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 64 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
2664.1.m.a	$2664$	$1$	2664.m	296.h	$2$	$2$	$2$	$1.330$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-74}) $	None	✓				296.1.h.a	$2$	$0$	$-2$	$0$	$1$	$0$		$1$		$q-q^{2}+q^{4}+(1-\beta )q^{5}-q^{8}+(-1+\cdots)q^{10}+\cdots$
2664.1.m.b	$2664$	$1$	2664.m	296.h	$2$	$2$	$2$	$1.330$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-74}) $	None	✓				296.1.h.a	$2$	$0$	$2$	$0$	$-1$	$0$		$1$		$q+q^{2}+q^{4}+(-1+\beta )q^{5}+q^{8}+(-1+\cdots)q^{10}+\cdots$
2664.1.m.c	$2664$	$1$	2664.m	296.h	$2$	$8$	$8$	$1.330$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-111}) $	None		✓	✓		2664.1.m.c	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{16}q^{2}+\zeta_{16}^{2}q^{4}+(-\zeta_{16}^{3}+\zeta_{16}^{5}+\cdots)q^{5}+\cdots$
2664.1.y.a	$2664$	$1$	2664.y	37.d	$4$	$2$	$1$	$1.330$	$\Q(\sqrt{-1}) $	$S_{4}$	None	None			✓	✓	296.1.k.a	$2$	$0$	$0$	$0$	$2$	$-2$		$1$		$q+(1-i)q^{5}-q^{7}-iq^{11}+(1-i)q^{13}+\cdots$
2664.1.ba.a	$2664$	$1$	2664.ba	296.m	$4$	$4$	$2$	$1.330$	$\Q(\zeta_{8})$	$S_{4}$	None	None		✓			2664.1.ba.a	$4$	$0$	$0$	$0$	$-4$	$-4$		$1$		$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(-1-\zeta_{8}^{2})q^{5}+\cdots$
2664.1.ba.b	$2664$	$1$	2664.ba	296.m	$4$	$4$	$2$	$1.330$	$\Q(\zeta_{8})$	$S_{4}$	None	None		✓			2664.1.ba.a	$4$	$0$	$0$	$0$	$4$	$-4$		$1$		$q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(1+\zeta_{8}^{2})q^{5}-q^{7}+\cdots$
2664.1.bg.a	$2664$	$1$	2664.bg	2664.ag	$6$	$4$	$2$	$1.330$	$\Q(\zeta_{12})$	$A_{4}$	None	None		✓	✓	✓	2664.1.bg.a	$4$	$0$	$4$	$-4$	$0$	$0$		$1$		$q+q^{2}-q^{3}+q^{4}-\zeta_{12}^{3}q^{5}-q^{6}+\cdots$
2664.1.bw.a	$2664$	$1$	2664.bw	2664.aw	$6$	$2$	$1$	$1.330$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-74}) $	None		✓			2664.1.bw.a	$4$	$0$	$-1$	$2$	$-2$	$0$		$1$		$q-\zeta_{6}q^{2}+q^{3}+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{5}+\cdots$
2664.1.bw.b	$2664$	$1$	2664.bw	2664.aw	$6$	$2$	$1$	$1.330$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-74}) $	None		✓			2664.1.bw.a	$4$	$0$	$1$	$2$	$2$	$0$		$1$		$q+\zeta_{6}q^{2}+q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{5}+\cdots$
2664.1.bw.c	$2664$	$1$	2664.bw	2664.aw	$6$	$8$	$4$	$1.330$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-74}) $	None		✓			2664.1.bw.c	$4$	$0$	$-4$	$-2$	$2$	$0$		$1$		$q+\zeta_{30}^{10}q^{2}+\zeta_{30}^{12}q^{3}-\zeta_{30}^{5}q^{4}+\cdots$
2664.1.bw.d	$2664$	$1$	2664.bw	2664.aw	$6$	$8$	$4$	$1.330$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-74}) $	None		✓			2664.1.bw.c	$4$	$0$	$4$	$-2$	$-2$	$0$		$1$		$q-\zeta_{30}^{10}q^{2}+\zeta_{30}^{12}q^{3}-\zeta_{30}^{5}q^{4}+\cdots$
2664.1.cg.a	$2664$	$1$	2664.cg	2664.bg	$6$	$4$	$2$	$1.330$	$\Q(\zeta_{12})$	$A_{4}$	None	None		✓	✓	✓	2664.1.bg.a	$4$	$0$	$-2$	$2$	$0$	$0$		$1$		$q-\zeta_{12}^{2}q^{2}-\zeta_{12}^{4}q^{3}+\zeta_{12}^{4}q^{4}+\cdots$
