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Level	Weight	Analytic conductor	$Nk^2$	Dim.

Bad $p$	Char.	Primitive character	Character order	Coefficient field

Self-twists	CM/RM discriminant	Inner twist count	Is self-dual	Analytic rank

Coefficient ring index	Coefficient ring gens.		Projective image	Projective image type
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Results (1-50 of 85 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	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	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
1452.1.e.a	$1452$	$1$	1452.e	3.b	$2$	$1$	$1$	$0.725$	$\Q$	$D_{3}$	$\Q(\sqrt{-3}) $	None	✓	$2$	$0$	$0$	$1$	$0$	$-1$		$1$		$q+q^{3}-q^{7}+q^{9}+2q^{13}-q^{19}-q^{21}+\cdots$
1452.1.e.b	$1452$	$1$	1452.e	3.b	$2$	$1$	$1$	$0.725$	$\Q$	$D_{3}$	$\Q(\sqrt{-3}) $	None	✓	$2$	$0$	$0$	$1$	$0$	$1$		$1$		$q+q^{3}+q^{7}+q^{9}-2q^{13}+q^{19}+q^{21}+\cdots$
1452.1.e.c	$1452$	$1$	1452.e	3.b	$2$	$2$	$2$	$0.725$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None	✓	$4$	$0$	$0$	$-2$	$0$	$0$		$1$		$q-q^{3}-\beta q^{7}+q^{9}+\beta q^{19}+\beta q^{21}+\cdots$
1452.1.e.d	$1452$	$1$	1452.e	3.b	$2$	$2$	$2$	$0.725$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$1$	$0$	$0$		$1$		$q-\zeta_{6}^{2}q^{3}+(-\zeta_{6}-\zeta_{6}^{2})q^{5}-\zeta_{6}q^{9}+\cdots$
1452.1.m.a	$1452$	$1$	1452.m	33.h	$10$	$4$	$1$	$0.725$	$\Q(\zeta_{10})$	$D_{3}$	$\Q(\sqrt{-3}) $	None		$8$	$0$	$0$	$-1$	$0$	$-1$		$1$		$q+\zeta_{10}^{2}q^{3}-\zeta_{10}^{3}q^{7}+\zeta_{10}^{4}q^{9}+\cdots$
1452.1.m.b	$1452$	$1$	1452.m	33.h	$10$	$4$	$1$	$0.725$	$\Q(\zeta_{10})$	$D_{3}$	$\Q(\sqrt{-3}) $	None		$8$	$0$	$0$	$-1$	$0$	$1$		$1$		$q+\zeta_{10}^{2}q^{3}+\zeta_{10}^{3}q^{7}+\zeta_{10}^{4}q^{9}+\cdots$
1452.1.m.c	$1452$	$1$	1452.m	33.h	$10$	$8$	$2$	$0.725$	$\Q(\zeta_{15})$	$D_{6}$	$\Q(\sqrt{-11}) $	None		$16$	$0$	$0$	$-1$	$0$	$0$		$1$		$q+\zeta_{30}q^{3}+(\zeta_{30}^{8}+\zeta_{30}^{13})q^{5}+\zeta_{30}^{2}q^{9}+\cdots$
1452.1.m.d	$1452$	$1$	1452.m	33.h	$10$	$8$	$2$	$0.725$	8.0.324000000.3	$D_{6}$	$\Q(\sqrt{-3}) $	None		$16$	$0$	$0$	$2$	$0$	$0$		$1$		$q+(1+\beta _{2}+\beta _{4}+\beta _{6})q^{3}-\beta _{7}q^{7}+\beta _{6}q^{9}+\cdots$
1452.2.a.a	$1452$	$2$	1452.a	1.a	$1$	$1$	$1$	$11.594$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-2q^{7}+q^{9}+3q^{13}+q^{15}+\cdots$
1452.2.a.b	$1452$	$2$	1452.a	1.a	$1$	$1$	$1$	$11.594$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$-1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+2q^{7}+q^{9}-3q^{13}+q^{15}+\cdots$
1452.2.a.c	$1452$	$2$	1452.a	1.a	$1$	$1$	$1$	$11.594$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{5}-2q^{7}+q^{9}-6q^{13}+\cdots$
1452.2.a.d	$1452$	$2$	1452.a	1.a	$1$	$1$	$1$	$11.594$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$-4$	$-5$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-4q^{5}-5q^{7}+q^{9}-2q^{13}+\cdots$
