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 155 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
1300.1.e.a	$1300$	$1$	1300.e	52.b	$2$	$1$	$1$	$0.649$	$\Q$	$D_{3}$	$\Q(\sqrt{-13}) $	None	✓	✓			1300.1.e.a	$2$	$0$	$-1$	$0$	$0$	$1$		$1$		$q-q^{2}+q^{4}+q^{7}-q^{8}+q^{9}-q^{11}+\cdots$
1300.1.e.b	$1300$	$1$	1300.e	52.b	$2$	$1$	$1$	$0.649$	$\Q$	$D_{3}$	$\Q(\sqrt{-13}) $	None	✓	✓			1300.1.e.a	$2$	$0$	$-1$	$0$	$0$	$1$		$1$		$q-q^{2}+q^{4}+q^{7}-q^{8}+q^{9}+q^{11}+\cdots$
1300.1.e.c	$1300$	$1$	1300.e	52.b	$2$	$1$	$1$	$0.649$	$\Q$	$D_{3}$	$\Q(\sqrt{-13}) $	None	✓	✓			1300.1.e.a	$2$	$0$	$1$	$0$	$0$	$-1$		$1$		$q+q^{2}+q^{4}-q^{7}+q^{8}+q^{9}-q^{11}+\cdots$
1300.1.e.d	$1300$	$1$	1300.e	52.b	$2$	$1$	$1$	$0.649$	$\Q$	$D_{3}$	$\Q(\sqrt{-13}) $	None	✓	✓			1300.1.e.a	$2$	$0$	$1$	$0$	$0$	$-1$		$1$		$q+q^{2}+q^{4}-q^{7}+q^{8}+q^{9}+q^{11}+\cdots$
1300.1.e.e	$1300$	$1$	1300.e	52.b	$2$	$2$	$2$	$0.649$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-65}) $	$\Q(\sqrt{65}) $			✓		260.1.g.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-i q^{2}-q^{4}+i q^{8}+q^{9}-i q^{13}+\cdots$
1300.1.g.a	$1300$	$1$	1300.g	260.g	$2$	$2$	$2$	$0.649$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-13}) $	None		✓			1300.1.e.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+i q^{2}-q^{4}-i q^{7}-i q^{8}-q^{9}+\cdots$
1300.1.g.b	$1300$	$1$	1300.g	260.g	$2$	$2$	$2$	$0.649$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-13}) $	None		✓			1300.1.e.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+i q^{2}-q^{4}-i q^{7}-i q^{8}-q^{9}+\cdots$
1300.1.k.a	$1300$	$1$	1300.k	65.g	$4$	$2$	$1$	$0.649$	$\Q(\sqrt{-1}) $	$S_{4}$	None	None		✓			1300.1.t.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$		$q+i q^{3}+(i+1)q^{11}-q^{13}+q^{23}+\cdots$
1300.1.k.b	$1300$	$1$	1300.k	65.g	$4$	$2$	$1$	$0.649$	$\Q(\sqrt{-1}) $	$S_{4}$	None	None		✓			1300.1.t.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$		$q-i q^{3}+(i+1)q^{11}+q^{13}-q^{23}+\cdots$
1300.1.l.a	$1300$	$1$	1300.l	260.l	$4$	$2$	$1$	$0.649$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None			✓	✓	260.1.l.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-i q^{2}-q^{4}+i q^{8}+i q^{9}+q^{13}+\cdots$
1300.1.s.a	$1300$	$1$	1300.s	260.s	$4$	$2$	$1$	$0.649$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None			✓	✓	260.1.l.a	$4$	$0$	$2$	$0$	$0$	$0$		$1$		$q+q^{2}+q^{4}+q^{8}+i q^{9}+i q^{13}+\cdots$
1300.1.t.a	$1300$	$1$	1300.t	13.d	$4$	$2$	$1$	$0.649$	$\Q(\sqrt{-1}) $	$S_{4}$	None	None		✓			1300.1.t.a	$2$	$0$	$0$	$-2$	$0$	$0$		$1$		$q-q^{3}+(i+1)q^{11}-i q^{13}+i q^{23}+\cdots$
1300.1.t.b	$1300$	$1$	1300.t	13.d	$4$	$2$	$1$	$0.649$	$\Q(\sqrt{-1}) $	$S_{4}$	None	None		✓			1300.1.t.a	$2$	$0$	$0$	$2$	$0$	$0$		$1$		$q+q^{3}+(i+1)q^{11}+i q^{13}-i q^{23}+\cdots$