2664.1.cy.a	$2664$	$1$	2664.cy	296.p	$6$	$8$	$4$	$1.330$	$\Q(\zeta_{24})$	$S_{4}$	None	None		✓	✓	✓	2664.1.cy.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+(-\zeta_{24}^{5}+\zeta_{24}^{11}+\cdots)q^{5}+\cdots$
2664.2.a.a	$2664$	$2$	2664.a	1.a	$1$	$1$	$1$	$21.272$	$\Q$	$_{}$	None	None	✓				888.2.a.d	$1$	$1$	$0$	$0$	$-4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-4q^{5}+2q^{13}+6q^{23}+11q^{25}+\cdots$
2664.2.a.b	$2664$	$2$	2664.a	1.a	$1$	$1$	$1$	$21.272$	$\Q$	$_{}$	None	None	✓	✓			2664.2.a.b	$1$	$1$	$0$	$0$	$-2$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+q^{7}-5q^{11}+3q^{13}-q^{17}+\cdots$
2664.2.a.c	$2664$	$2$	2664.a	1.a	$1$	$1$	$1$	$21.272$	$\Q$	$_{}$	None	None	✓				296.2.a.b	$1$	$1$	$0$	$0$	$0$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{7}+3q^{11}-2q^{17}-2q^{19}+6q^{23}+\cdots$
2664.2.a.d	$2664$	$2$	2664.a	1.a	$1$	$1$	$1$	$21.272$	$\Q$	$_{}$	None	None	✓				888.2.a.b	$1$	$1$	$0$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-6q^{13}+4q^{17}+4q^{19}-6q^{23}+\cdots$
2664.2.a.e	$2664$	$2$	2664.a	1.a	$1$	$1$	$1$	$21.272$	$\Q$	$_{}$	None	None	✓				888.2.a.c	$1$	$0$	$0$	$0$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+4q^{11}-2q^{13}+6q^{17}+4q^{23}+\cdots$
2664.2.a.f	$2664$	$2$	2664.a	1.a	$1$	$1$	$1$	$21.272$	$\Q$	$_{}$	None	None	✓				296.2.a.a	$1$	$1$	$0$	$0$	$2$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+q^{7}-q^{11}-6q^{13}+4q^{17}+\cdots$
2664.2.a.g	$2664$	$2$	2664.a	1.a	$1$	$1$	$1$	$21.272$	$\Q$	$_{}$	None	None	✓	✓			2664.2.a.b	$1$	$0$	$0$	$0$	$2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+q^{7}+5q^{11}+3q^{13}+q^{17}+\cdots$
2664.2.a.h	$2664$	$2$	2664.a	1.a	$1$	$1$	$1$	$21.272$	$\Q$	$_{}$	None	None	✓				888.2.a.a	$1$	$0$	$0$	$0$	$4$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{5}-q^{7}+3q^{11}-5q^{13}-7q^{17}+\cdots$
2664.2.a.i	$2664$	$2$	2664.a	1.a	$1$	$2$	$2$	$21.272$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓				888.2.a.e	$1$	$1$	$0$	$0$	$-2$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{5}-2q^{7}+(2-2\beta )q^{11}+\cdots$
2664.2.a.j	$2664$	$2$	2664.a	1.a	$1$	$2$	$2$	$21.272$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				888.2.a.f	$1$	$0$	$0$	$0$	$-2$	$8$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{5}+4q^{7}+(-2-2\beta )q^{11}+\cdots$
2664.2.a.k	$2664$	$2$	2664.a	1.a	$1$	$2$	$2$	$21.272$	$\Q(\sqrt{41}) $	$_{}$	None	None	✓		✓		888.2.a.h	$1$	$1$	$0$	$0$	$0$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{7}+(-1-\beta )q^{11}+(1-\beta )q^{13}+\cdots$
2664.2.a.l	$2664$	$2$	2664.a	1.a	$1$	$2$	$2$	$21.272$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				888.2.a.g	$1$	$0$	$0$	$0$	$4$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(2+\beta )q^{5}+(-2+2\beta )q^{7}+2\beta q^{11}+\cdots$
2664.2.a.m	$2664$	$2$	2664.a	1.a	$1$	$3$	$3$	$21.272$	3.3.316.1	$_{}$	None	None	✓				888.2.a.i	$1$	$0$	$0$	$0$	$-2$	$-5$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1}+\beta _{2})q^{5}+(-1-2\beta _{1}+\cdots)q^{7}+\cdots$
