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 55 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
3325.1.n.a	$3325$	$1$	3325.n	665.n	$4$	$2$	$1$	$1.659$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-19}) $	None					665.1.n.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-i q^{4}-i q^{7}-i q^{9}-q^{16}+(-i-1)q^{17}+\cdots$
3325.1.n.b	$3325$	$1$	3325.n	665.n	$4$	$2$	$1$	$1.659$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-19}) $	None					665.1.n.a	$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q-i q^{4}+q^{7}-i q^{9}-q^{16}+(i+1)q^{17}+\cdots$
3325.1.y.a	$3325$	$1$	3325.y	665.x	$6$	$4$	$2$	$1.659$	$\Q(\zeta_{12})$	$D_{3}$	$\Q(\sqrt{-19}) $	None			✓	✓	133.1.r.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{12}^{4}q^{4}+\zeta_{12}^{5}q^{7}+\zeta_{12}^{2}q^{9}+\cdots$
3325.1.bc.a	$3325$	$1$	3325.bc	133.m	$6$	$4$	$2$	$1.659$	$\Q(\zeta_{12})$	$A_{4}$	None	None			✓	✓	133.1.m.a	$4$	$0$	$2$	$0$	$0$	$0$		$1$		$q+\zeta_{12}^{2}q^{2}+\zeta_{12}^{5}q^{3}-\zeta_{12}q^{6}-\zeta_{12}^{3}q^{7}+\cdots$
3325.1.bi.a	$3325$	$1$	3325.bi	665.ah	$6$	$4$	$2$	$1.659$	$\Q(\zeta_{12})$	$A_{4}$	None	None					133.1.m.a	$4$	$0$	$0$	$-2$	$0$	$-4$		$1$		$q-\zeta_{12}^{5}q^{2}-\zeta_{12}^{2}q^{3}-\zeta_{12}q^{6}-q^{7}+\cdots$
3325.1.bi.b	$3325$	$1$	3325.bi	665.ah	$6$	$4$	$2$	$1.659$	$\Q(\zeta_{12})$	$A_{4}$	None	None					133.1.m.a	$4$	$0$	$0$	$2$	$0$	$4$		$1$		$q+\zeta_{12}^{5}q^{2}+\zeta_{12}^{2}q^{3}-\zeta_{12}q^{6}+q^{7}+\cdots$
3325.1.bm.a	$3325$	$1$	3325.bm	133.r	$6$	$2$	$1$	$1.659$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-19}) $	None					133.1.r.a	$4$	$0$	$0$	$0$	$0$	$1$		$1$		$q-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}+\zeta_{6}q^{11}+\cdots$
3325.1.bm.b	$3325$	$1$	3325.bm	133.r	$6$	$4$	$2$	$1.659$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-19}) $	None			✓		665.1.x.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{12}^{4}q^{4}+\zeta_{12}^{5}q^{7}-\zeta_{12}^{2}q^{9}+\cdots$
3325.1.ce.a	$3325$	$1$	3325.ce	665.aw	$12$	$8$	$2$	$1.659$	$\Q(\zeta_{24})$	$A_{4}$	None	None		✓	✓	✓	3325.1.ce.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}q^{3}-\zeta_{24}^{6}q^{4}+\zeta_{24}^{3}q^{7}+\zeta_{24}^{8}q^{11}+\cdots$
3325.1.ci.a	$3325$	$1$	3325.ci	665.ba	$12$	$4$	$1$	$1.659$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-19}) $	None					665.1.ca.a	$4$	$0$	$0$	$0$	$0$	$-2$		$1$		$q-\zeta_{12}q^{4}-\zeta_{12}^{2}q^{7}-\zeta_{12}^{5}q^{9}+(-\zeta_{12}^{3}+\cdots)q^{11}+\cdots$
3325.1.ci.b	$3325$	$1$	3325.ci	665.ba	$12$	$4$	$1$	$1.659$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-19}) $	None					665.1.ca.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{12}q^{4}-\zeta_{12}^{5}q^{7}-\zeta_{12}^{5}q^{9}+(\zeta_{12}^{3}+\cdots)q^{11}+\cdots$
3325.1.ck.a	$3325$	$1$	3325.ck	665.bc	$12$	$8$	$2$	$1.659$	$\Q(\zeta_{24})$	$A_{4}$	None	None		✓	✓	✓	3325.1.ce.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}^{9}q^{3}+\zeta_{24}^{10}q^{4}+\zeta_{24}^{3}q^{7}+\cdots$
