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 80 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
2232.1.i.a	$2232$	$1$	2232.i	248.g	$2$	$1$	$1$	$1.114$	$\Q$	$D_{2}$	$\Q(\sqrt{-31}) $, $\Q(\sqrt{-62}) $	$\Q(\sqrt{2}) $	✓				248.1.g.a	$4$	$0$	$-1$	$0$	$0$	$-2$		$1$		$q-q^{2}+q^{4}-2q^{7}-q^{8}+2q^{14}+q^{16}+\cdots$
2232.1.i.b	$2232$	$1$	2232.i	248.g	$2$	$2$	$2$	$1.114$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-6}) $, $\Q(\sqrt{-31}) $	$\Q(\sqrt{186}) $		✓			2232.1.i.b	$8$	$0$	$0$	$0$	$0$	$-4$		$1$		$q-iq^{2}-q^{4}-iq^{5}-q^{7}+iq^{8}-2q^{10}+\cdots$
2232.1.i.c	$2232$	$1$	2232.i	248.g	$2$	$2$	$2$	$1.114$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-31}) $	None					248.1.g.c	$4$	$0$	$1$	$0$	$0$	$2$		$1$		$q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+(\zeta_{6}+\zeta_{6}^{2})q^{5}+\cdots$
2232.1.i.d	$2232$	$1$	2232.i	248.g	$2$	$2$	$2$	$1.114$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-62}) $	None	✓				248.1.g.b	$4$	$0$	$2$	$0$	$0$	$0$		$1$		$q+q^{2}+q^{4}+q^{8}-\beta q^{11}+\beta q^{13}+\cdots$
2232.1.i.e	$2232$	$1$	2232.i	248.g	$2$	$4$	$4$	$1.114$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-31}) $	None		✓	✓		2232.1.i.e	$8$	$0$	$0$	$0$	$0$	$4$		$1$		$q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{3}q^{5}+q^{7}+\cdots$
2232.1.m.a	$2232$	$1$	2232.m	744.m	$2$	$4$	$4$	$1.114$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-31}) $	None		✓			2232.1.m.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(-\zeta_{8}+\zeta_{8}^{3})q^{5}+\cdots$
2232.1.m.b	$2232$	$1$	2232.m	744.m	$2$	$8$	$8$	$1.114$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-31}) $	None		✓	✓		2232.1.m.b	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}q^{2}+\zeta_{24}^{2}q^{4}+(\zeta_{24}^{5}-\zeta_{24}^{7}+\cdots)q^{5}+\cdots$
2232.1.ca.a	$2232$	$1$	2232.ca	2232.ba	$6$	$2$	$1$	$1.114$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-62}) $	None		✓			2232.1.ca.a	$4$	$0$	$-1$	$-1$	$0$	$1$		$1$		$q-\zeta_{6}q^{2}-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{6}+\cdots$
2232.1.ca.b	$2232$	$1$	2232.ca	2232.ba	$6$	$2$	$1$	$1.114$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-62}) $	None		✓			2232.1.ca.a	$4$	$0$	$-1$	$1$	$0$	$1$		$1$		$q-\zeta_{6}q^{2}+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{6}+\cdots$
2232.1.ca.c	$2232$	$1$	2232.ca	2232.ba	$6$	$4$	$2$	$1.114$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-62}) $	None		✓			2232.1.ca.c	$8$	$0$	$-2$	$0$	$0$	$-2$		$1$		$q+\zeta_{12}^{4}q^{2}-\zeta_{12}q^{3}-\zeta_{12}^{2}q^{4}-\zeta_{12}^{5}q^{6}+\cdots$