2664.2.a.n	$2664$	$2$	2664.a	1.a	$1$	$3$	$3$	$21.272$	3.3.148.1	$_{}$	None	None	✓	✓	✓		2664.2.a.n	$1$	$1$	$0$	$0$	$-2$	$4$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1+\beta _{2})q^{5}+(2-\beta _{1}-\beta _{2})q^{7}+\cdots$
2664.2.a.o	$2664$	$2$	2664.a	1.a	$1$	$3$	$3$	$21.272$	3.3.568.1	$_{}$	None	None	✓		✓		888.2.a.j	$1$	$1$	$0$	$0$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-\beta _{1}-\beta _{2})q^{5}+\beta _{2}q^{7}+(-2+\beta _{2})q^{11}+\cdots$
2664.2.a.p	$2664$	$2$	2664.a	1.a	$1$	$3$	$3$	$21.272$	3.3.229.1	$_{}$	None	None	✓				296.2.a.c	$1$	$0$	$0$	$0$	$1$	$7$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{5}+(2+\beta _{1}-\beta _{2})q^{7}+3\beta _{1}q^{11}+\cdots$
2664.2.a.q	$2664$	$2$	2664.a	1.a	$1$	$3$	$3$	$21.272$	3.3.148.1	$_{}$	None	None	✓	✓	✓		2664.2.a.n	$1$	$0$	$0$	$0$	$2$	$4$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1-\beta _{2})q^{5}+(2-\beta _{1}-\beta _{2})q^{7}-2q^{13}+\cdots$
2664.2.a.r	$2664$	$2$	2664.a	1.a	$1$	$4$	$4$	$21.272$	4.4.48389.1	$_{}$	None	None	✓		✓		296.2.a.d	$1$	$0$	$0$	$0$	$-5$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{3})q^{5}+(-\beta _{2}+\beta _{3})q^{7}+(-1+\cdots)q^{11}+\cdots$
2664.2.a.s	$2664$	$2$	2664.a	1.a	$1$	$5$	$5$	$21.272$	5.5.935504.1	$_{}$	None	None	✓	✓	✓	✓	2664.2.a.s	$1$	$1$	$0$	$0$	$-2$	$-7$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{5}+(-1+\beta _{4})q^{7}+(-1-\beta _{2}+\cdots)q^{11}+\cdots$
2664.2.a.t	$2664$	$2$	2664.a	1.a	$1$	$5$	$5$	$21.272$	5.5.935504.1	$_{}$	None	None	✓	✓	✓	✓	2664.2.a.s	$1$	$0$	$0$	$0$	$2$	$-7$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{5}+(-1+\beta _{4})q^{7}+(1+\beta _{2}-\beta _{3}+\cdots)q^{11}+\cdots$
2664.2.h.a	$2664$	$2$	2664.h	37.b	$2$	$2$	$2$	$21.272$	$\Q(\sqrt{-1}) $	$_{}$	None	None					888.2.h.a	$2$	$1$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-4q^{11}+2iq^{13}+2iq^{17}-iq^{19}+\cdots$
2664.2.h.b	$2664$	$2$	2664.h	37.b	$2$	$6$	$6$	$21.272$	6.0.27206656.1	$_{}$	None	None					888.2.h.b	$2$	$0$	$0$	$0$	$0$	$6$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{5}+(1-\beta _{1})q^{7}+(1+\beta _{1})q^{11}+\cdots$
2664.2.h.c	$2664$	$2$	2664.h	37.b	$2$	$10$	$10$	$21.272$	10.0.$\cdots$.1	$_{}$	None	None					296.2.g.a	$2$	$0$	$0$	$0$	$0$	$-4$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{7}q^{5}-\beta _{3}q^{7}-\beta _{5}q^{11}+\beta _{4}q^{13}+\cdots$
2664.2.h.d	$2664$	$2$	2664.h	37.b	$2$	$10$	$10$	$21.272$	10.0.$\cdots$.1	$_{}$	None	None					888.2.h.c	$2$	$0$	$0$	$0$	$0$	$-2$		$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{5}-\beta _{3}q^{7}+(-1+\beta _{1})q^{11}+\cdots$
2664.2.h.e	$2664$	$2$	2664.h	37.b	$2$	$20$	$20$	$21.272$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		✓	✓		2664.2.h.e	$4$	$0$	$0$	$0$	$0$	$4$		$2^{30}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{7}q^{5}+\beta _{1}q^{7}+\beta _{10}q^{11}-\beta _{12}q^{13}+\cdots$
2664.2.r.a	$2664$	$2$	2664.r	37.c	$3$	$2$	$1$	$21.272$	$\Q(\sqrt{-3}) $	$_{}$	None	None					888.2.q.b	$2$	$0$	$0$	$0$	$-2$	$-3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-2\zeta_{6}q^{5}-3\zeta_{6}q^{7}+7\zeta_{6}q^{13}+(-6+\cdots)q^{17}+\cdots$
