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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 146 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
279.1.d.a	$279$	$1$	279.d	31.b	$2$	$1$	$1$	$0.139$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-31}) $	$\Q(\sqrt{93}) $	✓	✓			279.1.d.a	$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q-q^{4}+2q^{7}+q^{16}-2q^{19}-q^{25}+\cdots$
279.1.d.b	$279$	$1$	279.d	31.b	$2$	$1$	$1$	$0.139$	$\Q$	$D_{3}$	$\Q(\sqrt{-31}) $	None	✓				31.1.b.a	$2$	$0$	$1$	$0$	$1$	$-1$		$1$		$q+q^{2}+q^{5}-q^{7}-q^{8}+q^{10}-q^{14}+\cdots$
279.1.d.c	$279$	$1$	279.d	31.b	$2$	$2$	$2$	$0.139$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-31}) $	None	✓	✓	✓		279.1.d.c	$4$	$0$	$0$	$0$	$0$	$-2$		$1$		$q-\beta q^{2}+2q^{4}+\beta q^{5}-q^{7}-\beta q^{8}+\cdots$
279.1.v.a	$279$	$1$	279.v	31.f	$10$	$4$	$1$	$0.139$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	279.1.v.a	$4$	$0$	$0$	$0$	$0$	$-2$		$1$		$q+\zeta_{10}q^{4}+(-\zeta_{10}^{3}+\zeta_{10}^{4})q^{7}+(-\zeta_{10}+\cdots)q^{13}+\cdots$
279.2.a.a	$279$	$2$	279.a	1.a	$1$	$2$	$2$	$2.228$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓		✓	✓	31.2.a.a	$1$	$1$	$-1$	$0$	$-2$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(-1+\beta )q^{4}-q^{5}+(-3+2\beta )q^{7}+\cdots$
279.2.a.b	$279$	$2$	279.a	1.a	$1$	$2$	$2$	$2.228$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				93.2.a.a	$1$	$0$	$3$	$0$	$4$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+3\beta q^{4}+(3-2\beta )q^{5}+(-1+\cdots)q^{7}+\cdots$
279.2.a.c	$279$	$2$	279.a	1.a	$1$	$3$	$3$	$2.228$	3.3.229.1	$_{}$	None	None	✓		✓		93.2.a.b	$1$	$0$	$0$	$0$	$2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1-\beta _{1}+\beta _{2})q^{5}+\cdots$
279.2.a.d	$279$	$2$	279.a	1.a	$1$	$6$	$6$	$2.228$	6.6.361944768.1	$_{}$	None	None	✓	✓	✓	✓	279.2.a.d	$2$	$0$	$0$	$0$	$0$	$8$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(2+\beta _{3})q^{4}-\beta _{2}q^{5}+(1+\beta _{5})q^{7}+\cdots$
279.2.c.a	$279$	$2$	279.c	93.c	$2$	$12$	$12$	$2.228$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	$\Q(\sqrt{-31}) $	None		✓	✓	✓	279.2.c.a	$4$	$0$	$0$	$0$	$0$	$0$		$3^{5}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{2}+(-2-\beta _{2})q^{4}+\beta _{10}q^{5}+\cdots$
279.2.e.a	$279$	$2$	279.e	279.e	$3$	$60$	$30$	$2.228$		$_{}$	None	None		✓	✓	✓	279.2.e.a	$2$	$0$	$-2$	$-5$	$2$	$0$			$\mathrm{SU}(2)[C_{3}]$
279.2.f.a	$279$	$2$	279.f	9.c	$3$	$30$	$15$	$2.228$		$_{}$	None	None		✓			279.2.f.a	$2$	$0$	$-5$	$-1$	$-10$	$0$			$\mathrm{SU}(2)[C_{3}]$
279.2.f.b	$279$	$2$	279.f	9.c	$3$	$30$	$15$	$2.228$		$_{}$	None	None		✓			279.2.f.b	$2$	$0$	$3$	$-1$	$6$	$0$			$\mathrm{SU}(2)[C_{3}]$