3325.1.du.a	$3325$	$1$	3325.du	3325.cu	$20$	$8$	$1$	$1.659$	$\Q(\zeta_{20})$	$D_{20}$	$\Q(\sqrt{-19}) $	None		✓			3325.1.du.a	$4$	$0$	$0$	$0$	$-2$	$0$		$1$		$q+\zeta_{20}q^{4}-\zeta_{20}^{2}q^{5}+\zeta_{20}^{7}q^{7}-\zeta_{20}^{7}q^{9}+\cdots$
3325.1.du.b	$3325$	$1$	3325.du	3325.cu	$20$	$8$	$1$	$1.659$	$\Q(\zeta_{20})$	$D_{20}$	$\Q(\sqrt{-19}) $	None		✓			3325.1.du.a	$4$	$0$	$0$	$0$	$2$	$2$		$1$		$q+\zeta_{20}q^{4}+\zeta_{20}^{2}q^{5}-\zeta_{20}^{8}q^{7}-\zeta_{20}^{7}q^{9}+\cdots$
3325.1.ec.a	$3325$	$1$	3325.ec	3325.dc	$30$	$8$	$1$	$1.659$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-19}) $	None		✓			3325.1.ec.a	$4$	$0$	$0$	$0$	$-2$	$1$		$1$		$q+\zeta_{30}^{8}q^{4}+\zeta_{30}^{6}q^{5}+\zeta_{30}^{4}q^{7}+\cdots$
3325.1.ec.b	$3325$	$1$	3325.ec	3325.dc	$30$	$8$	$1$	$1.659$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-19}) $	None		✓			3325.1.ec.a	$4$	$0$	$0$	$0$	$1$	$1$		$1$		$q+\zeta_{30}^{8}q^{4}-\zeta_{30}^{11}q^{5}-\zeta_{30}q^{7}+\cdots$
3325.1.eq.a	$3325$	$1$	3325.eq	3325.dq	$30$	$8$	$1$	$1.659$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-19}) $	None		✓			3325.1.eq.a	$4$	$0$	$0$	$0$	$-2$	$1$		$1$		$q+\zeta_{30}^{7}q^{4}-\zeta_{30}^{9}q^{5}-\zeta_{30}^{11}q^{7}+\cdots$
3325.1.eq.b	$3325$	$1$	3325.eq	3325.dq	$30$	$8$	$1$	$1.659$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-19}) $	None		✓			3325.1.eq.a	$4$	$0$	$0$	$0$	$1$	$-1$		$1$		$q+\zeta_{30}^{7}q^{4}+\zeta_{30}^{4}q^{5}-\zeta_{30}^{14}q^{7}+\cdots$
3325.1.fx.a	$3325$	$1$	3325.fx	3325.ex	$60$	$16$	$1$	$1.659$	$\Q(\zeta_{60})$	$D_{60}$	$\Q(\sqrt{-19}) $	None		✓			3325.1.fx.a	$4$	$0$	$0$	$0$	$2$	$0$		$1$		$q-\zeta_{60}^{23}q^{4}-\zeta_{60}^{26}q^{5}-\zeta_{60}q^{7}+\cdots$
3325.1.fx.b	$3325$	$1$	3325.fx	3325.ex	$60$	$16$	$1$	$1.659$	$\Q(\zeta_{60})$	$D_{60}$	$\Q(\sqrt{-19}) $	None		✓			3325.1.fx.a	$4$	$0$	$0$	$0$	$4$	$-2$		$1$		$q-\zeta_{60}^{23}q^{4}+\zeta_{60}^{6}q^{5}-\zeta_{60}^{4}q^{7}+\cdots$
3325.2.a.a	$3325$	$2$	3325.a	1.a	$1$	$1$	$1$	$26.550$	$\Q$	$_{}$	None	None	✓				665.2.b.a	$1$	$1$	$-2$	$-3$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-3q^{3}+2q^{4}+6q^{6}-q^{7}+\cdots$
3325.2.a.b	$3325$	$2$	3325.a	1.a	$1$	$1$	$1$	$26.550$	$\Q$	$_{}$	None	None	✓	✓			3325.2.a.b	$1$	$1$	$-1$	$-1$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}-q^{4}+q^{6}+q^{7}+3q^{8}+\cdots$
3325.2.a.c	$3325$	$2$	3325.a	1.a	$1$	$1$	$1$	$26.550$	$\Q$	$_{}$	None	None	✓	✓			3325.2.a.c	$1$	$0$	$-1$	$0$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}-q^{7}+3q^{8}-3q^{9}+6q^{11}+\cdots$
3325.2.a.d	$3325$	$2$	3325.a	1.a	$1$	$1$	$1$	$26.550$	$\Q$	$_{}$	None	None	✓				665.2.a.e	$1$	$1$	$-1$	$0$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+q^{7}+3q^{8}-3q^{9}-4q^{11}+\cdots$
3325.2.a.e	$3325$	$2$	3325.a	1.a	$1$	$1$	$1$	$26.550$	$\Q$	$_{}$	None	None	✓				665.2.a.d	$1$	$1$	$-1$	$1$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}-q^{4}-q^{6}-q^{7}+3q^{8}+\cdots$