2664.2.r.b	$2664$	$2$	2664.r	37.c	$3$	$2$	$1$	$21.272$	$\Q(\sqrt{-3}) $	$_{}$	None	None					888.2.q.a	$2$	$0$	$0$	$0$	$-2$	$-3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-2\zeta_{6}q^{5}-3\zeta_{6}q^{7}+4q^{11}-\zeta_{6}q^{13}+\cdots$
2664.2.r.c	$2664$	$2$	2664.r	37.c	$3$	$2$	$1$	$21.272$	$\Q(\sqrt{-3}) $	$_{}$	None	None					888.2.q.d	$2$	$0$	$0$	$0$	$-1$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{5}+4\zeta_{6}q^{7}+2\zeta_{6}q^{13}+(7-7\zeta_{6})q^{17}+\cdots$
2664.2.r.d	$2664$	$2$	2664.r	37.c	$3$	$2$	$1$	$21.272$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			2664.2.r.d	$2$	$0$	$0$	$0$	$0$	$3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+3\zeta_{6}q^{7}-6q^{11}+3\zeta_{6}q^{13}+(2-2\zeta_{6})q^{17}+\cdots$
2664.2.r.e	$2664$	$2$	2664.r	37.c	$3$	$2$	$1$	$21.272$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			2664.2.r.d	$2$	$0$	$0$	$0$	$0$	$3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+3\zeta_{6}q^{7}+6q^{11}+3\zeta_{6}q^{13}+(-2+\cdots)q^{17}+\cdots$
2664.2.r.f	$2664$	$2$	2664.r	37.c	$3$	$2$	$1$	$21.272$	$\Q(\sqrt{-3}) $	$_{}$	None	None					296.2.i.a	$2$	$0$	$0$	$0$	$3$	$-3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+3\zeta_{6}q^{5}-3\zeta_{6}q^{7}-3\zeta_{6}q^{13}+(-1+\cdots)q^{17}+\cdots$
2664.2.r.g	$2664$	$2$	2664.r	37.c	$3$	$2$	$1$	$21.272$	$\Q(\sqrt{-3}) $	$_{}$	None	None					888.2.q.c	$2$	$0$	$0$	$0$	$4$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+4\zeta_{6}q^{5}-\zeta_{6}q^{7}+2q^{11}-3\zeta_{6}q^{13}+\cdots$
2664.2.r.h	$2664$	$2$	2664.r	37.c	$3$	$6$	$3$	$21.272$	6.0.50898483.1	$_{}$	None	None					888.2.q.h	$2$	$0$	$0$	$0$	$-3$	$-3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{1}-\beta _{3})q^{5}-\beta _{3}q^{7}+(\beta _{2}-\beta _{4})q^{11}+\cdots$
2664.2.r.i	$2664$	$2$	2664.r	37.c	$3$	$6$	$3$	$21.272$	6.0.591408.1	$_{}$	None	None					296.2.i.b	$2$	$0$	$0$	$0$	$-1$	$2$		$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}-\beta _{5})q^{5}+(\beta _{3}-\beta _{4})q^{7}+2\beta _{3}q^{13}+\cdots$
2664.2.r.j	$2664$	$2$	2664.r	37.c	$3$	$6$	$3$	$21.272$	6.0.47545083.2	$_{}$	None	None					888.2.q.g	$2$	$0$	$0$	$0$	$-1$	$9$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{5}q^{5}-3\beta _{4}q^{7}+(-3-\beta _{1}-\beta _{2}+\cdots)q^{11}+\cdots$
2664.2.r.k	$2664$	$2$	2664.r	37.c	$3$	$6$	$3$	$21.272$	6.0.1415907.1	$_{}$	None	None					888.2.q.f	$2$	$0$	$0$	$0$	$2$	$-7$		$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}+\beta _{3}+\beta _{4})q^{5}+(-\beta _{1}-2\beta _{3}+\cdots)q^{7}+\cdots$
2664.2.r.l	$2664$	$2$	2664.r	37.c	$3$	$6$	$3$	$21.272$	6.0.1415907.1	$_{}$	None	None					888.2.q.e	$2$	$0$	$0$	$0$	$6$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{1}+\beta _{2}-2\beta _{4})q^{5}+(-\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots$

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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.