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 207 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
880.1.i.a	$880$	$1$	880.i	55.d	$2$	$1$	$1$	$0.439$	$\Q$	$D_{2}$	$\Q(\sqrt{-11}) $, $\Q(\sqrt{-55}) $	$\Q(\sqrt{5}) $	✓				55.1.d.a	$4$	$0$	$0$	$0$	$-1$	$0$		$1$		$q-q^{5}+q^{9}+q^{11}+q^{25}+2q^{31}+\cdots$
880.1.i.b	$880$	$1$	880.i	55.d	$2$	$2$	$2$	$0.439$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-11}) $	None			✓		220.1.e.a	$4$	$0$	$0$	$0$	$1$	$0$		$1$		$q+(-\zeta_{6}-\zeta_{6}^{2})q^{3}-\zeta_{6}^{2}q^{5}+(-1+\cdots)q^{9}+\cdots$
880.1.x.a	$880$	$1$	880.x	880.x	$4$	$8$	$4$	$0.439$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-55}) $	None		✓	✓	✓	880.1.x.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{16}^{5}q^{2}-\zeta_{16}^{2}q^{4}+\zeta_{16}^{6}q^{5}+\cdots$
880.1.y.a	$880$	$1$	880.y	220.i	$4$	$2$	$1$	$0.439$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-11}) $	None		✓			880.1.y.a	$4$	$0$	$0$	$-2$	$0$	$0$		$1$		$q+(-i-1)q^{3}-i q^{5}+i q^{9}-i q^{11}+\cdots$
880.1.y.b	$880$	$1$	880.y	220.i	$4$	$2$	$1$	$0.439$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-11}) $	None		✓			880.1.y.a	$4$	$0$	$0$	$2$	$0$	$0$		$1$		$q+(i+1)q^{3}-i q^{5}+i q^{9}+i q^{11}+\cdots$
880.1.y.c	$880$	$1$	880.y	220.i	$4$	$4$	$2$	$0.439$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-11}) $	None		✓			880.1.y.c	$4$	$0$	$0$	$-2$	$0$	$0$		$1$		$q+(-\zeta_{12}-\zeta_{12}^{2})q^{3}+\zeta_{12}^{5}q^{5}+(\zeta_{12}^{2}+\cdots)q^{9}+\cdots$
880.1.y.d	$880$	$1$	880.y	220.i	$4$	$4$	$2$	$0.439$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-11}) $	None		✓			880.1.y.c	$4$	$0$	$0$	$2$	$0$	$0$		$1$		$q+(-\zeta_{12}+\zeta_{12}^{2})q^{3}-\zeta_{12}^{5}q^{5}+(\zeta_{12}^{2}+\cdots)q^{9}+\cdots$
880.2.a.a	$880$	$2$	880.a	1.a	$1$	$1$	$1$	$7.027$	$\Q$	$_{}$	None	None	✓				440.2.a.d	$1$	$1$	$0$	$-3$	$1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}+q^{5}-q^{7}+6q^{9}+q^{11}-6q^{13}+\cdots$
880.2.a.b	$880$	$2$	880.a	1.a	$1$	$1$	$1$	$7.027$	$\Q$	$_{}$	None	None	✓				220.2.a.b	$1$	$1$	$0$	$-2$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{5}+q^{9}-q^{11}-2q^{15}+\cdots$
880.2.a.c	$880$	$2$	880.a	1.a	$1$	$1$	$1$	$7.027$	$\Q$	$_{}$	None	None	✓				110.2.a.a	$1$	$0$	$0$	$-1$	$-1$	$-5$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-5q^{7}-2q^{9}-q^{11}+2q^{13}+\cdots$
880.2.a.d	$880$	$2$	880.a	1.a	$1$	$1$	$1$	$7.027$	$\Q$	$_{}$	None	None	✓		✓	✓	110.2.a.c	$1$	$1$	$0$	$-1$	$-1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+q^{7}-2q^{9}+q^{11}+2q^{13}+\cdots$
880.2.a.e	$880$	$2$	880.a	1.a	$1$	$1$	$1$	$7.027$	$\Q$	$_{}$	None	None	✓				440.2.a.b	$1$	$1$	$0$	$0$	$-1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+2q^{7}-3q^{9}-q^{11}-4q^{13}+\cdots$