3325.2.a.f	$3325$	$2$	3325.a	1.a	$1$	$1$	$1$	$26.550$	$\Q$	$_{}$	None	None	✓	✓			3325.2.a.c	$1$	$0$	$1$	$0$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+q^{7}-3q^{8}-3q^{9}+6q^{11}+\cdots$
3325.2.a.g	$3325$	$2$	3325.a	1.a	$1$	$1$	$1$	$26.550$	$\Q$	$_{}$	None	None	✓	✓			3325.2.a.b	$1$	$1$	$1$	$1$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}-q^{4}+q^{6}-q^{7}-3q^{8}+\cdots$
3325.2.a.h	$3325$	$2$	3325.a	1.a	$1$	$1$	$1$	$26.550$	$\Q$	$_{}$	None	None	✓				665.2.a.c	$1$	$0$	$1$	$1$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}-q^{4}+q^{6}-q^{7}-3q^{8}+\cdots$
3325.2.a.i	$3325$	$2$	3325.a	1.a	$1$	$1$	$1$	$26.550$	$\Q$	$_{}$	None	None	✓				665.2.a.b	$1$	$0$	$2$	$-3$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-3q^{3}+2q^{4}-6q^{6}-q^{7}+\cdots$
3325.2.a.j	$3325$	$2$	3325.a	1.a	$1$	$1$	$1$	$26.550$	$\Q$	$_{}$	None	None	✓				665.2.a.a	$1$	$1$	$2$	$1$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+q^{3}+2q^{4}+2q^{6}-q^{7}-2q^{9}+\cdots$
3325.2.a.k	$3325$	$2$	3325.a	1.a	$1$	$1$	$1$	$26.550$	$\Q$	$_{}$	None	None	✓				665.2.b.a	$1$	$0$	$2$	$3$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+3q^{3}+2q^{4}+6q^{6}+q^{7}+\cdots$
3325.2.a.l	$3325$	$2$	3325.a	1.a	$1$	$2$	$2$	$26.550$	$\Q(\sqrt{33}) $	$_{}$	None	None	✓	✓			3325.2.a.l	$1$	$0$	$-2$	$1$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(1-\beta )q^{3}-q^{4}+(-1+\beta )q^{6}+\cdots$
3325.2.a.m	$3325$	$2$	3325.a	1.a	$1$	$2$	$2$	$26.550$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				133.2.a.c	$1$	$1$	$-1$	$-3$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(-2+\beta )q^{3}+(-1+\beta )q^{4}+\cdots$
3325.2.a.n	$3325$	$2$	3325.a	1.a	$1$	$2$	$2$	$26.550$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓				133.2.a.b	$1$	$0$	$1$	$3$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(2-\beta )q^{3}+(1+\beta )q^{4}+(-3+\cdots)q^{6}+\cdots$
3325.2.a.o	$3325$	$2$	3325.a	1.a	$1$	$2$	$2$	$26.550$	$\Q(\sqrt{33}) $	$_{}$	None	None	✓	✓			3325.2.a.l	$1$	$0$	$2$	$-1$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-1+\beta )q^{3}-q^{4}+(-1+\beta )q^{6}+\cdots$
3325.2.a.p	$3325$	$2$	3325.a	1.a	$1$	$2$	$2$	$26.550$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓				665.2.a.f	$1$	$1$	$2$	$1$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta q^{3}-q^{4}+\beta q^{6}+q^{7}-3q^{8}+\cdots$
3325.2.a.q	$3325$	$2$	3325.a	1.a	$1$	$2$	$2$	$26.550$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				133.2.a.a	$1$	$0$	$3$	$3$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+(1+\beta )q^{3}+3\beta q^{4}+(2+\cdots)q^{6}+\cdots$
3325.2.a.r	$3325$	$2$	3325.a	1.a	$1$	$3$	$3$	$26.550$	3.3.229.1	$_{}$	None	None	✓				133.2.a.d	$1$	$1$	$-2$	$-3$	$0$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{2}+(-1+\beta _{1})q^{3}+(2+\cdots)q^{4}+\cdots$
3325.2.a.s	$3325$	$2$	3325.a	1.a	$1$	$3$	$3$	$26.550$	3.3.148.1	$_{}$	None	None	✓				665.2.a.g	$1$	$0$	$-1$	$-1$	$0$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{1}q^{3}+(\beta _{1}+\beta _{2})q^{4}+(2+\cdots)q^{6}+\cdots$