2232.1.ca.d	$2232$	$1$	2232.ca	2232.ba	$6$	$8$	$4$	$1.114$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-62}) $	None		✓	✓		2232.1.ca.d	$8$	$0$	$4$	$0$	$0$	$0$		$1$		$q-\zeta_{24}^{8}q^{2}-\zeta_{24}^{5}q^{3}-\zeta_{24}^{4}q^{4}+\cdots$
2232.1.cb.a	$2232$	$1$	2232.cb	248.l	$6$	$4$	$2$	$1.114$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-6}) $	None		✓	✓	✓	2232.1.cb.a	$8$	$0$	$0$	$0$	$0$	$-2$		$1$		$q-\zeta_{12}^{3}q^{2}-q^{4}+\zeta_{12}q^{5}-\zeta_{12}^{2}q^{7}+\cdots$
2232.1.cf.a	$2232$	$1$	2232.cf	93.h	$6$	$4$	$2$	$1.114$	$\Q(\sqrt{-2}, \sqrt{-3})$	$S_{4}$	None	None		✓	✓	✓	2232.1.cf.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\beta _{1}q^{11}+(1-\beta _{2})q^{13}-\beta _{2}q^{19}+\cdots$
2232.1.dd.a	$2232$	$1$	2232.dd	248.r	$10$	$8$	$2$	$1.114$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-6}) $	None		✓	✓	✓	2232.1.dd.a	$8$	$0$	$0$	$0$	$0$	$-6$		$1$		$q-\zeta_{20}^{7}q^{2}-\zeta_{20}^{4}q^{4}+(\zeta_{20}+\zeta_{20}^{9}+\cdots)q^{5}+\cdots$
2232.1.ft.a	$2232$	$1$	2232.ft	248.af	$30$	$16$	$2$	$1.114$	$\Q(\zeta_{60})$	$D_{30}$	$\Q(\sqrt{-6}) $	None		✓	✓	✓	2232.1.ft.a	$8$	$0$	$0$	$0$	$0$	$12$		$1$		$q+\zeta_{60}^{9}q^{2}+\zeta_{60}^{18}q^{4}+(\zeta_{60}^{17}-\zeta_{60}^{23}+\cdots)q^{5}+\cdots$
2232.2.a.a	$2232$	$2$	2232.a	1.a	$1$	$1$	$1$	$17.823$	$\Q$	$_{}$	None	None	✓				744.2.a.d	$1$	$0$	$0$	$0$	$-3$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{5}+5q^{7}-4q^{11}-2q^{13}+8q^{17}+\cdots$
2232.2.a.b	$2232$	$2$	2232.a	1.a	$1$	$1$	$1$	$17.823$	$\Q$	$_{}$	None	None	✓				248.2.a.b	$1$	$0$	$0$	$0$	$-2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-2q^{11}+4q^{13}-6q^{17}+4q^{19}+\cdots$
2232.2.a.c	$2232$	$2$	2232.a	1.a	$1$	$1$	$1$	$17.823$	$\Q$	$_{}$	None	None	✓				248.2.a.a	$1$	$1$	$0$	$0$	$-1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-3q^{7}+2q^{11}-2q^{13}+6q^{17}+\cdots$
2232.2.a.d	$2232$	$2$	2232.a	1.a	$1$	$1$	$1$	$17.823$	$\Q$	$_{}$	None	None	✓				744.2.a.c	$1$	$1$	$0$	$0$	$-1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-3q^{7}+2q^{11}+4q^{13}+4q^{17}+\cdots$
2232.2.a.e	$2232$	$2$	2232.a	1.a	$1$	$1$	$1$	$17.823$	$\Q$	$_{}$	None	None	✓	✓			2232.2.a.e	$1$	$1$	$0$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-4q^{11}+2q^{13}-6q^{17}+4q^{19}+\cdots$
2232.2.a.f	$2232$	$2$	2232.a	1.a	$1$	$1$	$1$	$17.823$	$\Q$	$_{}$	None	None	✓	✓			2232.2.a.e	$1$	$0$	$0$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{11}+2q^{13}+6q^{17}+4q^{19}+\cdots$
