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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 114 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
1104.1.o.a	$1104$	$1$	1104.o	276.h	$2$	$2$	$2$	$0.551$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-69}) $	None	✓	✓			1104.1.o.a	$4$	$0$	$0$	$-2$	$0$	$0$		$1$		$q-q^{3}-\beta q^{5}-\beta q^{7}+q^{9}+\beta q^{15}+\cdots$
1104.1.o.b	$1104$	$1$	1104.o	276.h	$2$	$2$	$2$	$0.551$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-69}) $	None	✓	✓			1104.1.o.a	$4$	$0$	$0$	$2$	$0$	$0$		$1$		$q+q^{3}-\beta q^{5}+\beta q^{7}+q^{9}-\beta q^{15}+\cdots$
1104.1.s.a	$1104$	$1$	1104.s	1104.s	$4$	$2$	$1$	$0.551$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-23}) $	None		✓			1104.1.s.a	$4$	$0$	$0$	$-2$	$0$	$0$		$1$		$q+i q^{2}-q^{3}-q^{4}-i q^{6}-i q^{8}+\cdots$
1104.1.s.b	$1104$	$1$	1104.s	1104.s	$4$	$2$	$1$	$0.551$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-23}) $	None		✓			1104.1.s.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-i q^{2}+i q^{3}-q^{4}+q^{6}+i q^{8}+\cdots$
1104.1.s.c	$1104$	$1$	1104.s	1104.s	$4$	$4$	$2$	$0.551$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-23}) $	None		✓			1104.1.s.c	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{12}^{5}q^{2}-\zeta_{12}q^{3}-\zeta_{12}^{4}q^{4}+q^{6}+\cdots$
1104.1.s.d	$1104$	$1$	1104.s	1104.s	$4$	$4$	$2$	$0.551$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-23}) $	None		✓			1104.1.s.c	$4$	$0$	$0$	$2$	$0$	$0$		$1$		$q-\zeta_{12}q^{2}-\zeta_{12}^{4}q^{3}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{5}q^{6}+\cdots$
1104.2.a.a	$1104$	$2$	1104.a	1.a	$1$	$1$	$1$	$8.815$	$\Q$	$_{}$	None	None	✓				552.2.a.e	$1$	$0$	$0$	$-1$	$-2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{5}+4q^{7}+q^{9}-2q^{13}+\cdots$
1104.2.a.b	$1104$	$2$	1104.a	1.a	$1$	$1$	$1$	$8.815$	$\Q$	$_{}$	None	None	✓				138.2.a.b	$1$	$1$	$0$	$-1$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{7}+q^{9}+2q^{13}-2q^{19}+\cdots$
1104.2.a.c	$1104$	$2$	1104.a	1.a	$1$	$1$	$1$	$8.815$	$\Q$	$_{}$	None	None	✓				69.2.a.a	$1$	$1$	$0$	$-1$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{7}+q^{9}-4q^{11}-6q^{13}+\cdots$
1104.2.a.d	$1104$	$2$	1104.a	1.a	$1$	$1$	$1$	$8.815$	$\Q$	$_{}$	None	None	✓		✓	✓	552.2.a.a	$1$	$1$	$0$	$1$	$-2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}-2q^{7}+q^{9}+2q^{11}+\cdots$
1104.2.a.e	$1104$	$2$	1104.a	1.a	$1$	$1$	$1$	$8.815$	$\Q$	$_{}$	None	None	✓				138.2.a.a	$1$	$0$	$0$	$1$	$-2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}+2q^{7}+q^{9}+6q^{11}+\cdots$
1104.2.a.f	$1104$	$2$	1104.a	1.a	$1$	$1$	$1$	$8.815$	$\Q$	$_{}$	None	None	✓				552.2.a.b	$1$	$0$	$0$	$1$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{7}+q^{9}+2q^{13}+8q^{17}+\cdots$
1104.2.a.g	$1104$	$2$	1104.a	1.a	$1$	$1$	$1$	$8.815$	$\Q$	$_{}$	None	None	✓				138.2.a.c	$1$	$0$	$0$	$1$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{5}+q^{9}-2q^{13}+2q^{15}+\cdots$
1104.2.a.h	$1104$	$2$	1104.a	1.a	$1$	$1$	$1$	$8.815$	$\Q$	$_{}$	None	None	✓				552.2.a.c	$1$	$0$	$0$	$1$	$2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{5}+4q^{7}+q^{9}+4q^{11}+\cdots$
