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 51 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
2132.1.f.a	$2132$	$1$	2132.f	2132.f	$2$	$1$	$1$	$1.064$	$\Q$	$D_{3}$	$\Q(\sqrt{-533}) $	None	✓	✓			2132.1.f.a	$2$	$0$	$-1$	$-1$	$0$	$0$		$1$		$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}-q^{12}+\cdots$
2132.1.f.b	$2132$	$1$	2132.f	2132.f	$2$	$1$	$1$	$1.064$	$\Q$	$D_{3}$	$\Q(\sqrt{-533}) $	None	✓	✓			2132.1.f.a	$2$	$0$	$-1$	$1$	$0$	$0$		$1$		$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{12}+\cdots$
2132.1.f.c	$2132$	$1$	2132.f	2132.f	$2$	$1$	$1$	$1.064$	$\Q$	$D_{3}$	$\Q(\sqrt{-533}) $	None	✓	✓			2132.1.f.a	$2$	$0$	$1$	$-1$	$0$	$0$		$1$		$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}-q^{12}+\cdots$
2132.1.f.d	$2132$	$1$	2132.f	2132.f	$2$	$1$	$1$	$1.064$	$\Q$	$D_{3}$	$\Q(\sqrt{-533}) $	None	✓	✓			2132.1.f.a	$2$	$0$	$1$	$1$	$0$	$0$		$1$		$q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{12}+\cdots$
2132.1.r.a	$2132$	$1$	2132.r	2132.r	$4$	$2$	$1$	$1.064$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		✓			2132.1.r.a	$4$	$0$	$-2$	$0$	$0$	$0$		$1$		$q-q^{2}+q^{4}-q^{8}-iq^{9}-iq^{13}+q^{16}+\cdots$
2132.1.r.b	$2132$	$1$	2132.r	2132.r	$4$	$2$	$1$	$1.064$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		✓			2132.1.r.a	$4$	$0$	$2$	$0$	$0$	$0$		$1$		$q+q^{2}+q^{4}+q^{8}-iq^{9}+q^{13}+q^{16}+\cdots$
2132.1.r.c	$2132$	$1$	2132.r	2132.r	$4$	$4$	$2$	$1.064$	$\Q(\zeta_{8})$	$S_{4}$	None	None		✓			2132.1.r.c	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{8}^{2}q^{2}-\zeta_{8}^{3}q^{3}-q^{4}+(\zeta_{8}-\zeta_{8}^{3}+\cdots)q^{5}+\cdots$
2132.1.r.d	$2132$	$1$	2132.r	2132.r	$4$	$4$	$2$	$1.064$	$\Q(\zeta_{8})$	$S_{4}$	None	None		✓			2132.1.r.c	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}^{2}q^{2}-\zeta_{8}^{3}q^{3}-q^{4}+(-\zeta_{8}+\zeta_{8}^{3}+\cdots)q^{5}+\cdots$
2132.1.y.a	$2132$	$1$	2132.y	2132.y	$6$	$2$	$1$	$1.064$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-1}) $	None		✓			2132.1.y.a	$4$	$0$	$-1$	$0$	$2$	$0$		$1$		$q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+q^{5}+q^{8}-\zeta_{6}^{2}q^{9}+\cdots$
2132.1.y.b	$2132$	$1$	2132.y	2132.y	$6$	$2$	$1$	$1.064$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-1}) $	None		✓			2132.1.y.a	$4$	$0$	$-1$	$0$	$2$	$0$		$1$		$q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+q^{5}+q^{8}-\zeta_{6}^{2}q^{9}+\cdots$
2132.1.bd.a	$2132$	$1$	2132.bd	2132.ad	$8$	$4$	$1$	$1.064$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	2132.1.bd.a	$4$	$0$	$4$	$0$	$0$	$0$		$1$		$q+q^{2}+q^{4}+(-\zeta_{8}-\zeta_{8}^{3})q^{5}+q^{8}+\cdots$
2132.1.bj.a	$2132$	$1$	2132.bj	2132.aj	$8$	$4$	$1$	$1.064$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	2132.1.bd.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}^{2}q^{2}-q^{4}+(\zeta_{8}-\zeta_{8}^{3})q^{5}+\zeta_{8}^{2}q^{8}+\cdots$
