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 221 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
2100.1.m.a	$2100$	$1$	2100.m	84.h	$2$	$1$	$1$	$1.048$	$\Q$	$D_{2}$	$\Q(\sqrt{-5}) $, $\Q(\sqrt{-21}) $	$\Q(\sqrt{105}) $	✓				420.1.o.a	$4$	$0$	$-1$	$-1$	$0$	$1$		$1$		$q-q^{2}-q^{3}+q^{4}+q^{6}+q^{7}-q^{8}+\cdots$
2100.1.m.b	$2100$	$1$	2100.m	84.h	$2$	$1$	$1$	$1.048$	$\Q$	$D_{2}$	$\Q(\sqrt{-5}) $, $\Q(\sqrt{-21}) $	$\Q(\sqrt{105}) $	✓				420.1.o.a	$4$	$0$	$-1$	$1$	$0$	$-1$		$1$		$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots$
2100.1.m.c	$2100$	$1$	2100.m	84.h	$2$	$1$	$1$	$1.048$	$\Q$	$D_{2}$	$\Q(\sqrt{-5}) $, $\Q(\sqrt{-21}) $	$\Q(\sqrt{105}) $	✓				420.1.o.a	$4$	$0$	$1$	$-1$	$0$	$1$		$1$		$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots$
2100.1.m.d	$2100$	$1$	2100.m	84.h	$2$	$1$	$1$	$1.048$	$\Q$	$D_{2}$	$\Q(\sqrt{-5}) $, $\Q(\sqrt{-21}) $	$\Q(\sqrt{105}) $	✓				420.1.o.a	$4$	$0$	$1$	$1$	$0$	$-1$		$1$		$q+q^{2}+q^{3}+q^{4}+q^{6}-q^{7}+q^{8}+\cdots$
2100.1.u.a	$2100$	$1$	2100.u	105.k	$4$	$8$	$4$	$1.048$	$\Q(\zeta_{24})$	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓			2100.1.u.a	$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}^{9}q^{3}-\zeta_{24}^{7}q^{7}-\zeta_{24}^{6}q^{9}+\cdots$
2100.1.u.b	$2100$	$1$	2100.u	105.k	$4$	$8$	$4$	$1.048$	$\Q(\zeta_{24})$	$D_{6}$	$\Q(\sqrt{-35}) $	None		✓			2100.1.u.b	$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}q^{3}+\zeta_{24}^{3}q^{7}+\zeta_{24}^{2}q^{9}+(-\zeta_{24}^{4}+\cdots)q^{11}+\cdots$
2100.1.ba.a	$2100$	$1$	2100.ba	84.j	$6$	$2$	$1$	$1.048$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-5}) $	None					420.1.be.a	$4$	$0$	$-1$	$-2$	$0$	$-1$		$1$		$q+\zeta_{6}^{2}q^{2}-q^{3}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{6}+\cdots$
2100.1.ba.b	$2100$	$1$	2100.ba	84.j	$6$	$2$	$1$	$1.048$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-5}) $	None					420.1.be.a	$4$	$0$	$-1$	$-1$	$0$	$1$		$1$		$q+\zeta_{6}^{2}q^{2}+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{6}+\cdots$
2100.1.ba.c	$2100$	$1$	2100.ba	84.j	$6$	$2$	$1$	$1.048$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-5}) $	None					420.1.be.a	$4$	$0$	$1$	$1$	$0$	$-1$		$1$		$q-\zeta_{6}^{2}q^{2}-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{6}+\cdots$
2100.1.ba.d	$2100$	$1$	2100.ba	84.j	$6$	$2$	$1$	$1.048$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-5}) $	None					420.1.be.a	$4$	$0$	$1$	$2$	$0$	$1$		$1$		$q-\zeta_{6}^{2}q^{2}+q^{3}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{6}+\cdots$
2100.1.bh.a	$2100$	$1$	2100.bh	105.o	$6$	$4$	$2$	$1.048$	$\Q(\zeta_{12})$	$D_{3}$	$\Q(\sqrt{-3}) $	None					84.1.p.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{12}q^{3}+\zeta_{12}^{5}q^{7}+\zeta_{12}^{2}q^{9}-\zeta_{12}^{3}q^{13}+\cdots$
