240$	$3$	240.c	15.d	$2$	$12$	$12$	$6.540$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None			✓		120.3.c.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{15}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+\beta _{7}q^{5}-\beta _{9}q^{7}+(1-\beta _{4}+\cdots)q^{9}+\cdots$
240.3.e.a	$240$	$3$	240.e	4.b	$2$	$4$	$4$	$6.540$	$\Q(\sqrt{-3}, \sqrt{5})$	$_{}$	None	None		✓			240.3.e.a	$2$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{3}-\beta _{1}q^{5}+(-2\beta _{2}+2\beta _{3})q^{7}+\cdots$
240.3.e.b	$240$	$3$	240.e	4.b	$2$	$4$	$4$	$6.540$	$\Q(\sqrt{-3}, \sqrt{5})$	$_{}$	None	None		✓			240.3.e.b	$2$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{3}-\beta _{1}q^{5}+(-2\beta _{2}-2\beta _{3})q^{7}+\cdots$
240.3.j.a	$240$	$3$	240.j	20.d	$2$	$4$	$4$	$6.540$	$\Q(\zeta_{12})$	$_{}$	None	None		✓			240.3.j.a	$4$	$0$	$0$	$0$	$-20$	$0$		$2^{8}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta_1 q^{3}-5 q^{5}-4\beta_1 q^{7}+3 q^{9}+\cdots$
240.3.j.b	$240$	$3$	240.j	20.d	$2$	$4$	$4$	$6.540$	$\Q(\sqrt{3}, \sqrt{-7})$	$_{}$	None	None		✓			240.3.j.b	$4$	$0$	$0$	$0$	$-8$	$0$		$2^{2}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+(-2+\beta _{2})q^{5}+2\beta _{1}q^{7}+\cdots$

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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.