1104.2.a.i	$1104$	$2$	1104.a	1.a	$1$	$1$	$1$	$8.815$	$\Q$	$_{}$	None	None	✓				552.2.a.d	$1$	$0$	$0$	$1$	$4$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+4q^{5}-2q^{7}+q^{9}+2q^{13}+\cdots$
1104.2.a.j	$1104$	$2$	1104.a	1.a	$1$	$2$	$2$	$8.815$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				138.2.a.d	$1$	$0$	$0$	$-2$	$-2$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{3}+(-1-\beta )q^{5}-2\beta q^{7}+q^{9}+\cdots$
1104.2.a.k	$1104$	$2$	1104.a	1.a	$1$	$2$	$2$	$8.815$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓		✓	✓	552.2.a.f	$1$	$1$	$0$	$-2$	$2$	$-4$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{3}+(1+\beta )q^{5}-2q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots$
1104.2.a.l	$1104$	$2$	1104.a	1.a	$1$	$2$	$2$	$8.815$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				276.2.a.b	$1$	$0$	$0$	$-2$	$4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(2+\beta )q^{5}-\beta q^{7}+q^{9}+4\beta q^{11}+\cdots$
1104.2.a.m	$1104$	$2$	1104.a	1.a	$1$	$2$	$2$	$8.815$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓		✓	✓	69.2.a.b	$1$	$1$	$0$	$2$	$-2$	$-2$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{3}+(-1-\beta )q^{5}+(-1+\beta )q^{7}+\cdots$
1104.2.a.n	$1104$	$2$	1104.a	1.a	$1$	$2$	$2$	$8.815$	$\Q(\sqrt{10}) $	$_{}$	None	None	✓		✓		276.2.a.a	$1$	$0$	$0$	$2$	$0$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+\beta q^{5}+(-2+\beta )q^{7}+q^{9}+4q^{13}+\cdots$
1104.2.a.o	$1104$	$2$	1104.a	1.a	$1$	$3$	$3$	$8.815$	3.3.148.1	$_{}$	None	None	✓		✓		552.2.a.g	$1$	$0$	$0$	$-3$	$0$	$-2$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{3}+\beta _{2}q^{5}+(-1-\beta _{1})q^{7}+q^{9}+\cdots$
1104.2.e.a	$1104$	$2$	1104.e	12.b	$2$	$2$	$2$	$8.815$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			1104.2.e.a	$2$	$1$	$0$	$-3$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-2+\zeta_{6})q^{3}+(2-4\zeta_{6})q^{5}+(3-3\zeta_{6})q^{9}+\cdots$
1104.2.e.b	$1104$	$2$	1104.e	12.b	$2$	$2$	$2$	$8.815$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			1104.2.e.a	$2$	$0$	$0$	$3$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(2-\zeta_{6})q^{3}+(2-4\zeta_{6})q^{5}+(3-3\zeta_{6})q^{9}+\cdots$
1104.2.e.c	$1104$	$2$	1104.e	12.b	$2$	$4$	$4$	$8.815$	$\Q(\sqrt{-3}, \sqrt{-11})$	$_{}$	None	None		✓			1104.2.e.c	$2$	$0$	$0$	$-1$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+2\beta _{2}q^{7}+(1-\beta _{2}-\beta _{3})q^{9}+\cdots$
1104.2.e.d	$1104$	$2$	1104.e	12.b	$2$	$4$	$4$	$8.815$	$\Q(\sqrt{-3}, \sqrt{-11})$	$_{}$	None	None		✓			1104.2.e.c	$2$	$0$	$0$	$1$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+2\beta _{2}q^{7}+(1+\beta _{2}-\beta _{3})q^{9}+\cdots$
1104.2.e.e	$1104$	$2$	1104.e	12.b	$2$	$8$	$8$	$8.815$	$\Q(i, \sqrt{3}, \sqrt{5})$	$_{}$	None	None		✓			1104.2.e.e	$2$	$0$	$0$	$-4$	$0$	$0$		$2^{6}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1-\beta _{7})q^{3}+(\beta _{2}-\beta _{5})q^{5}+(-1+\cdots)q^{7}+\cdots$