2100.1.bh.b	$2100$	$1$	2100.bh	105.o	$6$	$4$	$2$	$1.048$	$\Q(\zeta_{12})$	$D_{3}$	$\Q(\sqrt{-3}) $	None		✓			2100.1.bn.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{12}q^{3}-\zeta_{12}^{3}q^{7}+\zeta_{12}^{2}q^{9}+\zeta_{12}^{3}q^{13}+\cdots$
2100.1.bn.a	$2100$	$1$	2100.bn	21.h	$6$	$2$	$1$	$1.048$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		✓			2100.1.bn.a	$4$	$0$	$0$	$-1$	$0$	$2$		$1$		$q+\zeta_{6}^{2}q^{3}+q^{7}-\zeta_{6}q^{9}+q^{13}-\zeta_{6}q^{19}+\cdots$
2100.1.bn.b	$2100$	$1$	2100.bn	21.h	$6$	$2$	$1$	$1.048$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		✓			2100.1.bn.a	$4$	$0$	$0$	$1$	$0$	$-2$		$1$		$q-\zeta_{6}^{2}q^{3}-q^{7}-\zeta_{6}q^{9}-q^{13}-\zeta_{6}q^{19}+\cdots$
2100.1.bn.c	$2100$	$1$	2100.bn	21.h	$6$	$2$	$1$	$1.048$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None					84.1.p.a	$4$	$0$	$0$	$1$	$0$	$1$		$1$		$q-\zeta_{6}^{2}q^{3}+\zeta_{6}q^{7}-\zeta_{6}q^{9}+q^{13}+\cdots$
2100.1.bq.a	$2100$	$1$	2100.bq	2100.aq	$10$	$8$	$2$	$1.048$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-21}) $	None		✓			2100.1.bq.a	$8$	$0$	$0$	$0$	$-2$	$0$		$1$		$q+\zeta_{20}^{7}q^{2}+\zeta_{20}^{9}q^{3}-\zeta_{20}^{4}q^{4}+\cdots$
2100.1.bq.b	$2100$	$1$	2100.bq	2100.aq	$10$	$8$	$2$	$1.048$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-21}) $	None		✓			2100.1.bq.a	$8$	$0$	$0$	$0$	$2$	$0$		$1$		$q+\zeta_{20}^{7}q^{2}-\zeta_{20}^{9}q^{3}-\zeta_{20}^{4}q^{4}+\cdots$
2100.1.bs.a	$2100$	$1$	2100.bs	2100.as	$10$	$4$	$1$	$1.048$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-21}) $	None		✓			2100.1.bs.a	$4$	$0$	$-1$	$-1$	$-1$	$4$		$1$		$q-\zeta_{10}^{3}q^{2}-\zeta_{10}q^{3}-\zeta_{10}q^{4}-\zeta_{10}q^{5}+\cdots$
2100.1.bs.b	$2100$	$1$	2100.bs	2100.as	$10$	$4$	$1$	$1.048$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-21}) $	None		✓			2100.1.bs.a	$4$	$0$	$-1$	$1$	$1$	$-4$		$1$		$q-\zeta_{10}^{3}q^{2}+\zeta_{10}q^{3}-\zeta_{10}q^{4}+\zeta_{10}q^{5}+\cdots$
2100.1.bs.c	$2100$	$1$	2100.bs	2100.as	$10$	$4$	$1$	$1.048$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-21}) $	None		✓			2100.1.bs.a	$4$	$0$	$1$	$-1$	$1$	$4$		$1$		$q+\zeta_{10}^{3}q^{2}-\zeta_{10}q^{3}-\zeta_{10}q^{4}+\zeta_{10}q^{5}+\cdots$
2100.1.bs.d	$2100$	$1$	2100.bs	2100.as	$10$	$4$	$1$	$1.048$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-21}) $	None		✓			2100.1.bs.a	$4$	$0$	$1$	$1$	$-1$	$-4$		$1$		$q+\zeta_{10}^{3}q^{2}+\zeta_{10}q^{3}-\zeta_{10}q^{4}-\zeta_{10}q^{5}+\cdots$
2100.1.cf.a	$2100$	$1$	2100.cf	420.ap	$12$	$8$	$2$	$1.048$	$\Q(\zeta_{24})$	$D_{6}$	$\Q(\sqrt{-5}) $	None		✓			2100.1.cf.a	$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{24}q^{2}+\zeta_{24}^{3}q^{3}+\zeta_{24}^{2}q^{4}+\zeta_{24}^{4}q^{6}+\cdots$
2100.1.cf.b	$2100$	$1$	2100.cf	420.ap	$12$	$8$	$2$	$1.048$	$\Q(\zeta_{24})$	$D_{6}$	$\Q(\sqrt{-5}) $	None		✓			2100.1.cf.a	$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{24}q^{2}-\zeta_{24}^{7}q^{3}+\zeta_{24}^{2}q^{4}-\zeta_{24}^{8}q^{6}+\cdots$