2132.1.cb.a	$2132$	$1$	2132.cb	2132.bb	$12$	$4$	$1$	$1.064$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-1}) $	None		✓			2132.1.cb.a	$4$	$0$	$-2$	$0$	$0$	$0$		$1$		$q+\zeta_{12}^{4}q^{2}-\zeta_{12}^{2}q^{4}+(\zeta_{12}-\zeta_{12}^{5}+\cdots)q^{5}+\cdots$
2132.1.cb.b	$2132$	$1$	2132.cb	2132.bb	$12$	$4$	$1$	$1.064$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-1}) $	None		✓			2132.1.cb.a	$4$	$0$	$2$	$0$	$0$	$0$		$1$		$q-\zeta_{12}^{4}q^{2}-\zeta_{12}^{2}q^{4}+(\zeta_{12}-\zeta_{12}^{5}+\cdots)q^{5}+\cdots$
2132.1.ci.a	$2132$	$1$	2132.ci	2132.bi	$20$	$8$	$1$	$1.064$	$\Q(\zeta_{20})$	$D_{20}$	$\Q(\sqrt{-1}) $	None		✓			2132.1.ci.a	$4$	$0$	$-2$	$0$	$0$	$0$		$1$		$q+\zeta_{20}^{4}q^{2}+\zeta_{20}^{8}q^{4}+(-\zeta_{20}^{7}-\zeta_{20}^{9}+\cdots)q^{5}+\cdots$
2132.1.ci.b	$2132$	$1$	2132.ci	2132.bi	$20$	$8$	$1$	$1.064$	$\Q(\zeta_{20})$	$D_{20}$	$\Q(\sqrt{-1}) $	None		✓			2132.1.ci.a	$4$	$0$	$2$	$0$	$0$	$0$		$1$		$q-\zeta_{20}^{4}q^{2}+\zeta_{20}^{8}q^{4}+(\zeta_{20}^{7}+\zeta_{20}^{9}+\cdots)q^{5}+\cdots$
2132.1.cs.a	$2132$	$1$	2132.cs	2132.bs	$24$	$8$	$1$	$1.064$	$\Q(\zeta_{24})$	$D_{24}$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	2132.1.cs.a	$4$	$0$	$-4$	$0$	$0$	$0$		$1$		$q-\zeta_{24}^{4}q^{2}+\zeta_{24}^{8}q^{4}+(\zeta_{24}^{5}+\zeta_{24}^{7}+\cdots)q^{5}+\cdots$
2132.1.cy.a	$2132$	$1$	2132.cy	2132.by	$24$	$8$	$1$	$1.064$	$\Q(\zeta_{24})$	$D_{24}$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	2132.1.cs.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}^{10}q^{2}-\zeta_{24}^{8}q^{4}+(\zeta_{24}^{5}-\zeta_{24}^{7}+\cdots)q^{5}+\cdots$
2132.1.cz.a	$2132$	$1$	2132.cz	2132.bz	$30$	$8$	$1$	$1.064$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-1}) $	None		✓			2132.1.cz.a	$4$	$0$	$1$	$0$	$-2$	$0$		$1$		$q+\zeta_{30}^{8}q^{2}-\zeta_{30}q^{4}+(-\zeta_{30}^{4}-\zeta_{30}^{8}+\cdots)q^{5}+\cdots$
2132.1.cz.b	$2132$	$1$	2132.cz	2132.bz	$30$	$8$	$1$	$1.064$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-1}) $	None		✓			2132.1.cz.a	$4$	$0$	$1$	$0$	$-2$	$0$		$1$		$q+\zeta_{30}^{8}q^{2}-\zeta_{30}q^{4}+(\zeta_{30}^{13}-\zeta_{30}^{14}+\cdots)q^{5}+\cdots$
2132.1.dd.a	$2132$	$1$	2132.dd	2132.cd	$30$	$8$	$1$	$1.064$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-1}) $	None		✓			2132.1.dd.a	$4$	$0$	$1$	$0$	$2$	$0$		$1$		$q+\zeta_{30}^{14}q^{2}-\zeta_{30}^{13}q^{4}+(-\zeta_{30}^{7}+\cdots)q^{5}+\cdots$
2132.1.dd.b	$2132$	$1$	2132.dd	2132.cd	$30$	$8$	$1$	$1.064$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-1}) $	None		✓			2132.1.dd.a	$4$	$0$	$1$	$0$	$2$	$0$		$1$		$q+\zeta_{30}^{14}q^{2}-\zeta_{30}^{13}q^{4}+(\zeta_{30}^{2}+\zeta_{30}^{4}+\cdots)q^{5}+\cdots$
2132.1.dd.c	$2132$	$1$	2132.dd	2132.cd	$30$	$16$	$2$	$1.064$	$\Q(\zeta_{60})$	$A_{5}$	None	None		✓	✓		2132.1.dd.c	$8$	$0$	$0$	$0$	$8$	$0$		$1$		$q+\zeta_{60}^{19}q^{2}-\zeta_{60}^{25}q^{3}-\zeta_{60}^{8}q^{4}+\cdots$