279.2.g.a	$279$	$2$	279.g	279.g	$3$	$60$	$30$	$2.228$		$_{}$	None	None		✓	✓	✓	279.2.e.a	$2$	$0$	$-2$	$1$	$-4$	$0$			$\mathrm{SU}(2)[C_{3}]$
279.2.h.a	$279$	$2$	279.h	31.c	$3$	$2$	$1$	$2.228$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		✓			279.2.h.a	$4$	$0$	$0$	$0$	$0$	$4$		$1$	$\mathrm{U}(1)[D_{3}]$	$q-2q^{4}+(4-4\zeta_{6})q^{7}-5\zeta_{6}q^{13}+4q^{16}+\cdots$
279.2.h.b	$279$	$2$	279.h	31.c	$3$	$4$	$2$	$2.228$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None					93.2.e.a	$2$	$0$	$0$	$0$	$-4$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{3}q^{2}+(-\beta _{1}+2\beta _{2}-\beta _{3})q^{5}+(2+\cdots)q^{7}+\cdots$
279.2.h.c	$279$	$2$	279.h	31.c	$3$	$4$	$2$	$2.228$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None					31.2.c.a	$2$	$0$	$4$	$0$	$2$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\beta _{3})q^{2}+(1+2\beta _{3})q^{4}+(1+\beta _{2}+\cdots)q^{5}+\cdots$
279.2.h.d	$279$	$2$	279.h	31.c	$3$	$6$	$3$	$2.228$	6.0.591408.1	$_{}$	None	None					93.2.e.b	$2$	$0$	$0$	$0$	$4$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{3}q^{2}+(1-\beta _{2}+\beta _{3})q^{4}+(-2\beta _{1}+\cdots)q^{5}+\cdots$
279.2.h.e	$279$	$2$	279.h	31.c	$3$	$8$	$4$	$2.228$	8.0.207360000.1	$_{}$	None	None		✓	✓		279.2.h.e	$4$	$0$	$0$	$0$	$0$	$-4$		$2^{4}$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{3}q^{2}+(1-\beta _{4})q^{4}+\beta _{7}q^{5}+(-1+\cdots)q^{7}+\cdots$
279.2.i.a	$279$	$2$	279.i	31.d	$5$	$4$	$1$	$2.228$	$\Q(\zeta_{10})$	$_{}$	None	None					31.2.d.a	$2$	$0$	$3$	$0$	$6$	$-3$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1+\zeta_{10}^{2})q^{2}+(\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{4}+\cdots$
279.2.i.b	$279$	$2$	279.i	31.d	$5$	$8$	$2$	$2.228$	$\Q(\zeta_{15})$	$_{}$	None	None					93.2.f.a	$2$	$0$	$-3$	$0$	$6$	$9$		$5$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\beta_{4}-\beta_{3}-1)q^{2}+(-\beta_{5}+\beta_{3}-\beta_1)q^{4}+\cdots$
279.2.i.c	$279$	$2$	279.i	31.d	$5$	$16$	$4$	$2.228$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None					93.2.f.b	$2$	$0$	$3$	$0$	$-6$	$-7$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{1}q^{2}+(-1-\beta _{8}-\beta _{9}-\beta _{11})q^{4}+\cdots$
279.2.i.d	$279$	$2$	279.i	31.d	$5$	$24$	$6$	$2.228$		$_{}$	None	None		✓	✓		279.2.i.d	$4$	$0$	$0$	$0$	$0$	$2$			$\mathrm{SU}(2)[C_{5}]$
279.2.j.a	$279$	$2$	279.j	93.g	$6$	$4$	$2$	$2.228$	$\Q(\sqrt{-2}, \sqrt{-3})$	$_{}$	None	None		✓			279.2.j.a	$4$	$0$	$0$	$0$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{3}q^{2}+2\beta _{1}q^{5}-2\beta _{2}q^{7}+2\beta _{3}q^{8}+\cdots$