1300.1.w.a	$1300$	$1$	1300.w	260.v	$6$	$4$	$2$	$0.649$	$\Q(\zeta_{12})$	$D_{3}$	$\Q(\sqrt{-1}) $	None			✓	✓	52.1.j.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}+\zeta_{12}^{3}q^{8}+\cdots$
1300.1.z.a	$1300$	$1$	1300.z	52.i	$6$	$4$	$2$	$0.649$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-1}) $	None			✓	✓	260.1.w.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{3}q^{8}-\zeta_{12}^{2}q^{9}+\cdots$
1300.1.bc.a	$1300$	$1$	1300.bc	52.j	$6$	$2$	$1$	$0.649$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-1}) $	None			✓	✓	52.1.j.a	$4$	$0$	$1$	$0$	$0$	$0$		$1$		$q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-q^{8}+\zeta_{6}^{2}q^{9}+\cdots$
1300.1.bd.a	$1300$	$1$	1300.bd	1300.ad	$10$	$4$	$1$	$0.649$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-1}) $	None		✓			1300.1.bd.a	$4$	$0$	$-1$	$0$	$1$	$0$		$1$		$q+\zeta_{10}^{4}q^{2}-\zeta_{10}^{3}q^{4}-\zeta_{10}^{2}q^{5}+\cdots$
1300.1.bd.b	$1300$	$1$	1300.bd	1300.ad	$10$	$4$	$1$	$0.649$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-1}) $	None		✓			1300.1.bd.a	$4$	$0$	$1$	$0$	$-1$	$0$		$1$		$q-\zeta_{10}^{4}q^{2}-\zeta_{10}^{3}q^{4}+\zeta_{10}^{2}q^{5}+\cdots$
1300.1.bm.a	$1300$	$1$	1300.bm	260.ae	$12$	$4$	$1$	$0.649$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-1}) $	None			✓	✓	260.1.be.a	$4$	$0$	$-2$	$0$	$0$	$0$		$1$		$q-\zeta_{12}^{2}q^{2}+\zeta_{12}^{4}q^{4}+q^{8}-\zeta_{12}q^{9}+\cdots$
1300.1.bt.a	$1300$	$1$	1300.bt	260.al	$12$	$4$	$1$	$0.649$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-1}) $	None			✓	✓	260.1.be.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{3}q^{8}+\zeta_{12}^{5}q^{9}+\cdots$
1300.1.ca.a	$1300$	$1$	1300.ca	1300.ba	$20$	$8$	$1$	$0.649$	$\Q(\zeta_{20})$	$D_{20}$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	1300.1.ca.a	$4$	$0$	$0$	$0$	$-2$	$0$		$1$		$q-\zeta_{20}q^{2}+\zeta_{20}^{2}q^{4}+\zeta_{20}^{8}q^{5}-\zeta_{20}^{3}q^{8}+\cdots$
1300.1.cf.a	$1300$	$1$	1300.cf	1300.bf	$20$	$8$	$1$	$0.649$	$\Q(\zeta_{20})$	$D_{20}$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	1300.1.ca.a	$4$	$0$	$2$	$0$	$0$	$0$		$1$		$q-\zeta_{20}^{8}q^{2}-\zeta_{20}^{6}q^{4}+\zeta_{20}^{9}q^{5}+\cdots$
1300.1.cl.a	$1300$	$1$	1300.cl	1300.bl	$30$	$8$	$1$	$0.649$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-1}) $	None		✓			1300.1.cl.a	$4$	$0$	$1$	$0$	$1$	$0$		$1$		$q+\zeta_{30}^{4}q^{2}+\zeta_{30}^{8}q^{4}+\zeta_{30}^{2}q^{5}+\cdots$
1300.1.cl.b	$1300$	$1$	1300.cl	1300.bl	$30$	$8$	$1$	$0.649$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-1}) $	None		✓			1300.1.cl.a	$4$	$0$	$1$	$0$	$1$	$0$		$1$		$q+\zeta_{30}^{4}q^{2}+\zeta_{30}^{8}q^{4}-\zeta_{30}^{7}q^{5}+\cdots$
1300.1.cp.a	$1300$	$1$	1300.cp	1300.bp	$30$	$8$	$1$	$0.649$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-1}) $	None		✓			1300.1.cp.a	$4$	$0$	$-1$	$0$	$1$	$0$		$1$		$q-\zeta_{30}^{2}q^{2}+\zeta_{30}^{4}q^{4}-\zeta_{30}q^{5}-\zeta_{30}^{6}q^{8}+\cdots$