3325.2.a.t	$3325$	$2$	3325.a	1.a	$1$	$4$	$4$	$26.550$	4.4.11348.1	$_{}$	None	None	✓				665.2.a.h	$1$	$1$	$-1$	$-2$	$0$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-1-\beta _{3})q^{3}+(1+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
3325.2.a.u	$3325$	$2$	3325.a	1.a	$1$	$6$	$6$	$26.550$	6.6.79799552.1	$_{}$	None	None	✓				665.2.a.i	$1$	$0$	$1$	$4$	$0$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{4})q^{3}+(1+\beta _{2})q^{4}+\cdots$
3325.2.a.v	$3325$	$2$	3325.a	1.a	$1$	$7$	$7$	$26.550$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓				665.2.a.j	$1$	$1$	$-3$	$-1$	$0$	$-7$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{3}q^{3}+(2+\beta _{2})q^{4}+(-1+\cdots)q^{6}+\cdots$
3325.2.a.w	$3325$	$2$	3325.a	1.a	$1$	$7$	$7$	$26.550$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	✓	✓		3325.2.a.w	$1$	$1$	$0$	$-1$	$0$	$7$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}-\beta _{1}q^{3}+(1+\beta _{2}+\beta _{5}-\beta _{6})q^{4}+\cdots$
3325.2.a.x	$3325$	$2$	3325.a	1.a	$1$	$7$	$7$	$26.550$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	✓			3325.2.a.w	$1$	$1$	$0$	$1$	$0$	$-7$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}+\beta _{1}q^{3}+(1+\beta _{2}+\beta _{5}-\beta _{6})q^{4}+\cdots$
3325.2.a.y	$3325$	$2$	3325.a	1.a	$1$	$8$	$8$	$26.550$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓				665.2.a.k	$1$	$0$	$-2$	$3$	$0$	$-8$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{2}q^{3}+(1-\beta _{2}+\beta _{3})q^{4}+\cdots$
3325.2.a.z	$3325$	$2$	3325.a	1.a	$1$	$8$	$8$	$26.550$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	✓			3325.2.a.z	$1$	$0$	$0$	$-2$	$0$	$-8$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{5}q^{3}+(2+\beta _{1}+\beta _{4}-\beta _{5}+\cdots)q^{4}+\cdots$
3325.2.a.ba	$3325$	$2$	3325.a	1.a	$1$	$8$	$8$	$26.550$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	✓	✓		3325.2.a.ba	$1$	$1$	$0$	$0$	$0$	$-8$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{4}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{6}+\cdots$
3325.2.a.bb	$3325$	$2$	3325.a	1.a	$1$	$8$	$8$	$26.550$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	✓			3325.2.a.ba	$1$	$1$	$0$	$0$	$0$	$8$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{4}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{6}+\cdots$
3325.2.a.bc	$3325$	$2$	3325.a	1.a	$1$	$8$	$8$	$26.550$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	✓			3325.2.a.z	$1$	$0$	$0$	$2$	$0$	$8$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{5}q^{3}+(2+\beta _{1}+\beta _{4}-\beta _{5}+\cdots)q^{4}+\cdots$
3325.2.a.bd	$3325$	$2$	3325.a	1.a	$1$	$9$	$9$	$26.550$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	$_{}$	None	None	✓	✓			3325.2.a.bd	$1$	$0$	$0$	$-3$	$0$	$-9$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{4}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{6}+\cdots$

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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.