2132.1.dh.a	$2132$	$1$	2132.dh	2132.ch	$40$	$16$	$1$	$1.064$	$\Q(\zeta_{40})$	$D_{40}$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	2132.1.dh.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{40}^{18}q^{2}-\zeta_{40}^{16}q^{4}+(\zeta_{40}^{13}+\cdots)q^{5}+\cdots$
2132.1.dn.a	$2132$	$1$	2132.dn	2132.cn	$40$	$16$	$1$	$1.064$	$\Q(\zeta_{40})$	$D_{40}$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	2132.1.dh.a	$4$	$0$	$-4$	$0$	$0$	$0$		$1$		$q-\zeta_{40}^{12}q^{2}-\zeta_{40}^{4}q^{4}+(-\zeta_{40}+\zeta_{40}^{7}+\cdots)q^{5}+\cdots$
2132.1.dq.a	$2132$	$1$	2132.dq	2132.cq	$60$	$16$	$1$	$1.064$	$\Q(\zeta_{60})$	$D_{60}$	$\Q(\sqrt{-1}) $	None		✓			2132.1.dq.a	$4$	$0$	$-2$	$0$	$0$	$0$		$1$		$q-\zeta_{60}^{8}q^{2}+\zeta_{60}^{16}q^{4}+(-\zeta_{60}^{19}+\cdots)q^{5}+\cdots$
2132.1.dq.b	$2132$	$1$	2132.dq	2132.cq	$60$	$16$	$1$	$1.064$	$\Q(\zeta_{60})$	$D_{60}$	$\Q(\sqrt{-1}) $	None		✓			2132.1.dq.a	$4$	$0$	$2$	$0$	$0$	$0$		$1$		$q+\zeta_{60}^{8}q^{2}+\zeta_{60}^{16}q^{4}+(\zeta_{60}^{13}-\zeta_{60}^{29}+\cdots)q^{5}+\cdots$
2132.1.ea.a	$2132$	$1$	2132.ea	2132.da	$120$	$32$	$1$	$1.064$	$\Q(\zeta_{120})$	$D_{120}$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	2132.1.ea.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{120}^{46}q^{2}-\zeta_{120}^{32}q^{4}+(\zeta_{120}+\zeta_{120}^{23}+\cdots)q^{5}+\cdots$
2132.1.eg.a	$2132$	$1$	2132.eg	2132.dg	$120$	$32$	$1$	$1.064$	$\Q(\zeta_{120})$	$D_{120}$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	2132.1.ea.a	$4$	$0$	$4$	$0$	$0$	$0$		$1$		$q+\zeta_{120}^{8}q^{2}+\zeta_{120}^{16}q^{4}+(-\zeta_{120}^{13}+\cdots)q^{5}+\cdots$
2132.2.a.a	$2132$	$2$	2132.a	1.a	$1$	$1$	$1$	$17.024$	$\Q$	$_{}$	None	None	✓	✓			2132.2.a.a	$1$	$1$	$0$	$-2$	$2$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+2q^{5}+4q^{7}+q^{9}-q^{13}+\cdots$
2132.2.a.b	$2132$	$2$	2132.a	1.a	$1$	$1$	$1$	$17.024$	$\Q$	$_{}$	None	None	✓	✓			2132.2.a.b	$1$	$0$	$0$	$1$	$4$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+4q^{5}+2q^{7}-2q^{9}+4q^{11}+\cdots$
2132.2.a.c	$2132$	$2$	2132.a	1.a	$1$	$1$	$1$	$17.024$	$\Q$	$_{}$	None	None	✓	✓			2132.2.a.c	$1$	$0$	$0$	$3$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}-2q^{7}+6q^{9}+q^{13}-2q^{17}+\cdots$
2132.2.a.d	$2132$	$2$	2132.a	1.a	$1$	$7$	$7$	$17.024$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	2132.2.a.d	$1$	$1$	$0$	$-2$	$-4$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(-1+\beta _{4})q^{5}+(\beta _{3}+\beta _{6})q^{7}+\cdots$
2132.2.a.e	$2132$	$2$	2132.a	1.a	$1$	$8$	$8$	$17.024$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	✓	✓		2132.2.a.e	$1$	$0$	$0$	$-3$	$-4$	$6$	$-$	$3^{2}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+\beta _{3}q^{5}+(1-\beta _{6})q^{7}+(2+\beta _{3}+\cdots)q^{9}+\cdots$
