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 68 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
3872.1.f.a	$3872$	$1$	3872.f	8.d	$2$	$2$	$2$	$1.932$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-2}) $	None	✓				88.1.l.a	$2$	$0$	$0$	$1$	$0$	$0$		$1$		$q+\beta q^{3}+\beta q^{9}+(-1+\beta )q^{17}+(1-\beta )q^{19}+\cdots$
3872.1.f.b	$3872$	$1$	3872.f	8.d	$2$	$2$	$2$	$1.932$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-2}) $	None	✓				88.1.l.a	$2$	$0$	$0$	$1$	$0$	$0$		$1$		$q+\beta q^{3}+\beta q^{9}+(1-\beta )q^{17}+(-1+\beta )q^{19}+\cdots$
3872.1.h.a	$3872$	$1$	3872.h	11.b	$2$	$2$	$2$	$1.932$	$\Q(\sqrt{-2}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		✓			3872.1.h.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-q^{9}-\beta q^{13}-\beta q^{17}-q^{25}+\beta q^{29}+\cdots$
3872.1.h.b	$3872$	$1$	3872.h	11.b	$2$	$4$	$4$	$1.932$	$\Q(\sqrt{-2}, \sqrt{3})$	$D_{12}$	$\Q(\sqrt{-1}) $	None		✓	✓		3872.1.h.b	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta _{2}q^{5}-q^{9}-\beta _{1}q^{13}+\beta _{3}q^{17}+\cdots$
3872.1.r.a	$3872$	$1$	3872.r	11.d	$10$	$8$	$2$	$1.932$	8.0.64000000.1	$D_{4}$	$\Q(\sqrt{-1}) $	None		✓			3872.1.h.a	$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\beta _{6}q^{9}-\beta _{1}q^{13}+(\beta _{1}-\beta _{3}+\beta _{5}+\cdots)q^{17}+\cdots$
3872.1.r.b	$3872$	$1$	3872.r	11.d	$10$	$16$	$4$	$1.932$	16.0.$\cdots$.7	$D_{12}$	$\Q(\sqrt{-1}) $	None		✓	✓		3872.1.h.b	$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\beta _{2}+\beta _{6}-\beta _{10}-\beta _{14})q^{5}+\beta _{4}q^{9}+\cdots$
3872.1.t.a	$3872$	$1$	3872.t	88.l	$10$	$4$	$1$	$1.932$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-2}) $	None					88.1.l.a	$4$	$0$	$0$	$-3$	$0$	$0$		$1$		$q+(-1-\zeta_{10}^{2})q^{3}+(1+\zeta_{10}^{2}+\zeta_{10}^{4}+\cdots)q^{9}+\cdots$
3872.1.t.b	$3872$	$1$	3872.t	88.l	$10$	$4$	$1$	$1.932$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-2}) $	None					88.1.l.a	$4$	$0$	$0$	$-3$	$0$	$0$		$1$		$q+(-1-\zeta_{10}^{2})q^{3}+(1+\zeta_{10}^{2}+\zeta_{10}^{4}+\cdots)q^{9}+\cdots$
3872.1.t.c	$3872$	$1$	3872.t	88.l	$10$	$4$	$1$	$1.932$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-2}) $	None					88.1.l.a	$4$	$0$	$0$	$2$	$0$	$0$		$1$		$q+(\zeta_{10}^{3}-\zeta_{10}^{4})q^{3}+(-\zeta_{10}+\zeta_{10}^{2}+\cdots)q^{9}+\cdots$
3872.1.bj.a	$3872$	$1$	3872.bj	968.x	$22$	$10$	$1$	$1.932$	$\Q(\zeta_{22})$	$D_{11}$	$\Q(\sqrt{-2}) $	None			✓	✓	968.1.x.a	$4$	$0$	$0$	$2$	$0$	$0$		$1$		$q+(\zeta_{22}-\zeta_{22}^{10})q^{3}+(1+\zeta_{22}^{2}-\zeta_{22}^{9}+\cdots)q^{9}+\cdots$
3872.1.bx.a	$3872$	$1$	3872.bx	968.z	$110$	$40$	$1$	$1.932$	$\Q(\zeta_{55})$	$D_{55}$	$\Q(\sqrt{-2}) $	None			✓	✓	968.1.z.a	$4$	$0$	$0$	$-2$	$0$	$0$		$1$		$q+(\zeta_{110}^{27}+\zeta_{110}^{39})q^{3}+(-\zeta_{110}^{11}+\cdots)q^{9}+\cdots$
3872.2.a.a	$3872$	$2$	3872.a	1.a	$1$	$1$	$1$	$30.918$	$\Q$	$_{}$	None	None	✓				352.2.a.a	$1$	$0$	$0$	$-3$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}+q^{5}+6q^{9}+6q^{13}-3q^{15}+\cdots$