1104.2.e.f	$1104$	$2$	1104.e	12.b	$2$	$8$	$8$	$8.815$	8.0.$\cdots$.1	$_{}$	None	None		✓			1104.2.e.f	$2$	$0$	$0$	$0$	$0$	$0$		$3$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{7}q^{3}-\beta _{1}q^{5}-\beta _{1}q^{7}+\beta _{2}q^{9}+\cdots$
1104.2.e.g	$1104$	$2$	1104.e	12.b	$2$	$8$	$8$	$8.815$	8.0.$\cdots$.1	$_{}$	None	None		✓			1104.2.e.f	$2$	$0$	$0$	$0$	$0$	$0$		$3$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{7}q^{3}-\beta _{1}q^{5}+\beta _{1}q^{7}+\beta _{2}q^{9}+\cdots$
1104.2.e.h	$1104$	$2$	1104.e	12.b	$2$	$8$	$8$	$8.815$	$\Q(i, \sqrt{3}, \sqrt{5})$	$_{}$	None	None		✓			1104.2.e.e	$2$	$0$	$0$	$4$	$0$	$0$		$2^{6}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+\beta _{7})q^{3}+(\beta _{2}-\beta _{5})q^{5}+(1-\beta _{5}+\cdots)q^{7}+\cdots$
1104.2.i.a	$1104$	$2$	1104.i	92.b	$2$	$8$	$8$	$8.815$	8.0.$\cdots$.8	$_{}$	None	None		✓			1104.2.i.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{3}+\beta _{3}q^{5}-\beta _{4}q^{7}-q^{9}-2\beta _{1}q^{11}+\cdots$
1104.2.i.b	$1104$	$2$	1104.i	92.b	$2$	$16$	$16$	$8.815$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓	✓		1104.2.i.b	$4$	$0$	$0$	$0$	$0$	$0$		$2^{16}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{3}-\beta _{14}q^{5}+\beta _{12}q^{7}-q^{9}+\cdots$
1104.2.m.a	$1104$	$2$	1104.m	69.c	$2$	$6$	$6$	$8.815$	6.0.8869743.1	$_{}$	$\Q(\sqrt{-23}) $	None					69.2.c.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{3}\cdot 3$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{2}q^{3}-\beta _{3}q^{9}+(-\beta _{2}-\beta _{3}-\beta _{4}+\cdots)q^{13}+\cdots$
1104.2.m.b	$1104$	$2$	1104.m	69.c	$2$	$8$	$8$	$8.815$	8.0.$\cdots$.7	$_{}$	None	None					276.2.g.a	$4$	$0$	$0$	$-2$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{3}-\beta _{5}q^{5}-\beta _{7}q^{7}+(-1-\beta _{3}+\cdots)q^{9}+\cdots$
1104.2.m.c	$1104$	$2$	1104.m	69.c	$2$	$8$	$8$	$8.815$	$\Q(i, \sqrt{2}, \sqrt{5})$	$_{}$	None	None					552.2.m.a	$4$	$0$	$0$	$4$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+\beta _{4})q^{3}-\beta _{3}q^{5}-\beta _{5}q^{7}+(1-2\beta _{1}+\cdots)q^{9}+\cdots$
1104.2.m.d	$1104$	$2$	1104.m	69.c	$2$	$8$	$8$	$8.815$	8.0.$\cdots$.3	$_{}$	None	None					138.2.d.a	$4$	$0$	$0$	$4$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}+\beta _{4})q^{3}+\beta _{3}q^{5}-\beta _{5}q^{7}+(-1+\cdots)q^{9}+\cdots$
1104.2.m.e	$1104$	$2$	1104.m	69.c	$2$	$16$	$16$	$8.815$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None			✓		552.2.m.b	$4$	$0$	$0$	$-4$	$0$	$0$		$2^{18}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{7}q^{3}+\beta _{5}q^{5}-\beta _{1}q^{7}+(\beta _{2}+\beta _{4}+\cdots)q^{9}+\cdots$
1104.3.c.a	$1104$	$3$	1104.c	23.b	$2$	$8$	$8$	$30.082$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	$_{}$	None	None					69.3.d.a	$2$	$0$	$0$	$0$	$0$	$0$		$2^{3}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{3}+\beta _{1}q^{5}-\beta _{5}q^{7}+3q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots$
1104.3.c.b	$1104$	$3$	1104.c	23.b	$2$	$8$	$8$	$30.082$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	$_{}$	None	None					276.3.b.a	$2$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+\beta _{2}q^{5}+(\beta _{2}+\beta _{7})q^{7}+3q^{9}+\cdots$
