LMFDB - Newform search results

Refine search

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

				Sort order	Select

Results (1-50 of 56 matches)

Next Download displayed columns for results to

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
2952.1.h.a	$2952$	$1$	2952.h	328.c	$2$	$1$	$1$	$1.473$	$\Q$	$D_{2}$	$\Q(\sqrt{-2}) $, $\Q(\sqrt{-82}) $	$\Q(\sqrt{41}) $	✓				328.1.c.a	$4$	$0$	$1$	$0$	$0$	$0$		$1$		$q+q^{2}+q^{4}+q^{8}+q^{16}+q^{25}+q^{32}+\cdots$
2952.1.h.b	$2952$	$1$	2952.h	328.c	$2$	$2$	$2$	$1.473$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-82}) $	None	✓	✓			2952.1.h.b	$4$	$0$	$-2$	$0$	$0$	$0$		$1$		$q-q^{2}+q^{4}-\beta q^{7}-q^{8}+\beta q^{13}+\beta q^{14}+\cdots$
2952.1.h.c	$2952$	$1$	2952.h	328.c	$2$	$2$	$2$	$1.473$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-82}) $	None	✓	✓			2952.1.h.b	$4$	$0$	$2$	$0$	$0$	$0$		$1$		$q+q^{2}+q^{4}-\beta q^{7}+q^{8}+\beta q^{13}-\beta q^{14}+\cdots$
2952.1.v.a	$2952$	$1$	2952.v	328.k	$4$	$2$	$1$	$1.473$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-2}) $	None			✓	✓	328.1.k.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-i q^{2}-q^{4}+i q^{8}+(i+1)q^{11}+\cdots$
2952.1.w.a	$2952$	$1$	2952.w	123.f	$4$	$4$	$2$	$1.473$	$\Q(\zeta_{8})$	$S_{4}$	None	None		✓	✓	✓	2952.1.w.a	$4$	$0$	$0$	$0$	$0$	$-4$		$1$		$q+(-1-\zeta_{8}^{2})q^{7}-\zeta_{8}^{3}q^{11}+(1+\zeta_{8}^{2}+\cdots)q^{13}+\cdots$
2952.1.be.a	$2952$	$1$	2952.be	2952.ae	$6$	$8$	$4$	$1.473$	$\Q(\zeta_{24})$	$D_{12}$	None	$\Q(\sqrt{82}) $		✓	✓	✓	2952.1.be.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}^{2}q^{2}-\zeta_{24}^{7}q^{3}+\zeta_{24}^{4}q^{4}+\cdots$
2952.1.bh.a	$2952$	$1$	2952.bh	2952.ah	$6$	$2$	$1$	$1.473$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-2}) $	None		✓			2952.1.bh.a	$4$	$0$	$1$	$-1$	$0$	$0$		$1$		$q+\zeta_{6}q^{2}-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{6}+\cdots$
2952.1.bh.b	$2952$	$1$	2952.bh	2952.ah	$6$	$2$	$1$	$1.473$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-2}) $	None		✓			2952.1.bh.a	$4$	$0$	$1$	$1$	$0$	$0$		$1$		$q+\zeta_{6}q^{2}+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{6}+\cdots$
2952.1.bp.a	$2952$	$1$	2952.bp	328.n	$8$	$4$	$1$	$1.473$	$\Q(\zeta_{8})$	$D_{8}$	None	$\Q(\sqrt{2}) $			✓	✓	328.1.n.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(-\zeta_{8}+\zeta_{8}^{2})q^{7}+\cdots$
2952.1.cf.a	$2952$	$1$	2952.cf	328.t	$10$	$4$	$1$	$1.473$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-2}) $	None			✓	✓	328.1.t.a	$4$	$0$	$-1$	$0$	$0$	$0$		$1$		$q+\zeta_{10}^{2}q^{2}+\zeta_{10}^{4}q^{4}-\zeta_{10}q^{8}+(1+\cdots)q^{11}+\cdots$
2952.1.ck.a	$2952$	$1$	2952.ck	328.x	$10$	$4$	$1$	$1.473$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-2}) $	None			✓	✓	328.1.x.a	$4$	$0$	$1$	$0$	$0$	$0$		$1$		$q-\zeta_{10}^{4}q^{2}-\zeta_{10}^{3}q^{4}-\zeta_{10}^{2}q^{8}+\cdots$
2952.1.cp.a	$2952$	$1$	2952.cp	2952.bp	$12$	$4$	$1$	$1.473$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-2}) $	None		✓			2952.1.cp.a	$4$	$0$	$0$	$-2$	$0$	$0$		$1$		$q-\zeta_{12}^{5}q^{2}-\zeta_{12}^{2}q^{3}-\zeta_{12}^{4}q^{4}+\cdots$