279.2.j.b	$279$	$2$	279.j	93.g	$6$	$4$	$2$	$2.228$	$\Q(\sqrt{-2}, \sqrt{-3})$	$_{}$	None	None		✓			279.2.j.b	$4$	$0$	$0$	$0$	$0$	$-4$		$3$	$\mathrm{SU}(2)[C_{6}]$	$q+2q^{4}+(\beta _{2}+\beta _{3})q^{5}-2\beta _{1}q^{7}+(2\beta _{2}+\cdots)q^{11}+\cdots$
279.2.j.c	$279$	$2$	279.j	93.g	$6$	$12$	$6$	$2.228$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		✓	✓		279.2.j.c	$4$	$0$	$0$	$0$	$0$	$0$		$3^{3}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{7}q^{2}+(-1-\beta _{1})q^{4}+(-\beta _{7}+\beta _{9}+\cdots)q^{5}+\cdots$
279.2.o.a	$279$	$2$	279.o	279.o	$6$	$60$	$30$	$2.228$		$_{}$	None	None		✓	✓	✓	279.2.o.a	$2$	$0$	$-6$	$-3$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
279.2.r.a	$279$	$2$	279.r	279.r	$6$	$60$	$30$	$2.228$		$_{}$	None	None		✓	✓	✓	279.2.o.a	$2$	$0$	$-6$	$-3$	$-6$	$0$			$\mathrm{SU}(2)[C_{6}]$
279.2.s.a	$279$	$2$	279.s	279.s	$6$	$60$	$30$	$2.228$		$_{}$	None	None		✓	✓	✓	279.2.s.a	$4$	$0$	$-6$	$0$	$-12$	$0$			$\mathrm{SU}(2)[C_{6}]$
279.2.w.a	$279$	$2$	279.w	93.k	$10$	$48$	$12$	$2.228$		$_{}$	None	None		✓	✓	✓	279.2.w.a	$4$	$0$	$0$	$0$	$0$	$-20$			$\mathrm{SU}(2)[C_{10}]$
279.2.y.a	$279$	$2$	279.y	31.g	$15$	$8$	$1$	$2.228$	$\Q(\zeta_{15})$	$_{}$	$\Q(\sqrt{-3}) $	None		✓			279.2.y.a	$4$	$0$	$0$	$0$	$0$	$-4$		$1$	$\mathrm{U}(1)[D_{15}]$	$q+(2\zeta_{15}^{2}+2\zeta_{15}^{7})q^{4}+(-3+2\zeta_{15}+\cdots)q^{7}+\cdots$
279.2.y.b	$279$	$2$	279.y	31.g	$15$	$16$	$2$	$2.228$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None					93.2.m.a	$2$	$0$	$0$	$0$	$-6$	$-9$		$1$	$\mathrm{SU}(2)[C_{15}]$	$q+(\beta _{7}-\beta _{12}-\beta _{13})q^{2}+(-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots$
279.2.y.c	$279$	$2$	279.y	31.g	$15$	$16$	$2$	$2.228$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None					31.2.g.a	$2$	$0$	$6$	$0$	$3$	$2$		$1$	$\mathrm{SU}(2)[C_{15}]$	$q+(-\beta _{1}-\beta _{4}+\beta _{5}-\beta _{9}-\beta _{10}-\beta _{11}+\cdots)q^{2}+\cdots$
279.2.y.d	$279$	$2$	279.y	31.g	$15$	$24$	$3$	$2.228$		$_{}$	None	None					93.2.m.b	$2$	$0$	$0$	$0$	$6$	$-1$			$\mathrm{SU}(2)[C_{15}]$
279.2.y.e	$279$	$2$	279.y	31.g	$15$	$32$	$4$	$2.228$		$_{}$	None	None		✓	✓		279.2.y.e	$4$	$0$	$0$	$0$	$0$	$-6$			$\mathrm{SU}(2)[C_{15}]$
279.2.z.a	$279$	$2$	279.z	279.z	$15$	$240$	$30$	$2.228$		$_{}$	None	None		✓	✓	✓	279.2.z.a	$4$	$0$	$-3$	$-8$	$-6$	$-5$			$\mathrm{SU}(2)[C_{15}]$
279.2.ba.a	$279$	$2$	279.ba	279.aa	$15$	$240$	$30$	$2.228$		$_{}$	None	None		✓	✓	✓	279.2.ba.a	$2$	$0$	$-3$	$-5$	$3$	$-5$			$\mathrm{SU}(2)[C_{15}]$
279.2.bb.a	$279$	$2$	279.bb	279.ab	$15$	$240$	$30$	$2.228$		$_{}$	None	None		✓	✓	✓	279.2.ba.a	$2$	$0$	$-3$	$-11$	$-6$	$-5$			$\mathrm{SU}(2)[C_{15}]$
279.2.be.a	$279$	$2$	279.be	279.ae	$30$	$240$	$30$	$2.228$		$_{}$	None	None		✓	✓	✓	279.2.be.a	$2$	$0$	$-9$	$-7$	$0$	$-5$			$\mathrm{SU}(2)[C_{30}]$