3872.2.a.b	$3872$	$2$	3872.a	1.a	$1$	$1$	$1$	$30.918$	$\Q$	$_{}$	None	None	✓	✓			3872.2.a.b	$1$	$0$	$0$	$-2$	$1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{5}-2q^{7}+q^{9}+q^{13}-2q^{15}+\cdots$
3872.2.a.c	$3872$	$2$	3872.a	1.a	$1$	$1$	$1$	$30.918$	$\Q$	$_{}$	None	None	✓	✓			3872.2.a.b	$1$	$1$	$0$	$-2$	$1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{5}+2q^{7}+q^{9}-q^{13}-2q^{15}+\cdots$
3872.2.a.d	$3872$	$2$	3872.a	1.a	$1$	$1$	$1$	$30.918$	$\Q$	$_{}$	None	None	✓				352.2.a.b	$1$	$1$	$0$	$-1$	$-3$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-3q^{5}-4q^{7}-2q^{9}+2q^{13}+\cdots$
3872.2.a.e	$3872$	$2$	3872.a	1.a	$1$	$1$	$1$	$30.918$	$\Q$	$_{}$	None	None	✓				352.2.a.c	$1$	$1$	$0$	$-1$	$1$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+4q^{7}-2q^{9}+2q^{13}+\cdots$
3872.2.a.f	$3872$	$2$	3872.a	1.a	$1$	$1$	$1$	$30.918$	$\Q$	$_{}$	$\Q(\sqrt{-1}) $	None	✓				32.2.a.a	$2$	$0$	$0$	$0$	$-2$	$0$	$-$	$1$	$N(\mathrm{U}(1))$	$q-2q^{5}-3q^{9}-6q^{13}-2q^{17}-q^{25}+\cdots$
3872.2.a.g	$3872$	$2$	3872.a	1.a	$1$	$1$	$1$	$30.918$	$\Q$	$_{}$	$\Q(\sqrt{-1}) $	None	✓	✓			3872.2.a.g	$2$	$0$	$0$	$0$	$2$	$0$	$-$	$1$	$N(\mathrm{U}(1))$	$q+2q^{5}-3q^{9}-4q^{13}+8q^{17}-q^{25}+\cdots$
3872.2.a.h	$3872$	$2$	3872.a	1.a	$1$	$1$	$1$	$30.918$	$\Q$	$_{}$	$\Q(\sqrt{-1}) $	None	✓	✓			3872.2.a.g	$2$	$1$	$0$	$0$	$2$	$0$	$+$	$1$	$N(\mathrm{U}(1))$	$q+2q^{5}-3q^{9}+4q^{13}-8q^{17}-q^{25}+\cdots$
3872.2.a.i	$3872$	$2$	3872.a	1.a	$1$	$1$	$1$	$30.918$	$\Q$	$_{}$	None	None	✓				352.2.a.b	$1$	$0$	$0$	$1$	$-3$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-3q^{5}+4q^{7}-2q^{9}+2q^{13}+\cdots$
3872.2.a.j	$3872$	$2$	3872.a	1.a	$1$	$1$	$1$	$30.918$	$\Q$	$_{}$	None	None	✓				352.2.a.c	$1$	$1$	$0$	$1$	$1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-4q^{7}-2q^{9}+2q^{13}+\cdots$
3872.2.a.k	$3872$	$2$	3872.a	1.a	$1$	$1$	$1$	$30.918$	$\Q$	$_{}$	None	None	✓	✓			3872.2.a.b	$1$	$1$	$0$	$2$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{5}-2q^{7}+q^{9}-q^{13}+2q^{15}+\cdots$
3872.2.a.l	$3872$	$2$	3872.a	1.a	$1$	$1$	$1$	$30.918$	$\Q$	$_{}$	None	None	✓	✓			3872.2.a.b	$1$	$0$	$0$	$2$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{5}+2q^{7}+q^{9}+q^{13}+2q^{15}+\cdots$
3872.2.a.m	$3872$	$2$	3872.a	1.a	$1$	$1$	$1$	$30.918$	$\Q$	$_{}$	None	None	✓				352.2.a.a	$1$	$0$	$0$	$3$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}+q^{5}+6q^{9}+6q^{13}+3q^{15}+\cdots$
3872.2.a.n	$3872$	$2$	3872.a	1.a	$1$	$2$	$2$	$30.918$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				352.2.m.a	$1$	$0$	$0$	$-1$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+2\beta q^{5}+(2-4\beta )q^{7}+(-2+\cdots)q^{9}+\cdots$
3872.2.a.o	$3872$	$2$	3872.a	1.a	$1$	$2$	$2$	$30.918$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				352.2.m.a	$1$	$0$	$0$	$-1$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+2\beta q^{5}+(-2+4\beta )q^{7}+(-2+\cdots)q^{9}+\cdots$