2952.1.cp.b	$2952$	$1$	2952.cp	2952.bp	$12$	$4$	$1$	$1.473$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-2}) $	None		✓			2952.1.cp.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{12}^{5}q^{2}-\zeta_{12}^{5}q^{3}-\zeta_{12}^{4}q^{4}+\cdots$
2952.1.cy.a	$2952$	$1$	2952.cy	328.z	$20$	$8$	$1$	$1.473$	$\Q(\zeta_{20})$	$D_{20}$	$\Q(\sqrt{-2}) $	None			✓	✓	328.1.z.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{20}^{9}q^{2}-\zeta_{20}^{8}q^{4}-\zeta_{20}^{7}q^{8}+\cdots$
2952.1.dh.a	$2952$	$1$	2952.dh	2952.ch	$24$	$8$	$1$	$1.473$	$\Q(\zeta_{24})$	$D_{24}$	$\Q(\sqrt{-2}) $	None		✓			2952.1.dh.a	$4$	$0$	$0$	$-4$	$0$	$0$		$1$		$q-\zeta_{24}q^{2}-\zeta_{24}^{4}q^{3}+\zeta_{24}^{2}q^{4}+\zeta_{24}^{5}q^{6}+\cdots$
2952.1.dh.b	$2952$	$1$	2952.dh	2952.ch	$24$	$8$	$1$	$1.473$	$\Q(\zeta_{24})$	$D_{24}$	$\Q(\sqrt{-2}) $	None		✓			2952.1.dh.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{24}q^{2}-\zeta_{24}q^{3}+\zeta_{24}^{2}q^{4}-\zeta_{24}^{2}q^{6}+\cdots$
2952.1.dl.a	$2952$	$1$	2952.dl	2952.cl	$30$	$8$	$1$	$1.473$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-2}) $	None		✓			2952.1.dl.a	$4$	$0$	$1$	$1$	$0$	$0$		$1$		$q-\zeta_{30}^{13}q^{2}-\zeta_{30}^{7}q^{3}-\zeta_{30}^{11}q^{4}+\cdots$
2952.1.dl.b	$2952$	$1$	2952.dl	2952.cl	$30$	$8$	$1$	$1.473$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-2}) $	None		✓			2952.1.dl.a	$4$	$0$	$1$	$1$	$0$	$0$		$1$		$q-\zeta_{30}^{13}q^{2}-\zeta_{30}^{13}q^{3}-\zeta_{30}^{11}q^{4}+\cdots$
2952.1.dl.c	$2952$	$1$	2952.dl	2952.cl	$30$	$16$	$2$	$1.473$	$\Q(\zeta_{60})$	$A_{5}$	None	None		✓	✓		2952.1.dl.c	$8$	$0$	$0$	$-8$	$0$	$0$		$1$		$q+\zeta_{60}^{23}q^{2}+\zeta_{60}^{20}q^{3}-\zeta_{60}^{16}q^{4}+\cdots$
2952.1.ds.a	$2952$	$1$	2952.ds	2952.cs	$30$	$8$	$1$	$1.473$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-2}) $	None		✓			2952.1.ds.a	$4$	$0$	$-1$	$-1$	$0$	$0$		$1$		$q-\zeta_{30}^{2}q^{2}-\zeta_{30}^{8}q^{3}+\zeta_{30}^{4}q^{4}+\cdots$
2952.1.ds.b	$2952$	$1$	2952.ds	2952.cs	$30$	$8$	$1$	$1.473$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-2}) $	None		✓			2952.1.ds.a	$4$	$0$	$-1$	$1$	$0$	$0$		$1$		$q-\zeta_{30}^{2}q^{2}+\zeta_{30}^{2}q^{3}+\zeta_{30}^{4}q^{4}+\cdots$
2952.1.em.a	$2952$	$1$	2952.em	2952.dm	$60$	$16$	$1$	$1.473$	$\Q(\zeta_{60})$	$D_{60}$	$\Q(\sqrt{-2}) $	None		✓			2952.1.em.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{60}^{17}q^{2}-\zeta_{60}^{23}q^{3}-\zeta_{60}^{4}q^{4}+\cdots$
2952.1.em.b	$2952$	$1$	2952.em	2952.dm	$60$	$16$	$1$	$1.473$	$\Q(\zeta_{60})$	$D_{60}$	$\Q(\sqrt{-2}) $	None		✓			2952.1.em.a	$4$	$0$	$0$	$2$	$0$	$0$		$1$		$q+\zeta_{60}^{17}q^{2}-\zeta_{60}^{2}q^{3}-\zeta_{60}^{4}q^{4}+\cdots$
2952.1.et.a	$2952$	$1$	2952.et	2952.dt	$120$	$32$	$1$	$1.473$	$\Q(\zeta_{120})$	$D_{120}$	$\Q(\sqrt{-2}) $	None		✓			2952.1.et.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{120}^{29}q^{2}-\zeta_{120}^{41}q^{3}+\zeta_{120}^{58}q^{4}+\cdots$