1452.2.a.e	$1452$	$2$	1452.a	1.a	$1$	$1$	$1$	$11.594$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$-4$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-4q^{5}+5q^{7}+q^{9}+2q^{13}+\cdots$
1452.2.a.f	$1452$	$2$	1452.a	1.a	$1$	$1$	$1$	$11.594$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{5}+2q^{7}+q^{9}+2q^{13}+\cdots$
1452.2.a.g	$1452$	$2$	1452.a	1.a	$1$	$1$	$1$	$11.594$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$3$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+3q^{5}-2q^{7}+q^{9}-5q^{13}+\cdots$
1452.2.a.h	$1452$	$2$	1452.a	1.a	$1$	$1$	$1$	$11.594$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$3$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+3q^{5}+2q^{7}+q^{9}+5q^{13}+\cdots$
1452.2.a.i	$1452$	$2$	1452.a	1.a	$1$	$2$	$2$	$11.594$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$-1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(1-3\beta )q^{5}+(-3+2\beta )q^{7}+\cdots$
1452.2.a.j	$1452$	$2$	1452.a	1.a	$1$	$2$	$2$	$11.594$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$-2$	$-1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(1-3\beta )q^{5}+(3-2\beta )q^{7}+q^{9}+\cdots$
1452.2.a.k	$1452$	$2$	1452.a	1.a	$1$	$2$	$2$	$11.594$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$2$	$0$	$0$	$-2$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-\beta q^{7}+q^{9}+\beta q^{19}+\beta q^{21}+\cdots$
1452.2.a.l	$1452$	$2$	1452.a	1.a	$1$	$2$	$2$	$11.594$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$2$	$-1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-\beta q^{5}+(-3+2\beta )q^{7}+q^{9}+\cdots$
1452.2.a.m	$1452$	$2$	1452.a	1.a	$1$	$2$	$2$	$11.594$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$-1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-\beta q^{5}+(3-2\beta )q^{7}+q^{9}+(1+\cdots)q^{13}+\cdots$
1452.2.b.a	$1452$	$2$	1452.b	33.d	$2$	$4$	$4$	$11.594$	$\Q(\sqrt{-2}, \sqrt{-11})$	$_{}$	None	None		$4$	$0$	$0$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{3}+(-1+2\beta _{3})q^{5}-3\beta _{2}q^{7}+\cdots$
1452.2.b.b	$1452$	$2$	1452.b	33.d	$2$	$4$	$4$	$11.594$	$\Q(\sqrt{-2}, \sqrt{3})$	$_{}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{2}q^{3}+(-2\beta _{1}+\beta _{3})q^{7}+3q^{9}+\cdots$
1452.2.b.c	$1452$	$2$	1452.b	33.d	$2$	$4$	$4$	$11.594$	$\Q(\sqrt{-2}, \sqrt{3})$	$_{}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{2}q^{3}+(2\beta _{1}+\beta _{3})q^{7}+3q^{9}+(-\beta _{1}+\cdots)q^{13}+\cdots$
1452.2.b.d	$1452$	$2$	1452.b	33.d	$2$	$8$	$8$	$11.594$	8.0.3588489216.5	$_{}$	None	None		$4$	$0$	$0$	$-4$	$0$	$0$		$2\cdot 11^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1-\beta _{1})q^{3}+\beta _{2}q^{5}+(-1+\beta _{1}+\cdots)q^{9}+\cdots$
1452.2.b.e	$1452$	$2$	1452.b	33.d	$2$	$16$	$16$	$11.594$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$6$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{4}q^{3}+\beta _{15}q^{5}+(\beta _{1}+\beta _{2}+\beta _{14}+\cdots)q^{7}+\cdots$