3872.2.a.p	$3872$	$2$	3872.a	1.a	$1$	$2$	$2$	$30.918$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓				352.2.a.g	$1$	$0$	$0$	$-1$	$3$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+(2-\beta )q^{5}+(1+\beta )q^{9}-2q^{13}+\cdots$
3872.2.a.q	$3872$	$2$	3872.a	1.a	$1$	$2$	$2$	$30.918$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	✓			3872.2.a.q	$2$	$1$	$0$	$0$	$-6$	$0$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta q^{3}-3q^{5}-2\beta q^{7}+2q^{9}-6q^{13}+\cdots$
3872.2.a.r	$3872$	$2$	3872.a	1.a	$1$	$2$	$2$	$30.918$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	✓			3872.2.a.q	$2$	$0$	$0$	$0$	$-6$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta q^{3}-3q^{5}+2\beta q^{7}+2q^{9}+6q^{13}+\cdots$
3872.2.a.s	$3872$	$2$	3872.a	1.a	$1$	$2$	$2$	$30.918$	$\Q(\sqrt{3}) $	$_{}$	$\Q(\sqrt{-1}) $	None	✓	✓			3872.2.a.s	$2$	$1$	$0$	$0$	$-2$	$0$	$+$	$1$	$N(\mathrm{U}(1))$	$q+(-1+2\beta )q^{5}-3q^{9}+(-2-3\beta )q^{13}+\cdots$
3872.2.a.t	$3872$	$2$	3872.a	1.a	$1$	$2$	$2$	$30.918$	$\Q(\sqrt{3}) $	$_{}$	$\Q(\sqrt{-1}) $	None	✓	✓			3872.2.a.s	$2$	$0$	$0$	$0$	$-2$	$0$	$-$	$1$	$N(\mathrm{U}(1))$	$q+(-1+2\beta )q^{5}-3q^{9}+(2+3\beta )q^{13}+\cdots$
3872.2.a.u	$3872$	$2$	3872.a	1.a	$1$	$2$	$2$	$30.918$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	✓			3872.2.a.u	$2$	$1$	$0$	$0$	$2$	$-4$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta q^{3}+q^{5}-2q^{7}+2q^{9}+2\beta q^{13}+\cdots$
3872.2.a.v	$3872$	$2$	3872.a	1.a	$1$	$2$	$2$	$30.918$	$\Q(\sqrt{3}) $	$_{}$	$\Q(\sqrt{-1}) $	None	✓	✓			3872.2.a.v	$2$	$1$	$0$	$0$	$2$	$0$	$+$	$2$	$N(\mathrm{U}(1))$	$q+(1-\beta )q^{5}-3q^{9}+(-3+\beta )q^{13}+\cdots$
3872.2.a.w	$3872$	$2$	3872.a	1.a	$1$	$2$	$2$	$30.918$	$\Q(\sqrt{3}) $	$_{}$	$\Q(\sqrt{-1}) $	None	✓	✓			3872.2.a.v	$2$	$0$	$0$	$0$	$2$	$0$	$-$	$2$	$N(\mathrm{U}(1))$	$q+(1+\beta )q^{5}-3q^{9}+(3+\beta )q^{13}+(1+\cdots)q^{17}+\cdots$
3872.2.a.x	$3872$	$2$	3872.a	1.a	$1$	$2$	$2$	$30.918$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	✓			3872.2.a.u	$2$	$0$	$0$	$0$	$2$	$4$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta q^{3}+q^{5}+2q^{7}+2q^{9}-2\beta q^{13}+\cdots$
3872.2.a.y	$3872$	$2$	3872.a	1.a	$1$	$2$	$2$	$30.918$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				352.2.m.a	$1$	$0$	$0$	$1$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+2\beta q^{5}+(-2+4\beta )q^{7}+(-2+\cdots)q^{9}+\cdots$
3872.2.a.z	$3872$	$2$	3872.a	1.a	$1$	$2$	$2$	$30.918$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				352.2.m.a	$1$	$0$	$0$	$1$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+2\beta q^{5}+(2-4\beta )q^{7}+(-2+\cdots)q^{9}+\cdots$
3872.2.a.ba	$3872$	$2$	3872.a	1.a	$1$	$2$	$2$	$30.918$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓				352.2.a.g	$1$	$1$	$0$	$1$	$3$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(2-\beta )q^{5}+(1+\beta )q^{9}-2q^{13}+\cdots$
