LMFDB - Newform search results

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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 130 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
1520.1.m.a	$1520$	$1$	1520.m	95.d	$2$	$1$	$1$	$0.759$	$\Q$	$D_{2}$	$\Q(\sqrt{-19}) $, $\Q(\sqrt{-95}) $	$\Q(\sqrt{5}) $	✓				95.1.d.a	$4$	$0$	$0$	$0$	$1$	$0$		$1$		$q+q^{5}-q^{9}+2q^{11}-q^{19}+q^{25}+\cdots$
1520.1.m.b	$1520$	$1$	1520.m	95.d	$2$	$2$	$2$	$0.759$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-95}) $	None	✓				95.1.d.b	$4$	$0$	$0$	$0$	$-2$	$0$		$1$		$q-\beta q^{3}-q^{5}+q^{9}-\beta q^{13}+\beta q^{15}+\cdots$
1520.1.m.c	$1520$	$1$	1520.m	95.d	$2$	$2$	$2$	$0.759$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-19}) $	None					380.1.g.a	$4$	$0$	$0$	$0$	$-1$	$0$		$1$		$q-\zeta_{6}q^{5}+(\zeta_{6}+\zeta_{6}^{2})q^{7}-q^{9}-q^{11}+\cdots$
1520.1.ba.a	$1520$	$1$	1520.ba	380.j	$4$	$2$	$1$	$0.759$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-19}) $	None		✓			1520.1.ba.a	$4$	$0$	$0$	$0$	$-2$	$-2$		$1$		$q-q^{5}+(-i-1)q^{7}-i q^{9}+2 i q^{11}+\cdots$
1520.1.ba.b	$1520$	$1$	1520.ba	380.j	$4$	$2$	$1$	$0.759$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-19}) $	None		✓			1520.1.ba.a	$4$	$0$	$0$	$0$	$-2$	$2$		$1$		$q-q^{5}+(i+1)q^{7}-i q^{9}-2 i q^{11}+\cdots$
1520.1.ba.c	$1520$	$1$	1520.ba	380.j	$4$	$4$	$2$	$0.759$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-19}) $	None		✓			1520.1.ba.c	$4$	$0$	$0$	$0$	$2$	$-2$		$1$		$q+\zeta_{12}^{2}q^{5}+(-\zeta_{12}-\zeta_{12}^{2})q^{7}-\zeta_{12}^{3}q^{9}+\cdots$
1520.1.ba.d	$1520$	$1$	1520.ba	380.j	$4$	$4$	$2$	$0.759$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-19}) $	None		✓			1520.1.ba.c	$4$	$0$	$0$	$0$	$2$	$2$		$1$		$q+\zeta_{12}^{2}q^{5}+(-\zeta_{12}+\zeta_{12}^{2})q^{7}+\zeta_{12}^{3}q^{9}+\cdots$
1520.1.bh.a	$1520$	$1$	1520.bh	1520.ah	$4$	$4$	$2$	$0.759$	$\Q(\zeta_{8})$	$S_{4}$	None	None		✓			1520.1.bh.a	$4$	$0$	$0$	$0$	$0$	$-4$		$1$		$q-\zeta_{8}^{3}q^{2}-\zeta_{8}q^{3}-\zeta_{8}^{2}q^{4}-\zeta_{8}^{2}q^{5}+\cdots$
1520.1.bh.b	$1520$	$1$	1520.bh	1520.ah	$4$	$4$	$2$	$0.759$	$\Q(\zeta_{8})$	$S_{4}$	None	None		✓			1520.1.bh.a	$4$	$0$	$0$	$0$	$4$	$4$		$1$		$q-\zeta_{8}^{3}q^{2}-\zeta_{8}q^{3}-\zeta_{8}^{2}q^{4}+q^{5}+\cdots$
1520.1.bh.c	$1520$	$1$	1520.bh	1520.ah	$4$	$16$	$8$	$0.759$	$\Q(\zeta_{32})$	$D_{16}$	$\Q(\sqrt{-95}) $	None		✓	✓		1520.1.bh.c	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{32}^{3}q^{2}+(\zeta_{32}-\zeta_{32}^{7})q^{3}+\zeta_{32}^{6}q^{4}+\cdots$
1520.1.br.a	$1520$	$1$	1520.br	95.h	$6$	$2$	$1$	$0.759$	$\Q(\sqrt{-3}) $	$D_{6}$	None	$\Q(\sqrt{5}) $			✓	✓	380.1.o.a	$4$	$0$	$0$	$0$	$-1$	$0$		$1$		$q-\zeta_{6}q^{5}-\zeta_{6}^{2}q^{9}-q^{11}-\zeta_{6}^{2}q^{19}+\cdots$
1520.1.bu.a	$1520$	$1$	1520.bu	380.p	$6$	$2$	$1$	$0.759$	$\Q(\sqrt{-3}) $	$D_{6}$	None	$\Q(\sqrt{5}) $		✓			1520.1.bu.a	$4$	$0$	$0$	$0$	$1$	$0$		$1$		$q+\zeta_{6}q^{5}-\zeta_{6}^{2}q^{9}+(\zeta_{6}+\zeta_{6}^{2})q^{11}+\cdots$