1452.2.i.a	$1452$	$2$	1452.i	11.c	$5$	$4$	$1$	$11.594$	$\Q(\zeta_{10})$	$_{}$	None	None		$4$	$0$	$0$	$-1$	$-3$	$-2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\zeta_{10}^{2}q^{3}-3\zeta_{10}q^{5}-2\zeta_{10}^{3}q^{7}+\cdots$
1452.2.i.b	$1452$	$2$	1452.i	11.c	$5$	$4$	$1$	$11.594$	$\Q(\zeta_{10})$	$_{}$	None	None		$4$	$0$	$0$	$-1$	$-3$	$2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\zeta_{10}^{2}q^{3}-3\zeta_{10}q^{5}+2\zeta_{10}^{3}q^{7}+\cdots$
1452.2.i.c	$1452$	$2$	1452.i	11.c	$5$	$4$	$1$	$11.594$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$0$	$-1$	$-2$	$-3$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\zeta_{10}^{2}q^{3}+(-1+\zeta_{10}-\zeta_{10}^{2})q^{5}+\cdots$
1452.2.i.d	$1452$	$2$	1452.i	11.c	$5$	$4$	$1$	$11.594$	$\Q(\zeta_{10})$	$_{}$	None	None		$4$	$0$	$0$	$-1$	$-2$	$-2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\zeta_{10}^{2}q^{3}-2\zeta_{10}q^{5}-2\zeta_{10}^{3}q^{7}+\cdots$
1452.2.i.e	$1452$	$2$	1452.i	11.c	$5$	$4$	$1$	$11.594$	$\Q(\zeta_{10})$	$_{}$	None	None		$4$	$0$	$0$	$-1$	$-2$	$2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\zeta_{10}^{2}q^{3}-2\zeta_{10}q^{5}+2\zeta_{10}^{3}q^{7}+\cdots$
1452.2.i.f	$1452$	$2$	1452.i	11.c	$5$	$4$	$1$	$11.594$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$0$	$-1$	$-2$	$3$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\zeta_{10}^{2}q^{3}+(-1+\zeta_{10}-\zeta_{10}^{2})q^{5}+\cdots$
1452.2.i.g	$1452$	$2$	1452.i	11.c	$5$	$4$	$1$	$11.594$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$0$	$-1$	$3$	$-7$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\zeta_{10}^{2}q^{3}+(1+\zeta_{10}^{2})q^{5}+(-2+2\zeta_{10}+\cdots)q^{7}+\cdots$
1452.2.i.h	$1452$	$2$	1452.i	11.c	$5$	$4$	$1$	$11.594$	$\Q(\zeta_{10})$	$_{}$	None	None		$4$	$0$	$0$	$-1$	$4$	$-5$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\zeta_{10}^{2}q^{3}+4\zeta_{10}q^{5}-5\zeta_{10}^{3}q^{7}+\cdots$
1452.2.i.i	$1452$	$2$	1452.i	11.c	$5$	$4$	$1$	$11.594$	$\Q(\zeta_{10})$	$_{}$	None	None		$4$	$0$	$0$	$-1$	$4$	$5$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\zeta_{10}^{2}q^{3}+4\zeta_{10}q^{5}+5\zeta_{10}^{3}q^{7}+\cdots$
1452.2.i.j	$1452$	$2$	1452.i	11.c	$5$	$4$	$1$	$11.594$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$0$	$1$	$-7$	$-3$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\zeta_{10}^{2}q^{3}+(-3+2\zeta_{10}-3\zeta_{10}^{2}+\cdots)q^{5}+\cdots$
1452.2.i.k	$1452$	$2$	1452.i	11.c	$5$	$4$	$1$	$11.594$	$\Q(\zeta_{10})$	$_{}$	None	None		$4$	$0$	$0$	$1$	$-2$	$-2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\zeta_{10}^{2}q^{3}-2\zeta_{10}q^{5}-2\zeta_{10}^{3}q^{7}+\cdots$
1452.2.i.l	$1452$	$2$	1452.i	11.c	$5$	$4$	$1$	$11.594$	$\Q(\zeta_{10})$	$_{}$	None	None		$4$	$0$	$0$	$1$	$-2$	$2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\zeta_{10}^{2}q^{3}-2\zeta_{10}q^{5}+2\zeta_{10}^{3}q^{7}+\cdots$