880.2.a.f	$880$	$2$	880.a	1.a	$1$	$1$	$1$	$7.027$	$\Q$	$_{}$	None	None	✓				440.2.a.a	$1$	$0$	$0$	$0$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+2q^{7}-3q^{9}+q^{11}+8q^{19}+\cdots$
880.2.a.g	$880$	$2$	880.a	1.a	$1$	$1$	$1$	$7.027$	$\Q$	$_{}$	None	None	✓				440.2.a.c	$1$	$1$	$0$	$0$	$1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-4q^{7}-3q^{9}+q^{11}+6q^{13}+\cdots$
880.2.a.h	$880$	$2$	880.a	1.a	$1$	$1$	$1$	$7.027$	$\Q$	$_{}$	None	None	✓				55.2.a.a	$1$	$0$	$0$	$0$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-3q^{9}+q^{11}+2q^{13}+6q^{17}+\cdots$
880.2.a.i	$880$	$2$	880.a	1.a	$1$	$1$	$1$	$7.027$	$\Q$	$_{}$	None	None	✓				110.2.a.b	$1$	$1$	$0$	$1$	$1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-3q^{7}-2q^{9}-q^{11}-6q^{13}+\cdots$
880.2.a.j	$880$	$2$	880.a	1.a	$1$	$1$	$1$	$7.027$	$\Q$	$_{}$	None	None	✓				220.2.a.a	$1$	$0$	$0$	$2$	$1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{5}+4q^{7}+q^{9}+q^{11}-4q^{13}+\cdots$
880.2.a.k	$880$	$2$	880.a	1.a	$1$	$2$	$2$	$7.027$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓		✓		440.2.a.g	$1$	$0$	$0$	$-1$	$-2$	$-5$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}-q^{5}+(-2-\beta )q^{7}+(1+\beta )q^{9}+\cdots$
880.2.a.l	$880$	$2$	880.a	1.a	$1$	$2$	$2$	$7.027$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓		✓		440.2.a.f	$1$	$1$	$0$	$-1$	$-2$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}-q^{5}+(-2+\beta )q^{7}+(1+\beta )q^{9}+\cdots$
880.2.a.m	$880$	$2$	880.a	1.a	$1$	$2$	$2$	$7.027$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓		✓		55.2.a.b	$1$	$0$	$0$	$0$	$-2$	$4$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta q^{3}-q^{5}+2q^{7}+5q^{9}-q^{11}+\cdots$
880.2.a.n	$880$	$2$	880.a	1.a	$1$	$2$	$2$	$7.027$	$\Q(\sqrt{33}) $	$_{}$	None	None	✓		✓		110.2.a.d	$1$	$0$	$0$	$1$	$2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+q^{5}-\beta q^{7}+(5+\beta )q^{9}+q^{11}+\cdots$
880.2.a.o	$880$	$2$	880.a	1.a	$1$	$2$	$2$	$7.027$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓		✓	✓	440.2.a.e	$1$	$0$	$0$	$1$	$2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+q^{5}+\beta q^{7}+(1+\beta )q^{9}-q^{11}+\cdots$
880.2.b.a	$880$	$2$	880.b	5.b	$2$	$2$	$2$	$7.027$	$\Q(\sqrt{-1}) $	$_{}$	None	None					110.2.b.a	$2$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{3}+(-i-2)q^{5}+3 i q^{7}+2 q^{9}+\cdots$
880.2.b.b	$880$	$2$	880.b	5.b	$2$	$2$	$2$	$7.027$	$\Q(\sqrt{-1}) $	$_{}$	None	None					440.2.b.a	$2$	$0$	$0$	$0$	$-2$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{3}+(-\beta-1)q^{5}+\beta q^{7}-q^{9}+\cdots$
880.2.b.c	$880$	$2$	880.b	5.b	$2$	$2$	$2$	$7.027$	$\Q(\sqrt{-1}) $	$_{}$	None	None					220.2.b.a	$2$	$0$	$0$	$0$	$-2$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta-1)q^{5}-\beta q^{7}+3 q^{9}+q^{11}+\cdots$