1300.1.cp.b	$1300$	$1$	1300.cp	1300.bp	$30$	$8$	$1$	$0.649$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-1}) $	None		✓			1300.1.cp.a	$4$	$0$	$1$	$0$	$-1$	$0$		$1$		$q+\zeta_{30}^{2}q^{2}+\zeta_{30}^{4}q^{4}+\zeta_{30}^{11}q^{5}+\cdots$
1300.1.ct.a	$1300$	$1$	1300.ct	1300.bt	$60$	$16$	$1$	$0.649$	$\Q(\zeta_{60})$	$D_{60}$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	1300.1.ct.a	$4$	$0$	$-2$	$0$	$0$	$0$		$1$		$q-\zeta_{60}^{8}q^{2}+\zeta_{60}^{16}q^{4}-\zeta_{60}^{29}q^{5}+\cdots$
1300.1.cy.a	$1300$	$1$	1300.cy	1300.by	$60$	$16$	$1$	$0.649$	$\Q(\zeta_{60})$	$D_{60}$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	1300.1.ct.a	$4$	$0$	$0$	$0$	$2$	$0$		$1$		$q-\zeta_{60}^{23}q^{2}-\zeta_{60}^{16}q^{4}+\zeta_{60}^{4}q^{5}+\cdots$
1300.2.a.a	$1300$	$2$	1300.a	1.a	$1$	$1$	$1$	$10.381$	$\Q$	$_{}$	None	None	✓				260.2.a.a	$1$	$1$	$0$	$-2$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-2q^{7}+q^{9}+4q^{11}+q^{13}+\cdots$
1300.2.a.b	$1300$	$2$	1300.a	1.a	$1$	$1$	$1$	$10.381$	$\Q$	$_{}$	None	None	✓	✓			1300.2.a.b	$1$	$1$	$0$	$-1$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{7}-2q^{9}-2q^{11}-q^{13}+\cdots$
1300.2.a.c	$1300$	$2$	1300.a	1.a	$1$	$1$	$1$	$10.381$	$\Q$	$_{}$	None	None	✓	✓			1300.2.a.c	$1$	$0$	$0$	$0$	$0$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{7}-3q^{9}+3q^{11}+q^{13}-q^{17}+\cdots$
1300.2.a.d	$1300$	$2$	1300.a	1.a	$1$	$1$	$1$	$10.381$	$\Q$	$_{}$	None	None	✓				52.2.a.a	$1$	$1$	$0$	$0$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{7}-3q^{9}-2q^{11}+q^{13}-6q^{17}+\cdots$
1300.2.a.e	$1300$	$2$	1300.a	1.a	$1$	$1$	$1$	$10.381$	$\Q$	$_{}$	None	None	✓	✓			1300.2.a.c	$1$	$0$	$0$	$0$	$0$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{7}-3q^{9}+3q^{11}-q^{13}+q^{17}+\cdots$
1300.2.a.f	$1300$	$2$	1300.a	1.a	$1$	$1$	$1$	$10.381$	$\Q$	$_{}$	None	None	✓	✓			1300.2.a.b	$1$	$1$	$0$	$1$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{7}-2q^{9}-2q^{11}+q^{13}+\cdots$
1300.2.a.g	$1300$	$2$	1300.a	1.a	$1$	$2$	$2$	$10.381$	$\Q(\sqrt{33}) $	$_{}$	None	None	✓	✓			1300.2.a.g	$1$	$0$	$0$	$-1$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+(1-\beta )q^{7}+(5+\beta )q^{9}+(-1+\cdots)q^{11}+\cdots$
1300.2.a.h	$1300$	$2$	1300.a	1.a	$1$	$2$	$2$	$10.381$	$\Q(\sqrt{33}) $	$_{}$	None	None	✓	✓			1300.2.a.g	$1$	$0$	$0$	$1$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(-1+\beta )q^{7}+(5+\beta )q^{9}+(-1+\cdots)q^{11}+\cdots$
1300.2.a.i	$1300$	$2$	1300.a	1.a	$1$	$3$	$3$	$10.381$	3.3.564.1	$_{}$	None	None	✓		✓		260.2.a.b	$1$	$0$	$0$	$-2$	$0$	$2$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{3}+(1+\beta _{1})q^{7}+(4+\beta _{1}+\cdots)q^{9}+\cdots$
1300.2.a.j	$1300$	$2$	1300.a	1.a	$1$	$3$	$3$	$10.381$	3.3.148.1	$_{}$	None	None	✓		✓		260.2.c.a	$1$	$1$	$0$	$0$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{3}+(-1-\beta _{1}-\beta _{2})q^{7}+(-\beta _{1}+\cdots)q^{9}+\cdots$