2100.1.cj.a	$2100$	$1$	2100.cj	105.w	$12$	$8$	$2$	$1.048$	$\Q(\zeta_{24})$	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓			2100.1.cj.a	$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}q^{3}+\zeta_{24}^{3}q^{7}+\zeta_{24}^{2}q^{9}+\zeta_{24}^{9}q^{13}+\cdots$
2100.1.cj.b	$2100$	$1$	2100.cj	105.w	$12$	$8$	$2$	$1.048$	$\Q(\zeta_{24})$	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓			2100.1.cj.b	$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{24}q^{3}-\zeta_{24}^{11}q^{7}+\zeta_{24}^{2}q^{9}+\cdots$
2100.2.a.a	$2100$	$2$	2100.a	1.a	$1$	$1$	$1$	$16.769$	$\Q$	$_{}$	None	None	✓				84.2.a.b	$1$	$0$	$0$	$-1$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{7}+q^{9}-6q^{11}-2q^{13}+\cdots$
2100.2.a.b	$2100$	$2$	2100.a	1.a	$1$	$1$	$1$	$16.769$	$\Q$	$_{}$	None	None	✓	✓			2100.2.a.b	$1$	$0$	$0$	$-1$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{7}+q^{9}-3q^{11}+4q^{13}+\cdots$
2100.2.a.c	$2100$	$2$	2100.a	1.a	$1$	$1$	$1$	$16.769$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	2100.2.a.c	$1$	$1$	$0$	$-1$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{7}+q^{9}-q^{11}-2q^{13}+6q^{19}+\cdots$
2100.2.a.d	$2100$	$2$	2100.a	1.a	$1$	$1$	$1$	$16.769$	$\Q$	$_{}$	None	None	✓				420.2.a.c	$1$	$0$	$0$	$-1$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{7}+q^{9}+6q^{11}+4q^{13}+\cdots$
2100.2.a.e	$2100$	$2$	2100.a	1.a	$1$	$1$	$1$	$16.769$	$\Q$	$_{}$	None	None	✓				420.2.k.a	$1$	$0$	$0$	$-1$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}-4q^{11}-6q^{13}+\cdots$
2100.2.a.f	$2100$	$2$	2100.a	1.a	$1$	$1$	$1$	$16.769$	$\Q$	$_{}$	None	None	✓	✓			2100.2.a.f	$1$	$1$	$0$	$-1$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}-q^{11}+2q^{13}-8q^{17}+\cdots$
2100.2.a.g	$2100$	$2$	2100.a	1.a	$1$	$1$	$1$	$16.769$	$\Q$	$_{}$	None	None	✓	✓			2100.2.a.g	$1$	$0$	$0$	$-1$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}+q^{11}+4q^{13}+2q^{17}+\cdots$
2100.2.a.h	$2100$	$2$	2100.a	1.a	$1$	$1$	$1$	$16.769$	$\Q$	$_{}$	None	None	✓				420.2.a.d	$1$	$1$	$0$	$-1$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}+2q^{11}-4q^{13}+\cdots$
2100.2.a.i	$2100$	$2$	2100.a	1.a	$1$	$1$	$1$	$16.769$	$\Q$	$_{}$	None	None	✓				420.2.k.b	$1$	$0$	$0$	$-1$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots$
2100.2.a.j	$2100$	$2$	2100.a	1.a	$1$	$1$	$1$	$16.769$	$\Q$	$_{}$	None	None	✓				420.2.k.a	$1$	$0$	$0$	$1$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}-4q^{11}+6q^{13}+\cdots$
2100.2.a.k	$2100$	$2$	2100.a	1.a	$1$	$1$	$1$	$16.769$	$\Q$	$_{}$	None	None	✓				420.2.a.b	$1$	$1$	$0$	$1$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}-2q^{11}-4q^{13}+\cdots$
2100.2.a.l	$2100$	$2$	2100.a	1.a	$1$	$1$	$1$	$16.769$	$\Q$	$_{}$	None	None	✓	✓			2100.2.a.f	$1$	$0$	$0$	$1$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}-q^{11}-2q^{13}+8q^{17}+\cdots$
2100.2.a.m	$2100$	$2$	2100.a	1.a	$1$	$1$	$1$	$16.769$	$\Q$	$_{}$	None	None	✓	✓			2100.2.a.g	$1$	$1$	$0$	$1$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}+q^{11}-4q^{13}-2q^{17}+\cdots$