880.2.b.d	$880$	$2$	880.b	5.b	$2$	$2$	$2$	$7.027$	$\Q(\sqrt{-1}) $	$_{}$	None	None					440.2.b.b	$2$	$0$	$0$	$0$	$2$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{3}+(\beta+1)q^{5}-2\beta q^{7}-q^{9}+\cdots$
880.2.b.e	$880$	$2$	880.b	5.b	$2$	$2$	$2$	$7.027$	$\Q(\sqrt{-1}) $	$_{}$	None	None					110.2.b.b	$2$	$0$	$0$	$0$	$2$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{3}+(-\beta+1)q^{5}-q^{9}-q^{11}+\cdots$
880.2.b.f	$880$	$2$	880.b	5.b	$2$	$2$	$2$	$7.027$	$\Q(\sqrt{-1}) $	$_{}$	None	None					110.2.b.c	$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+3 i q^{3}+(i+2)q^{5}-i q^{7}-6 q^{9}+\cdots$
880.2.b.g	$880$	$2$	880.b	5.b	$2$	$2$	$2$	$7.027$	$\Q(\sqrt{-1}) $	$_{}$	None	None					440.2.b.c	$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{3}+(-i+2)q^{5}+i q^{7}+2 q^{9}+\cdots$
880.2.b.h	$880$	$2$	880.b	5.b	$2$	$4$	$4$	$7.027$	$\Q(\sqrt{-3}, \sqrt{-11})$	$_{}$	None	None					55.2.b.a	$2$	$0$	$0$	$0$	$-3$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{3}+(-1+\beta _{3})q^{5}+(-\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots$
880.2.b.i	$880$	$2$	880.b	5.b	$2$	$4$	$4$	$7.027$	$\Q(\sqrt{-3}, \sqrt{-19})$	$_{}$	None	None					220.2.b.b	$2$	$0$	$0$	$0$	$1$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}-\beta _{2})q^{3}+\beta _{1}q^{5}+(\beta _{1}-\beta _{2}-\beta _{3})q^{7}+\cdots$
880.2.b.j	$880$	$2$	880.b	5.b	$2$	$8$	$8$	$7.027$	8.0.$\cdots$.2	$_{}$	None	None			✓		440.2.b.d	$2$	$0$	$0$	$0$	$0$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}-\beta _{4}q^{5}+(\beta _{1}-\beta _{3}-\beta _{4})q^{7}+\cdots$
880.2.f.a	$880$	$2$	880.f	44.c	$2$	$2$	$2$	$7.027$	$\Q(\sqrt{-2}) $	$_{}$	None	None		✓			880.2.f.a	$2$	$0$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{3}-q^{5}+q^{9}+(-3-\beta )q^{11}+\cdots$
880.2.f.b	$880$	$2$	880.f	44.c	$2$	$2$	$2$	$7.027$	$\Q(\sqrt{-2}) $	$_{}$	None	None		✓			880.2.f.a	$2$	$0$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{3}-q^{5}+q^{9}+(3-\beta )q^{11}-3\beta q^{13}+\cdots$
880.2.f.c	$880$	$2$	880.f	44.c	$2$	$4$	$4$	$7.027$	$\Q(\sqrt{-2}, \sqrt{3})$	$_{}$	None	None		✓			880.2.f.c	$4$	$0$	$0$	$0$	$4$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{3}+q^{5}-2\beta _{2}q^{7}+q^{9}+(-2\beta _{1}+\cdots)q^{11}+\cdots$
880.2.f.d	$880$	$2$	880.f	44.c	$2$	$8$	$8$	$7.027$	8.0.170772624.1	$_{}$	None	None		✓			880.2.f.d	$4$	$0$	$0$	$0$	$-8$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{3}-q^{5}+\beta _{1}q^{7}+(-1-\beta _{4}+\cdots)q^{9}+\cdots$
880.2.f.e	$880$	$2$	880.f	44.c	$2$	$8$	$8$	$7.027$	8.0.170772624.1	$_{}$	None	None		✓			880.2.f.e	$4$	$0$	$0$	$0$	$8$	$0$		$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{3}+q^{5}+\beta _{2}q^{7}+(-1-\beta _{4}+\cdots)q^{9}+\cdots$
880.2.m.a	$880$	$2$	880.m	220.g	$2$	$2$	$2$	$7.027$	$\Q(\sqrt{-11}) $	$_{}$	$\Q(\sqrt{-11}) $	None		✓			880.2.m.a	$4$	$0$	$0$	$-2$	$-3$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-q^{3}+(-1-\beta )q^{5}-2q^{9}+(-1+2\beta )q^{11}+\cdots$