1520.1.bu.b	$1520$	$1$	1520.bu	380.p	$6$	$2$	$1$	$0.759$	$\Q(\sqrt{-3}) $	$D_{6}$	None	$\Q(\sqrt{5}) $		✓			1520.1.bu.a	$4$	$0$	$0$	$0$	$1$	$0$		$1$		$q+\zeta_{6}q^{5}-\zeta_{6}^{2}q^{9}+(-\zeta_{6}-\zeta_{6}^{2})q^{11}+\cdots$
1520.1.cr.a	$1520$	$1$	1520.cr	95.m	$12$	$4$	$1$	$0.759$	$\Q(\zeta_{12})$	$S_{4}$	None	None					760.1.bt.a	$4$	$0$	$0$	$-2$	$0$	$0$		$1$		$q+(-\zeta_{12}+\zeta_{12}^{4})q^{3}-\zeta_{12}q^{5}-\zeta_{12}^{5}q^{9}+\cdots$
1520.1.cr.b	$1520$	$1$	1520.cr	95.m	$12$	$4$	$1$	$0.759$	$\Q(\zeta_{12})$	$S_{4}$	None	None					380.1.x.a	$4$	$0$	$0$	$2$	$2$	$0$		$1$		$q+(\zeta_{12}-\zeta_{12}^{4})q^{3}-\zeta_{12}^{4}q^{5}-\zeta_{12}^{5}q^{9}+\cdots$
1520.2.a.a	$1520$	$2$	1520.a	1.a	$1$	$1$	$1$	$12.137$	$\Q$	$_{}$	None	None	✓				760.2.a.e	$1$	$1$	$0$	$-3$	$1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}+q^{5}+q^{7}+6q^{9}-4q^{11}+\cdots$
1520.2.a.b	$1520$	$2$	1520.a	1.a	$1$	$1$	$1$	$12.137$	$\Q$	$_{}$	None	None	✓				380.2.a.b	$1$	$1$	$0$	$-2$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-q^{5}-2q^{7}+q^{9}+6q^{13}+\cdots$
1520.2.a.c	$1520$	$2$	1520.a	1.a	$1$	$1$	$1$	$12.137$	$\Q$	$_{}$	None	None	✓				760.2.a.d	$1$	$1$	$0$	$-2$	$1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{5}-4q^{7}+q^{9}+4q^{11}+\cdots$
1520.2.a.d	$1520$	$2$	1520.a	1.a	$1$	$1$	$1$	$12.137$	$\Q$	$_{}$	None	None	✓				190.2.a.c	$1$	$1$	$0$	$-1$	$1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+q^{7}-2q^{9}-q^{13}-q^{15}+\cdots$
1520.2.a.e	$1520$	$2$	1520.a	1.a	$1$	$1$	$1$	$12.137$	$\Q$	$_{}$	None	None	✓				380.2.a.a	$1$	$0$	$0$	$0$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+2q^{7}-3q^{9}+4q^{11}-4q^{13}+\cdots$
1520.2.a.f	$1520$	$2$	1520.a	1.a	$1$	$1$	$1$	$12.137$	$\Q$	$_{}$	None	None	✓				760.2.a.c	$1$	$1$	$0$	$0$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-3q^{9}+4q^{11}-6q^{13}-6q^{17}+\cdots$
1520.2.a.g	$1520$	$2$	1520.a	1.a	$1$	$1$	$1$	$12.137$	$\Q$	$_{}$	None	None	✓				190.2.a.a	$1$	$1$	$0$	$1$	$-1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+q^{7}-2q^{9}-3q^{13}-q^{15}+\cdots$
1520.2.a.h	$1520$	$2$	1520.a	1.a	$1$	$1$	$1$	$12.137$	$\Q$	$_{}$	None	None	✓				760.2.a.b	$1$	$1$	$0$	$2$	$1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{5}-4q^{7}+q^{9}-4q^{11}+\cdots$
1520.2.a.i	$1520$	$2$	1520.a	1.a	$1$	$1$	$1$	$12.137$	$\Q$	$_{}$	None	None	✓				760.2.a.a	$1$	$0$	$0$	$2$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{5}+q^{9}+4q^{11}+4q^{13}+\cdots$
1520.2.a.j	$1520$	$2$	1520.a	1.a	$1$	$1$	$1$	$12.137$	$\Q$	$_{}$	None	None	✓				190.2.a.b	$1$	$0$	$0$	$3$	$-1$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}-q^{5}+5q^{7}+6q^{9}+4q^{11}+\cdots$
1520.2.a.k	$1520$	$2$	1520.a	1.a	$1$	$2$	$2$	$12.137$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓				760.2.a.g	$1$	$1$	$0$	$-2$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}-q^{5}+(1-2\beta )q^{9}-2q^{11}+\cdots$