2132.2.a.f	$2132$	$2$	2132.a	1.a	$1$	$9$	$9$	$17.024$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	$_{}$	None	None	✓	✓	✓		2132.2.a.f	$1$	$1$	$0$	$2$	$-10$	$-10$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{6}q^{3}+(-1+\beta _{3})q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots$
2132.2.a.g	$2132$	$2$	2132.a	1.a	$1$	$13$	$13$	$17.024$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	$_{}$	None	None	✓	✓	✓		2132.2.a.g	$1$	$0$	$0$	$-3$	$4$	$10$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+\beta _{5}q^{5}+(1-\beta _{7})q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots$
2132.2.b.a	$2132$	$2$	2132.b	533.b	$2$	$48$	$48$	$17.024$		$_{}$	None	None		✓	✓	✓	2132.2.b.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
2132.2.d.a	$2132$	$2$	2132.d	41.b	$2$	$42$	$42$	$17.024$		$_{}$	None	None		✓	✓	✓	2132.2.d.a	$2$	$0$	$0$	$0$	$4$	$0$			$\mathrm{SU}(2)[C_{2}]$
2132.2.g.a	$2132$	$2$	2132.g	13.b	$2$	$48$	$48$	$17.024$		$_{}$	None	None		✓	✓	✓	2132.2.g.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
2132.2.i.a	$2132$	$2$	2132.i	13.c	$3$	$46$	$23$	$17.024$		$_{}$	None	None		✓			2132.2.i.a	$2$	$0$	$0$	$1$	$-8$	$-3$			$\mathrm{SU}(2)[C_{3}]$
2132.2.i.b	$2132$	$2$	2132.i	13.c	$3$	$46$	$23$	$17.024$		$_{}$	None	None		✓			2132.2.i.b	$2$	$0$	$0$	$1$	$8$	$-3$			$\mathrm{SU}(2)[C_{3}]$
2132.2.m.a	$2132$	$2$	2132.m	41.c	$4$	$84$	$42$	$17.024$		$_{}$	None	None		✓	✓	✓	2132.2.m.a	$2$	$0$	$0$	$-4$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
2132.2.s.a	$2132$	$2$	2132.s	533.k	$4$	$100$	$50$	$17.024$		$_{}$	None	None		✓	✓	✓	2132.2.s.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
2132.2.w.a	$2132$	$2$	2132.w	13.e	$6$	$92$	$46$	$17.024$		$_{}$	None	None		✓	✓	✓	2132.2.w.a	$2$	$0$	$0$	$-2$	$0$	$6$			$\mathrm{SU}(2)[C_{6}]$
2132.2.ba.a	$2132$	$2$	2132.ba	533.o	$6$	$96$	$48$	$17.024$		$_{}$	None	None		✓	✓	✓	2132.2.ba.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
2132.2.bc.a	$2132$	$2$	2132.bc	533.m	$6$	$100$	$50$	$17.024$		$_{}$	None	None		✓	✓	✓	2132.2.bc.a	$4$	$0$	$0$	$0$	$4$	$0$			$\mathrm{SU}(2)[C_{6}]$
2132.4.a.a	$2132$	$4$	2132.a	1.a	$1$	$1$	$1$	$125.792$	$\Q$	$_{}$	None	None	✓	✓			2132.4.a.a	$1$	$1$	$0$	$9$	$-19$	$-29$	$-$	$1$	$\mathrm{SU}(2)$	$q+9q^{3}-19q^{5}-29q^{7}+54q^{9}+46q^{11}+\cdots$
2132.4.a.b	$2132$	$4$	2132.a	1.a	$1$	$26$	$26$	$125.792$		$_{}$	None	None	✓	✓	✓	✓	2132.4.a.b	$1$	$1$	$0$	$-1$	$-30$	$-57$	$-$		$\mathrm{SU}(2)$
2132.4.a.c	$2132$	$4$	2132.a	1.a	$1$	$30$	$30$	$125.792$		$_{}$	None	None	✓	✓	✓		2132.4.a.c	$1$	$1$	$0$	$-4$	$9$	$-28$	$-$		$\mathrm{SU}(2)$
2132.4.a.d	$2132$	$4$	2132.a	1.a	$1$	$30$	$30$	$125.792$		$_{}$	None	None	✓	✓	✓	✓	2132.4.a.d	$1$	$0$	$0$	$-1$	$30$	$41$	$+$		$\mathrm{SU}(2)$

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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.