1300.2.a.k	$1300$	$2$	1300.a	1.a	$1$	$3$	$3$	$10.381$	3.3.148.1	$_{}$	None	None	✓		✓		260.2.c.a	$1$	$0$	$0$	$0$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{3}+(1+\beta _{1}+\beta _{2})q^{7}+(-\beta _{1}+\cdots)q^{9}+\cdots$
1300.2.c.a	$1300$	$2$	1300.c	5.b	$2$	$2$	$2$	$10.381$	$\Q(\sqrt{-1}) $	$_{}$	None	None					260.2.a.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2 i q^{3}-2 i q^{7}-q^{9}+4 q^{11}+\cdots$
1300.2.c.b	$1300$	$2$	1300.c	5.b	$2$	$2$	$2$	$10.381$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			1300.2.a.b	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{3}+2 i q^{7}+2 q^{9}-2 q^{11}+\cdots$
1300.2.c.c	$1300$	$2$	1300.c	5.b	$2$	$2$	$2$	$10.381$	$\Q(\sqrt{-1}) $	$_{}$	None	None					52.2.a.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2 i q^{7}+3 q^{9}-2 q^{11}-i q^{13}+\cdots$
1300.2.c.d	$1300$	$2$	1300.c	5.b	$2$	$2$	$2$	$10.381$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			1300.2.a.c	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+3 i q^{7}+3 q^{9}+3 q^{11}+i q^{13}+\cdots$
1300.2.c.e	$1300$	$2$	1300.c	5.b	$2$	$4$	$4$	$10.381$	$\Q(i, \sqrt{33})$	$_{}$	None	None		✓			1300.2.a.g	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{2})q^{7}+(-6+\beta _{3})q^{9}+\cdots$
1300.2.c.f	$1300$	$2$	1300.c	5.b	$2$	$6$	$6$	$10.381$	6.0.5089536.1	$_{}$	None	None			✓		260.2.a.b	$2$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{1}-\beta _{4})q^{3}+(-\beta _{4}-\beta _{5})q^{7}+\cdots$
1300.2.d.a	$1300$	$2$	1300.d	65.d	$2$	$4$	$4$	$10.381$	$\Q(\zeta_{12})$	$_{}$	None	None		✓			1300.2.f.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-2\beta_1 q^{3}-\beta_{3} q^{7}-q^{9}+3\beta_{2} q^{11}+\cdots$
1300.2.d.b	$1300$	$2$	1300.d	65.d	$2$	$4$	$4$	$10.381$	$\Q(\zeta_{12})$	$_{}$	None	None		✓			1300.2.f.b	$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta_1 q^{3}+\beta_{3} q^{7}+2 q^{9}+(\beta_{3}+\beta_1)q^{13}+\cdots$
1300.2.d.c	$1300$	$2$	1300.d	65.d	$2$	$6$	$6$	$10.381$	6.0.9144576.1	$_{}$	None	None					260.2.f.a	$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+\beta _{3}q^{7}+(-1+\beta _{3})q^{9}+(\beta _{4}+\cdots)q^{11}+\cdots$
1300.2.d.d	$1300$	$2$	1300.d	65.d	$2$	$6$	$6$	$10.381$	6.0.9144576.1	$_{}$	None	None					260.2.f.a	$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}-\beta _{3}q^{7}+(-1+\beta _{3})q^{9}+(-\beta _{4}+\cdots)q^{11}+\cdots$
1300.2.f.a	$1300$	$2$	1300.f	13.b	$2$	$2$	$2$	$10.381$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			1300.2.f.a	$2$	$0$	$0$	$-4$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-2 q^{3}-\beta q^{7}+q^{9}+3\beta q^{11}+(-2\beta+1)q^{13}+\cdots$

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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.