1104.3.c.c	$1104$	$3$	1104.c	23.b	$2$	$8$	$8$	$30.082$	8.0.1358954496.3	$_{}$	None	None					138.3.b.a	$2$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{3}+(\beta _{2}-2\beta _{3}+\beta _{6})q^{5}+(2\beta _{2}+\cdots)q^{7}+\cdots$
1104.3.c.d	$1104$	$3$	1104.c	23.b	$2$	$24$	$24$	$30.082$		$_{}$	None	None			✓		552.3.c.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1104.3.g.a	$1104$	$3$	1104.g	3.b	$2$	$14$	$14$	$30.082$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None					276.3.d.a	$2$	$0$	$0$	$-4$	$0$	$4$		$2^{10}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{3}-\beta _{5}q^{5}+\beta _{2}q^{7}+(1+\beta _{3}+\cdots)q^{9}+\cdots$
1104.3.g.b	$1104$	$3$	1104.g	3.b	$2$	$14$	$14$	$30.082$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	$_{}$	None	None					69.3.b.a	$2$	$0$	$0$	$4$	$0$	$4$		$2^{10}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{6}q^{3}+\beta _{4}q^{5}-\beta _{5}q^{7}+(\beta _{3}-\beta _{7}+\cdots)q^{9}+\cdots$
1104.3.g.c	$1104$	$3$	1104.g	3.b	$2$	$16$	$16$	$30.082$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None					138.3.c.a	$2$	$0$	$0$	$-4$	$0$	$0$		$2^{8}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{9}q^{3}-\beta _{8}q^{5}+\beta _{4}q^{7}+(-\beta _{2}+\beta _{11}+\cdots)q^{9}+\cdots$
1104.3.g.d	$1104$	$3$	1104.g	3.b	$2$	$44$	$44$	$30.082$		$_{}$	None	None			✓		552.3.g.a	$2$	$0$	$0$	$4$	$0$	$-24$			$\mathrm{SU}(2)[C_{2}]$
1104.3.k.a	$1104$	$3$	1104.k	4.b	$2$	$8$	$8$	$30.082$	8.0.3830743449.1	$_{}$	None	None		✓			1104.3.k.a	$2$	$0$	$0$	$0$	$-16$	$0$		$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{4}q^{3}+(-2-\beta _{3})q^{5}+(\beta _{2}+2\beta _{4}+\cdots)q^{7}+\cdots$
1104.3.k.b	$1104$	$3$	1104.k	4.b	$2$	$8$	$8$	$30.082$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None		✓			1104.3.k.b	$2$	$0$	$0$	$0$	$8$	$0$		$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{3}+(1+\beta _{2})q^{5}+(2\beta _{3}+\beta _{4}+\beta _{5}+\cdots)q^{7}+\cdots$
1104.3.k.c	$1104$	$3$	1104.k	4.b	$2$	$12$	$12$	$30.082$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		✓			1104.3.k.c	$2$	$0$	$0$	$0$	$-8$	$0$		$2^{16}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{3}+(-1-\beta _{3})q^{5}+\beta _{10}q^{7}+\cdots$
1104.3.k.d	$1104$	$3$	1104.k	4.b	$2$	$16$	$16$	$30.082$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓	✓		1104.3.k.d	$2$	$0$	$0$	$0$	$-8$	$0$		$2^{24}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{8}q^{3}+\beta _{3}q^{5}+(-\beta _{8}+\beta _{13})q^{7}+\cdots$
1104.3.o.a	$1104$	$3$	1104.o	276.h	$2$	$4$	$4$	$30.082$	$\Q(\sqrt{3}, \sqrt{23})$	$_{}$	$\Q(\sqrt{-69}) $	None	✓	✓			1104.3.o.a	$4$	$0$	$0$	$-12$	$0$	$0$		$2^{6}$	$\mathrm{U}(1)[D_{2}]$	$q-3q^{3}+\beta _{1}q^{5}+\beta _{2}q^{7}+9q^{9}-\beta _{3}q^{13}+\cdots$
1104.3.o.b	$1104$	$3$	1104.o	276.h	$2$	$4$	$4$	$30.082$	$\Q(\sqrt{3}, \sqrt{23})$	$_{}$	$\Q(\sqrt{-69}) $	None	✓	✓			1104.3.o.a	$4$	$0$	$0$	$12$	$0$	$0$		$2^{6}$	$\mathrm{U}(1)[D_{2}]$	$q+3q^{3}+\beta _{1}q^{5}-\beta _{2}q^{7}+9q^{9}-\beta _{3}q^{13}+\cdots$

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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.