2952.1.et.b	$2952$	$1$	2952.et	2952.dt	$120$	$32$	$1$	$1.473$	$\Q(\zeta_{120})$	$D_{120}$	$\Q(\sqrt{-2}) $	None		✓			2952.1.et.a	$4$	$0$	$0$	$4$	$0$	$0$		$1$		$q+\zeta_{120}^{29}q^{2}-\zeta_{120}^{44}q^{3}+\zeta_{120}^{58}q^{4}+\cdots$
2952.2.a.a	$2952$	$2$	2952.a	1.a	$1$	$1$	$1$	$23.572$	$\Q$	$_{}$	None	None	✓	✓			2952.2.a.a	$1$	$0$	$0$	$0$	$-3$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{5}+4q^{7}-3q^{13}-5q^{17}+3q^{19}+\cdots$
2952.2.a.b	$2952$	$2$	2952.a	1.a	$1$	$1$	$1$	$23.572$	$\Q$	$_{}$	None	None	✓				328.2.a.b	$1$	$1$	$0$	$0$	$-2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-2q^{7}-2q^{11}+6q^{13}+6q^{17}+\cdots$
2952.2.a.c	$2952$	$2$	2952.a	1.a	$1$	$1$	$1$	$23.572$	$\Q$	$_{}$	None	None	✓				984.2.a.c	$1$	$1$	$0$	$0$	$-2$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+4q^{7}-5q^{11}+3q^{17}-2q^{19}+\cdots$
2952.2.a.d	$2952$	$2$	2952.a	1.a	$1$	$1$	$1$	$23.572$	$\Q$	$_{}$	None	None	✓				984.2.a.d	$1$	$1$	$0$	$0$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{7}+3q^{11}-6q^{13}+7q^{17}-2q^{23}+\cdots$
2952.2.a.e	$2952$	$2$	2952.a	1.a	$1$	$1$	$1$	$23.572$	$\Q$	$_{}$	None	None	✓				984.2.a.b	$1$	$1$	$0$	$0$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-2q^{7}-2q^{11}-3q^{13}+3q^{17}+\cdots$
2952.2.a.f	$2952$	$2$	2952.a	1.a	$1$	$1$	$1$	$23.572$	$\Q$	$_{}$	None	None	✓				328.2.a.a	$1$	$0$	$0$	$0$	$2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-2q^{7}-4q^{13}+2q^{17}+4q^{19}+\cdots$
2952.2.a.g	$2952$	$2$	2952.a	1.a	$1$	$1$	$1$	$23.572$	$\Q$	$_{}$	None	None	✓				984.2.a.a	$1$	$0$	$0$	$0$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-q^{11}+4q^{13}+7q^{17}+2q^{19}+\cdots$
2952.2.a.h	$2952$	$2$	2952.a	1.a	$1$	$1$	$1$	$23.572$	$\Q$	$_{}$	None	None	✓	✓			2952.2.a.a	$1$	$0$	$0$	$0$	$3$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{5}+4q^{7}-3q^{13}+5q^{17}+3q^{19}+\cdots$
2952.2.a.i	$2952$	$2$	2952.a	1.a	$1$	$2$	$2$	$23.572$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓				328.2.a.c	$1$	$1$	$0$	$0$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta )q^{7}+(-3+\beta )q^{11}-2q^{17}+\cdots$
2952.2.a.j	$2952$	$2$	2952.a	1.a	$1$	$2$	$2$	$23.572$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				984.2.a.e	$1$	$1$	$0$	$0$	$4$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(2+\beta )q^{5}+(-2+\beta )q^{7}+(-1-3\beta )q^{11}+\cdots$
2952.2.a.k	$2952$	$2$	2952.a	1.a	$1$	$3$	$3$	$23.572$	3.3.1436.1	$_{}$	None	None	✓		✓		984.2.a.g	$1$	$1$	$0$	$0$	$-3$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{5}+(-1-\beta _{1}-\beta _{2})q^{7}+\cdots$
2952.2.a.l	$2952$	$2$	2952.a	1.a	$1$	$3$	$3$	$23.572$	3.3.788.1	$_{}$	None	None	✓		✓		328.2.a.e	$1$	$1$	$0$	$0$	$-2$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{2})q^{5}+(1+\beta _{1})q^{7}+(1+\beta _{1}+\cdots)q^{11}+\cdots$
2952.2.a.m	$2952$	$2$	2952.a	1.a	$1$	$3$	$3$	$23.572$	3.3.961.1	$_{}$	None	None	✓				984.2.a.h	$1$	$0$	$0$	$0$	$-1$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{5}+2q^{7}+(1-\beta _{1}+\beta _{2})q^{11}+\cdots$