1520.2.a.l	$1520$	$2$	1520.a	1.a	$1$	$2$	$2$	$12.137$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓		✓		380.2.a.d	$1$	$1$	$0$	$-2$	$2$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}+q^{5}-2q^{7}+(1-2\beta )q^{9}+\cdots$
1520.2.a.m	$1520$	$2$	1520.a	1.a	$1$	$2$	$2$	$12.137$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				760.2.a.f	$1$	$0$	$0$	$0$	$-2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-q^{5}+2\beta q^{7}-q^{9}+(-2+2\beta )q^{11}+\cdots$
1520.2.a.n	$1520$	$2$	1520.a	1.a	$1$	$2$	$2$	$12.137$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓				190.2.a.d	$1$	$0$	$0$	$1$	$2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+q^{5}+\beta q^{7}+(1+\beta )q^{9}-4q^{11}+\cdots$
1520.2.a.o	$1520$	$2$	1520.a	1.a	$1$	$2$	$2$	$12.137$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				380.2.a.c	$1$	$0$	$0$	$4$	$2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(2+\beta )q^{3}+q^{5}+(2-2\beta )q^{7}+(3+4\beta )q^{9}+\cdots$
1520.2.a.p	$1520$	$2$	1520.a	1.a	$1$	$3$	$3$	$12.137$	3.3.148.1	$_{}$	None	None	✓		✓		95.2.a.a	$1$	$0$	$0$	$-2$	$3$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+q^{5}+(-\beta _{1}+\beta _{2})q^{7}+\cdots$
1520.2.a.q	$1520$	$2$	1520.a	1.a	$1$	$3$	$3$	$12.137$	3.3.316.1	$_{}$	None	None	✓		✓		760.2.a.i	$1$	$1$	$0$	$1$	$-3$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}-q^{5}+(1-2\beta _{1}+\beta _{2})q^{7}+\cdots$
1520.2.a.r	$1520$	$2$	1520.a	1.a	$1$	$3$	$3$	$12.137$	3.3.568.1	$_{}$	None	None	✓		✓		760.2.a.h	$1$	$0$	$0$	$1$	$-3$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}-q^{5}+(2+\beta _{2})q^{7}+(1+2\beta _{1}+\cdots)q^{9}+\cdots$
1520.2.a.s	$1520$	$2$	1520.a	1.a	$1$	$3$	$3$	$12.137$	3.3.229.1	$_{}$	None	None	✓		✓		760.2.a.j	$1$	$0$	$0$	$1$	$3$	$1$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{3}+q^{5}-\beta _{1}q^{7}+(1-\beta _{1})q^{9}+\cdots$
1520.2.a.t	$1520$	$2$	1520.a	1.a	$1$	$4$	$4$	$12.137$	4.4.11344.1	$_{}$	None	None	✓		✓		95.2.a.b	$1$	$0$	$0$	$-2$	$-4$	$-4$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{3}-q^{5}+(-1+\beta _{1})q^{7}+(2-\beta _{3})q^{9}+\cdots$
1520.2.d.a	$1520$	$2$	1520.d	5.b	$2$	$2$	$2$	$12.137$	$\Q(\sqrt{-1}) $	$_{}$	None	None					760.2.d.a	$2$	$0$	$0$	$0$	$-2$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{3}+(-\beta-1)q^{5}+\beta q^{7}-q^{9}+\cdots$
1520.2.d.b	$1520$	$2$	1520.d	5.b	$2$	$2$	$2$	$12.137$	$\Q(\sqrt{-1}) $	$_{}$	None	None					95.2.b.a	$2$	$0$	$0$	$0$	$-2$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta-1)q^{5}-\beta q^{7}+3 q^{9}+4 q^{11}+\cdots$
1520.2.d.c	$1520$	$2$	1520.d	5.b	$2$	$4$	$4$	$12.137$	$\Q(i, \sqrt{5})$	$_{}$	None	None					760.2.d.b	$2$	$0$	$0$	$0$	$-4$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+(-1-\beta _{2})q^{5}+(2\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots$
1520.2.d.d	$1520$	$2$	1520.d	5.b	$2$	$4$	$4$	$12.137$	$\Q(\zeta_{8})$	$_{}$	None	None					760.2.d.c	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(\zeta_{8}+\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+(2\zeta_{8}-\zeta_{8}^{3})q^{5}+\cdots$