2100.2.a.n	$2100$	$2$	2100.a	1.a	$1$	$1$	$1$	$16.769$	$\Q$	$_{}$	None	None	✓				420.2.k.b	$1$	$0$	$0$	$1$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots$
2100.2.a.o	$2100$	$2$	2100.a	1.a	$1$	$1$	$1$	$16.769$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	2100.2.a.b	$1$	$1$	$0$	$1$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{7}+q^{9}-3q^{11}-4q^{13}+\cdots$
2100.2.a.p	$2100$	$2$	2100.a	1.a	$1$	$1$	$1$	$16.769$	$\Q$	$_{}$	None	None	✓	✓			2100.2.a.c	$1$	$0$	$0$	$1$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{7}+q^{9}-q^{11}+2q^{13}+6q^{19}+\cdots$
2100.2.a.q	$2100$	$2$	2100.a	1.a	$1$	$1$	$1$	$16.769$	$\Q$	$_{}$	None	None	✓				420.2.a.a	$1$	$0$	$0$	$1$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{7}+q^{9}+2q^{11}-4q^{13}+\cdots$
2100.2.a.r	$2100$	$2$	2100.a	1.a	$1$	$1$	$1$	$16.769$	$\Q$	$_{}$	None	None	✓				84.2.a.a	$1$	$0$	$0$	$1$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{7}+q^{9}+2q^{11}+6q^{13}+\cdots$
2100.2.d.a	$2100$	$2$	2100.d	21.c	$2$	$2$	$2$	$16.769$	$\Q(\sqrt{-3}) $	$_{}$	None	None					420.2.d.a	$2$	$0$	$0$	$-3$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1-\zeta_{6})q^{3}+(-3+2\zeta_{6})q^{7}+3\zeta_{6}q^{9}+\cdots$
2100.2.d.b	$2100$	$2$	2100.d	21.c	$2$	$2$	$2$	$16.769$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None					84.2.f.a	$4$	$0$	$0$	$0$	$0$	$-4$		$2$	$\mathrm{U}(1)[D_{2}]$	$q-\beta q^{3}+(-\beta-2)q^{7}-3 q^{9}+4\beta q^{13}+\cdots$
2100.2.d.c	$2100$	$2$	2100.d	21.c	$2$	$2$	$2$	$16.769$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		✓			2100.2.d.c	$4$	$0$	$0$	$0$	$0$	$-1$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+(-1+2\zeta_{6})q^{3}+(1-3\zeta_{6})q^{7}-3q^{9}+\cdots$
2100.2.d.d	$2100$	$2$	2100.d	21.c	$2$	$2$	$2$	$16.769$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		✓			2100.2.d.c	$4$	$0$	$0$	$0$	$0$	$1$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+(1-2\zeta_{6})q^{3}+(-1+3\zeta_{6})q^{7}-3q^{9}+\cdots$
2100.2.d.e	$2100$	$2$	2100.d	21.c	$2$	$2$	$2$	$16.769$	$\Q(\sqrt{-3}) $	$_{}$	None	None					420.2.d.a	$2$	$0$	$0$	$3$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+\zeta_{6})q^{3}+(-1-2\zeta_{6})q^{7}+3\zeta_{6}q^{9}+\cdots$
2100.2.d.f	$2100$	$2$	2100.d	21.c	$2$	$4$	$4$	$16.769$	$\Q(\sqrt{-2}, \sqrt{5})$	$_{}$	None	None					420.2.f.b	$4$	$0$	$0$	$-4$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1-\beta _{1})q^{3}+(\beta _{1}+\beta _{3})q^{7}+(-1+\cdots)q^{9}+\cdots$
2100.2.d.g	$2100$	$2$	2100.d	21.c	$2$	$4$	$4$	$16.769$	$\Q(i, \sqrt{5})$	$_{}$	None	None					420.2.d.c	$2$	$0$	$0$	$-2$	$0$	$6$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1+\beta _{3})q^{3}+(1+\beta _{2}+\beta _{3})q^{7}+\cdots$

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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.