279.2.bg.a	$279$	$2$	279.bg	279.ag	$30$	$240$	$30$	$2.228$		$_{}$	None	None		✓	✓	✓	279.2.bg.a	$4$	$0$	$-9$	$-10$	$-18$	$-5$			$\mathrm{SU}(2)[C_{30}]$
279.2.bh.a	$279$	$2$	279.bh	279.ah	$30$	$240$	$30$	$2.228$		$_{}$	None	None		✓	✓	✓	279.2.be.a	$2$	$0$	$-9$	$-7$	$-9$	$-5$			$\mathrm{SU}(2)[C_{30}]$
279.2.bn.a	$279$	$2$	279.bn	93.p	$30$	$80$	$10$	$2.228$		$_{}$	None	None		✓	✓	✓	279.2.bn.a	$4$	$0$	$0$	$0$	$0$	$28$			$\mathrm{SU}(2)[C_{30}]$
279.3.b.a	$279$	$3$	279.b	3.b	$2$	$20$	$20$	$7.602$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		✓	✓	✓	279.3.b.a	$2$	$0$	$0$	$0$	$0$	$0$		$2^{6}\cdot 3^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-2+\beta _{2})q^{4}+\beta _{13}q^{5}+\cdots$
279.3.d.a	$279$	$3$	279.d	31.b	$2$	$2$	$2$	$7.602$	$\Q(\sqrt{-26}) $	$_{}$	None	None					31.3.b.a	$2$	$0$	$2$	$0$	$-4$	$16$		$3$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}-3q^{4}-2q^{5}+8q^{7}-7q^{8}+\cdots$
279.3.d.b	$279$	$3$	279.d	31.b	$2$	$2$	$2$	$7.602$	$\Q(\sqrt{-3}) $	$_{}$	None	None					93.3.d.a	$2$	$0$	$6$	$0$	$12$	$4$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+3q^{2}+5q^{4}+6q^{5}+2q^{7}+3q^{8}+\cdots$
279.3.d.c	$279$	$3$	279.d	31.b	$2$	$3$	$3$	$7.602$	3.3.837.1	$_{}$	$\Q(\sqrt{-31}) $	None	✓				31.3.b.b	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{2}q^{2}+(4+\beta _{1}-2\beta _{2})q^{4}+(3\beta _{1}+\cdots)q^{5}+\cdots$
279.3.d.d	$279$	$3$	279.d	31.b	$2$	$4$	$4$	$7.602$	$\Q(\sqrt{3}, \sqrt{-53})$	$_{}$	None	None		✓			279.3.d.d	$4$	$0$	$0$	$0$	$0$	$-16$		$2^{2}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-q^{4}-\beta _{1}q^{5}-4q^{7}-5\beta _{1}q^{8}+\cdots$
279.3.d.e	$279$	$3$	279.d	31.b	$2$	$6$	$6$	$7.602$	6.6.1389928896.1	$_{}$	$\Q(\sqrt{-31}) $	None	✓	✓			279.3.d.e	$4$	$0$	$0$	$0$	$0$	$0$		$3^{2}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{3}q^{2}+(4+\beta _{4}-\beta _{5})q^{4}+(\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots$
279.3.d.f	$279$	$3$	279.d	31.b	$2$	$8$	$8$	$7.602$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None			✓		93.3.d.b	$2$	$0$	$-6$	$0$	$-12$	$-20$		$2^{8}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1-\beta _{3})q^{2}+(2+\beta _{2}+\beta _{3})q^{4}+\cdots$
279.3.k.a	$279$	$3$	279.k	93.h	$6$	$44$	$22$	$7.602$		$_{}$	None	None		✓	✓	✓	279.3.k.a	$4$	$0$	$0$	$0$	$0$	$32$			$\mathrm{SU}(2)[C_{6}]$
279.3.l.a	$279$	$3$	279.l	279.l	$6$	$124$	$62$	$7.602$		$_{}$	None	None		✓	✓	✓	279.3.l.a	$2$	$0$	$-2$	$-3$	$-2$	$2$			$\mathrm{SU}(2)[C_{6}]$

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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.