2952.2.a.n	$2952$	$2$	2952.a	1.a	$1$	$3$	$3$	$23.572$	3.3.892.1	$_{}$	None	None	✓				984.2.a.f	$1$	$0$	$0$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{5}+\beta _{2}q^{7}+(3-\beta _{1})q^{11}+(-2\beta _{1}+\cdots)q^{13}+\cdots$
2952.2.a.o	$2952$	$2$	2952.a	1.a	$1$	$3$	$3$	$23.572$	3.3.148.1	$_{}$	None	None	✓				328.2.a.d	$1$	$0$	$0$	$0$	$2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1}+\beta _{2})q^{5}+(-1+\beta _{1}+2\beta _{2})q^{7}+\cdots$
2952.2.a.p	$2952$	$2$	2952.a	1.a	$1$	$4$	$4$	$23.572$	4.4.20308.1	$_{}$	None	None	✓	✓	✓	✓	2952.2.a.p	$1$	$1$	$0$	$0$	$-3$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{3})q^{5}+(-1-\beta _{1}-\beta _{3})q^{7}+\cdots$
2952.2.a.q	$2952$	$2$	2952.a	1.a	$1$	$4$	$4$	$23.572$	4.4.20308.1	$_{}$	None	None	✓	✓	✓	✓	2952.2.a.p	$1$	$1$	$0$	$0$	$3$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{3})q^{5}+(-1-\beta _{1}-\beta _{3})q^{7}+\cdots$
2952.2.a.r	$2952$	$2$	2952.a	1.a	$1$	$5$	$5$	$23.572$	5.5.40129248.1	$_{}$	None	None	✓	✓	✓		2952.2.a.r	$1$	$0$	$0$	$0$	$-4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{5}+\beta _{3}q^{7}+(2+\beta _{4})q^{11}+\cdots$
2952.2.a.s	$2952$	$2$	2952.a	1.a	$1$	$5$	$5$	$23.572$	5.5.3858104.1	$_{}$	None	None	✓		✓		984.2.a.i	$1$	$0$	$0$	$0$	$-1$	$2$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{4}q^{5}+\beta _{3}q^{7}+(-2-\beta _{2})q^{11}+\cdots$
2952.2.a.t	$2952$	$2$	2952.a	1.a	$1$	$5$	$5$	$23.572$	5.5.40129248.1	$_{}$	None	None	✓	✓	✓		2952.2.a.r	$1$	$0$	$0$	$0$	$4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{5}+\beta _{3}q^{7}+(-2-\beta _{4})q^{11}+\cdots$
2952.2.j.a	$2952$	$2$	2952.j	41.b	$2$	$2$	$2$	$23.572$	$\Q(\sqrt{-1}) $	$_{}$	None	None					984.2.j.a	$2$	$0$	$0$	$0$	$4$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+2 q^{5}-\beta q^{7}-2\beta q^{11}+3\beta q^{13}+\cdots$
2952.2.j.b	$2952$	$2$	2952.j	41.b	$2$	$4$	$4$	$23.572$	$\Q(\sqrt{-2}, \sqrt{5})$	$_{}$	None	None					328.2.d.a	$2$	$0$	$0$	$0$	$-4$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1+\beta _{2})q^{5}-\beta _{1}q^{7}+\beta _{3}q^{11}+\cdots$
2952.2.j.c	$2952$	$2$	2952.j	41.b	$2$	$6$	$6$	$23.572$	6.0.1229312.1	$_{}$	None	None					328.2.d.b	$2$	$0$	$0$	$0$	$4$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+\beta _{2})q^{5}-\beta _{3}q^{7}+\beta _{1}q^{11}+(\beta _{1}+\cdots)q^{13}+\cdots$
2952.2.j.d	$2952$	$2$	2952.j	41.b	$2$	$8$	$8$	$23.572$	8.0.$\cdots$.1	$_{}$	None	None					984.2.j.b	$2$	$0$	$0$	$0$	$-10$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1-\beta _{4})q^{5}+(-\beta _{1}-\beta _{7})q^{7}+(-\beta _{3}+\cdots)q^{11}+\cdots$
2952.2.j.e	$2952$	$2$	2952.j	41.b	$2$	$10$	$10$	$23.572$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	$_{}$	None	None		✓			2952.2.j.e	$2$	$0$	$0$	$0$	$-2$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{5}-\beta _{8}q^{7}+\beta _{7}q^{11}+\beta _{5}q^{13}+\cdots$

Next Download displayed columns for results to

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Learn more

Refine search

Results (1-50 of 56 matches)

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.