880.2.m.b	$880$	$2$	880.m	220.g	$2$	$2$	$2$	$7.027$	$\Q(\sqrt{-11}) $	$_{}$	$\Q(\sqrt{-11}) $	None		✓			880.2.m.a	$4$	$0$	$0$	$2$	$-3$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+q^{3}+(-1-\beta )q^{5}-2q^{9}+(1-2\beta )q^{11}+\cdots$
880.2.m.c	$880$	$2$	880.m	220.g	$2$	$4$	$4$	$7.027$	$\Q(\sqrt{-3}, \sqrt{-11})$	$_{}$	$\Q(\sqrt{-11}) $	None		✓			880.2.m.c	$4$	$0$	$0$	$-2$	$3$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+(\beta _{1}+\beta _{3})q^{3}+(1-\beta _{2}+\beta _{3})q^{5}+(5+\cdots)q^{9}+\cdots$
880.2.m.d	$880$	$2$	880.m	220.g	$2$	$4$	$4$	$7.027$	$\Q(\sqrt{-3}, \sqrt{-11})$	$_{}$	$\Q(\sqrt{-11}) $	None		✓			880.2.m.c	$4$	$0$	$0$	$2$	$3$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+(-\beta _{1}-\beta _{3})q^{3}+(1-\beta _{2}+\beta _{3})q^{5}+\cdots$
880.2.m.e	$880$	$2$	880.m	220.g	$2$	$8$	$8$	$7.027$	8.0.303595776.1	$_{}$	None	None		✓			880.2.m.e	$8$	$0$	$0$	$0$	$-16$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{3}+(-2+\beta _{2})q^{5}+\beta _{5}q^{7}+\beta _{6}q^{11}+\cdots$
880.2.m.f	$880$	$2$	880.m	220.g	$2$	$8$	$8$	$7.027$	$\Q(\zeta_{24})$	$_{}$	None	None		✓			880.2.m.f	$8$	$0$	$0$	$0$	$8$	$0$		$2^{14}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta_1+1)q^{5}+\beta_{2} q^{7}-3 q^{9}+\cdots$
880.2.m.g	$880$	$2$	880.m	220.g	$2$	$8$	$8$	$7.027$	8.0.3317760000.9	$_{}$	None	None		✓			880.2.m.g	$8$	$0$	$0$	$0$	$8$	$0$		$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{7}q^{3}+(1-\beta _{2})q^{5}-\beta _{4}q^{7}+3q^{9}+\cdots$
880.2.s.a	$880$	$2$	880.s	80.j	$4$	$4$	$2$	$7.027$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			880.2.s.a	$2$	$0$	$0$	$0$	$-8$	$4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(\zeta_{8}-\zeta_{8}^{3})q^{2}+(\zeta_{8}+\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+\cdots$
880.2.s.b	$880$	$2$	880.s	80.j	$4$	$236$	$118$	$7.027$		$_{}$	None	None		✓	✓		880.2.s.b	$2$	$0$	$0$	$0$	$8$	$-4$			$\mathrm{SU}(2)[C_{4}]$
880.2.t.a	$880$	$2$	880.t	880.t	$4$	$8$	$4$	$7.027$	8.0.40960000.1	$_{}$	None	None		✓			880.2.t.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	$q+(-\beta _{1}+\beta _{6})q^{2}+\beta _{3}q^{3}+2q^{4}+\beta _{4}q^{5}+\cdots$
880.2.t.b	$880$	$2$	880.t	880.t	$4$	$272$	$136$	$7.027$		$_{}$	None	None		✓	✓		880.2.t.b	$4$	$0$	$0$	$0$	$-4$	$0$			$\mathrm{SU}(2)[C_{4}]$
880.2.v.a	$880$	$2$	880.v	176.i	$4$	$192$	$96$	$7.027$		$_{}$	None	None		✓	✓	✓	880.2.v.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
880.2.w.a	$880$	$2$	880.w	16.e	$4$	$72$	$36$	$7.027$		$_{}$	None	None		✓			880.2.w.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$

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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.