3872.2.a.bb	$3872$	$2$	3872.a	1.a	$1$	$3$	$3$	$30.918$	3.3.404.1	$_{}$	None	None	✓	✓			3872.2.a.bb	$1$	$1$	$0$	$0$	$-3$	$-4$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{3}+(-1-\beta _{2})q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots$
3872.2.a.bc	$3872$	$2$	3872.a	1.a	$1$	$3$	$3$	$30.918$	3.3.404.1	$_{}$	None	None	✓	✓			3872.2.a.bb	$1$	$1$	$0$	$0$	$-3$	$-4$	$+$	$2$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{3}+(-1-\beta _{2})q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots$
3872.2.a.bd	$3872$	$2$	3872.a	1.a	$1$	$3$	$3$	$30.918$	3.3.404.1	$_{}$	None	None	✓	✓			3872.2.a.bb	$1$	$0$	$0$	$0$	$-3$	$4$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{3}+(-1-\beta _{2})q^{5}+(1-\beta _{1})q^{7}+\cdots$
3872.2.a.be	$3872$	$2$	3872.a	1.a	$1$	$3$	$3$	$30.918$	3.3.404.1	$_{}$	None	None	✓	✓			3872.2.a.bb	$1$	$0$	$0$	$0$	$-3$	$4$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{3}+(-1-\beta _{2})q^{5}+(1-\beta _{1})q^{7}+\cdots$
3872.2.a.bf	$3872$	$2$	3872.a	1.a	$1$	$4$	$4$	$30.918$	4.4.4400.1	$_{}$	None	None	✓				352.2.m.c	$2$	$1$	$0$	$0$	$-6$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(-2-\beta _{2})q^{5}+\beta _{1}q^{7}+(1+\cdots)q^{9}+\cdots$
3872.2.a.bg	$3872$	$2$	3872.a	1.a	$1$	$4$	$4$	$30.918$	4.4.4400.1	$_{}$	None	None	✓				352.2.m.c	$2$	$1$	$0$	$0$	$-6$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(-2-\beta _{2})q^{5}-\beta _{1}q^{7}+(1+\cdots)q^{9}+\cdots$
3872.2.a.bh	$3872$	$2$	3872.a	1.a	$1$	$4$	$4$	$30.918$	4.4.7488.1	$_{}$	None	None	✓	✓			3872.2.a.bh	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{3}-\beta _{1}q^{5}-\beta _{3}q^{7}+(5+2\beta _{1}+\cdots)q^{9}+\cdots$
3872.2.a.bi	$3872$	$2$	3872.a	1.a	$1$	$4$	$4$	$30.918$	4.4.7488.1	$_{}$	None	None	✓	✓			3872.2.a.bh	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{3}-\beta _{1}q^{5}+\beta _{3}q^{7}+(5+2\beta _{1}+\cdots)q^{9}+\cdots$
3872.2.a.bj	$3872$	$2$	3872.a	1.a	$1$	$4$	$4$	$30.918$	4.4.22000.1	$_{}$	None	None	✓				352.2.m.d	$2$	$0$	$0$	$0$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(2+3\beta _{2})q^{5}-\beta _{1}q^{7}+(5+\cdots)q^{9}+\cdots$
3872.2.a.bk	$3872$	$2$	3872.a	1.a	$1$	$4$	$4$	$30.918$	4.4.22000.1	$_{}$	None	None	✓				352.2.m.d	$2$	$0$	$0$	$0$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(2+3\beta _{2})q^{5}+\beta _{1}q^{7}+(5+\cdots)q^{9}+\cdots$
3872.2.a.bl	$3872$	$2$	3872.a	1.a	$1$	$4$	$4$	$30.918$	$\Q(\zeta_{24})^+$	$_{}$	None	None	✓	✓			3872.2.a.bl	$2$	$1$	$0$	$0$	$4$	$-8$	$+$	$2$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{3}+(1-\beta _{3})q^{5}+(-2+\beta _{3})q^{7}+\cdots$
3872.2.a.bm	$3872$	$2$	3872.a	1.a	$1$	$4$	$4$	$30.918$	$\Q(\zeta_{24})^+$	$_{}$	None	None	✓	✓			3872.2.a.bl	$2$	$0$	$0$	$0$	$4$	$8$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{3}+(1+\beta _{3})q^{5}+(2+\beta _{3})q^{7}+\cdots$

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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.