1452.2.i.m	$1452$	$2$	1452.i	11.c	$5$	$4$	$1$	$11.594$	$\Q(\zeta_{10})$	$_{}$	None	None		$4$	$0$	$0$	$1$	$1$	$-2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\zeta_{10}^{2}q^{3}+\zeta_{10}q^{5}-2\zeta_{10}^{3}q^{7}+\cdots$
1452.2.i.n	$1452$	$2$	1452.i	11.c	$5$	$4$	$1$	$11.594$	$\Q(\zeta_{10})$	$_{}$	None	None		$4$	$0$	$0$	$1$	$1$	$2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\zeta_{10}^{2}q^{3}+\zeta_{10}q^{5}+2\zeta_{10}^{3}q^{7}+\cdots$
1452.2.i.o	$1452$	$2$	1452.i	11.c	$5$	$4$	$1$	$11.594$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$0$	$1$	$8$	$-7$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\zeta_{10}^{2}q^{3}+(3-\zeta_{10}+3\zeta_{10}^{2})q^{5}+\cdots$
1452.2.i.p	$1452$	$2$	1452.i	11.c	$5$	$4$	$1$	$11.594$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$0$	$1$	$8$	$7$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\zeta_{10}^{2}q^{3}+(3-\zeta_{10}+3\zeta_{10}^{2})q^{5}+\cdots$
1452.2.i.q	$1452$	$2$	1452.i	11.c	$5$	$8$	$2$	$11.594$	8.0.324000000.3	$_{}$	None	None		$8$	$0$	$0$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1+\beta _{2}+\beta _{4}+\beta _{6})q^{3}+\beta _{7}q^{7}+\beta _{6}q^{9}+\cdots$
1452.3.e.a	$1452$	$3$	1452.e	3.b	$2$	$1$	$1$	$39.564$	$\Q$	$_{}$	$\Q(\sqrt{-3}) $	None	✓	$2$	$0$	$0$	$-3$	$0$	$-13$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-3q^{3}-13q^{7}+9q^{9}-22q^{13}-37q^{19}+\cdots$
1452.3.e.b	$1452$	$3$	1452.e	3.b	$2$	$1$	$1$	$39.564$	$\Q$	$_{}$	$\Q(\sqrt{-3}) $	None	✓	$2$	$0$	$0$	$-3$	$0$	$-2$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-3q^{3}-2q^{7}+9q^{9}+22q^{13}-26q^{19}+\cdots$
1452.3.e.c	$1452$	$3$	1452.e	3.b	$2$	$1$	$1$	$39.564$	$\Q$	$_{}$	$\Q(\sqrt{-3}) $	None	✓	$2$	$0$	$0$	$-3$	$0$	$13$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-3q^{3}+13q^{7}+9q^{9}+22q^{13}+37q^{19}+\cdots$
1452.3.e.d	$1452$	$3$	1452.e	3.b	$2$	$2$	$2$	$39.564$	$\Q(\sqrt{-11}) $	$_{}$	None	None		$2$	$0$	$0$	$5$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(3-\beta )q^{3}+(1-2\beta )q^{5}-2q^{7}+(6+\cdots)q^{9}+\cdots$
1452.3.e.e	$1452$	$3$	1452.e	3.b	$2$	$2$	$2$	$39.564$	$\Q(\sqrt{3}) $	$_{}$	$\Q(\sqrt{-3}) $	None	✓	$4$	$0$	$0$	$6$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+3q^{3}-3\beta q^{7}+9q^{9}+8\beta q^{13}-5\beta q^{19}+\cdots$
1452.3.e.f	$1452$	$3$	1452.e	3.b	$2$	$2$	$2$	$39.564$	$\Q(\sqrt{3}) $	$_{}$	$\Q(\sqrt{-3}) $	None	✓	$4$	$0$	$0$	$6$	$0$	$0$		$2^{3}$	$\mathrm{U}(1)[D_{2}]$	$q+3q^{3}+\beta q^{7}+9q^{9}+\beta q^{13}-2\beta q^{19}+\cdots$
1452.3.e.g	$1452$	$3$	1452.e	3.b	$2$	$4$	$4$	$39.564$	$\Q(\sqrt{-3}, \sqrt{-11})$	$_{}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$-5$	$0$	$0$		$2^{4}$	$\mathrm{U}(1)[D_{2}]$	$q+(-1+\beta _{2})q^{3}+\beta _{3}q^{5}+(-3-2\beta _{1}+\cdots)q^{9}+\cdots$

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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.