1520.2.d.e	$1520$	$2$	1520.d	5.b	$2$	$4$	$4$	$12.137$	$\Q(\zeta_{8})$	$_{}$	None	None					190.2.b.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(\zeta_{8}+\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+(-2\zeta_{8}-\zeta_{8}^{3})q^{5}+\cdots$
1520.2.d.f	$1520$	$2$	1520.d	5.b	$2$	$4$	$4$	$12.137$	$\Q(\sqrt{-2}, \sqrt{5})$	$_{}$	None	None					380.2.c.a	$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+\beta _{2}q^{5}+(\beta _{1}-\beta _{3})q^{7}+\beta _{2}q^{9}+\cdots$
1520.2.d.g	$1520$	$2$	1520.d	5.b	$2$	$4$	$4$	$12.137$	$\Q(\zeta_{8})$	$_{}$	None	None					760.2.d.d	$2$	$0$	$0$	$0$	$4$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta_{2} q^{3}+(-\beta_1+1)q^{5}+(-2\beta_{2}-\beta_1)q^{7}+\cdots$
1520.2.d.h	$1520$	$2$	1520.d	5.b	$2$	$6$	$6$	$12.137$	6.0.16516096.1	$_{}$	None	None					95.2.b.b	$2$	$0$	$0$	$0$	$-1$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{3}+\beta _{3}q^{5}+(\beta _{1}+\beta _{4})q^{7}+(-3+\cdots)q^{9}+\cdots$
1520.2.d.i	$1520$	$2$	1520.d	5.b	$2$	$6$	$6$	$12.137$	6.0.14077504.2	$_{}$	None	None					380.2.c.b	$2$	$0$	$0$	$0$	$-1$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{3}+\beta _{5}q^{5}+(-\beta _{3}-\beta _{4})q^{7}+\cdots$
1520.2.d.j	$1520$	$2$	1520.d	5.b	$2$	$6$	$6$	$12.137$	6.0.5161984.1	$_{}$	None	None					190.2.b.b	$2$	$0$	$0$	$0$	$2$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{5}q^{3}+(\beta _{2}+\beta _{3})q^{5}+(-\beta _{4}+\beta _{5})q^{7}+\cdots$
1520.2.d.k	$1520$	$2$	1520.d	5.b	$2$	$12$	$12$	$12.137$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None			✓		760.2.d.e	$2$	$0$	$0$	$0$	$6$	$0$		$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{11}q^{3}-\beta _{6}q^{5}+(\beta _{5}+\beta _{11})q^{7}+\cdots$
1520.2.g.a	$1520$	$2$	1520.g	380.d	$2$	$2$	$2$	$12.137$	$\Q(\sqrt{-19}) $	$_{}$	$\Q(\sqrt{-19}) $	None		✓			1520.2.g.a	$4$	$0$	$0$	$0$	$-1$	$-6$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-\beta q^{5}-3q^{7}+3q^{9}+(1-2\beta )q^{11}+\cdots$
1520.2.g.b	$1520$	$2$	1520.g	380.d	$2$	$2$	$2$	$12.137$	$\Q(\sqrt{-19}) $	$_{}$	$\Q(\sqrt{-19}) $	None		✓			1520.2.g.a	$4$	$0$	$0$	$0$	$-1$	$6$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+(-1+\beta )q^{5}+3q^{7}+3q^{9}+(1-2\beta )q^{11}+\cdots$
1520.2.g.c	$1520$	$2$	1520.g	380.d	$2$	$4$	$4$	$12.137$	$\Q(\sqrt{-3}, \sqrt{-19})$	$_{}$	$\Q(\sqrt{-19}) $	None		✓			1520.2.g.c	$4$	$0$	$0$	$0$	$1$	$-6$		$2$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{3}q^{5}+(-2-\beta _{1}-\beta _{3})q^{7}+3q^{9}+\cdots$
1520.2.g.d	$1520$	$2$	1520.g	380.d	$2$	$4$	$4$	$12.137$	$\Q(\sqrt{-3}, \sqrt{-19})$	$_{}$	$\Q(\sqrt{-19}) $	None		✓			1520.2.g.c	$4$	$0$	$0$	$0$	$1$	$6$		$2$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{1}q^{5}+(2+\beta _{1}+\beta _{3})q^{7}+3q^{9}+\cdots$

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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.