2232.2.a.g	$2232$	$2$	2232.a	1.a	$1$	$1$	$1$	$17.823$	$\Q$	$_{}$	None	None	✓				744.2.a.g	$1$	$0$	$0$	$0$	$1$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-3q^{7}+4q^{11}-2q^{13}+q^{19}+\cdots$
2232.2.a.h	$2232$	$2$	2232.a	1.a	$1$	$1$	$1$	$17.823$	$\Q$	$_{}$	None	None	✓				744.2.a.b	$1$	$1$	$0$	$0$	$1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+q^{7}-6q^{13}-3q^{19}-6q^{23}+\cdots$
2232.2.a.i	$2232$	$2$	2232.a	1.a	$1$	$1$	$1$	$17.823$	$\Q$	$_{}$	None	None	✓				744.2.a.f	$1$	$1$	$0$	$0$	$2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-4q^{11}-2q^{13}-6q^{17}+4q^{19}+\cdots$
2232.2.a.j	$2232$	$2$	2232.a	1.a	$1$	$1$	$1$	$17.823$	$\Q$	$_{}$	None	None	✓				248.2.a.c	$1$	$1$	$0$	$0$	$3$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+3q^{5}-3q^{7}-2q^{11}-4q^{13}+q^{19}+\cdots$
2232.2.a.k	$2232$	$2$	2232.a	1.a	$1$	$1$	$1$	$17.823$	$\Q$	$_{}$	None	None	✓				744.2.a.e	$1$	$0$	$0$	$0$	$3$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{5}+q^{7}+6q^{11}+4q^{17}-3q^{19}+\cdots$
2232.2.a.l	$2232$	$2$	2232.a	1.a	$1$	$1$	$1$	$17.823$	$\Q$	$_{}$	None	None	✓				744.2.a.a	$1$	$0$	$0$	$0$	$3$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{5}+2q^{7}+5q^{11}+q^{13}-q^{17}+\cdots$
2232.2.a.m	$2232$	$2$	2232.a	1.a	$1$	$2$	$2$	$17.823$	$\Q(\sqrt{41}) $	$_{}$	None	None	✓		✓		744.2.a.i	$1$	$1$	$0$	$0$	$-6$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{5}-\beta q^{7}+(1+\beta )q^{11}+(3+\beta )q^{13}+\cdots$
2232.2.a.n	$2232$	$2$	2232.a	1.a	$1$	$2$	$2$	$17.823$	$\Q(\sqrt{33}) $	$_{}$	None	None	✓		✓		248.2.a.d	$1$	$0$	$0$	$0$	$-3$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{5}+(1-\beta )q^{7}+2q^{11}+\cdots$
2232.2.a.o	$2232$	$2$	2232.a	1.a	$1$	$2$	$2$	$17.823$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓		✓		744.2.a.h	$1$	$1$	$0$	$0$	$-2$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+(1+\beta )q^{7}+(-2+\beta )q^{11}-\beta q^{13}+\cdots$
2232.2.a.p	$2232$	$2$	2232.a	1.a	$1$	$2$	$2$	$17.823$	$\Q(\sqrt{33}) $	$_{}$	None	None	✓	✓			2232.2.a.p	$1$	$1$	$0$	$0$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{5}+(-4+\beta )q^{11}+(2+\beta )q^{13}+\cdots$
2232.2.a.q	$2232$	$2$	2232.a	1.a	$1$	$2$	$2$	$17.823$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	✓			2232.2.a.q	$1$	$0$	$0$	$0$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{5}+(-1+2\beta )q^{7}-2q^{11}+(-2+\cdots)q^{13}+\cdots$
2232.2.a.r	$2232$	$2$	2232.a	1.a	$1$	$2$	$2$	$17.823$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	✓			2232.2.a.q	$1$	$1$	$0$	$0$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{5}+(-1-2\beta )q^{7}+2q^{11}+(-2+\cdots)q^{13}+\cdots$
2232.2.a.s	$2232$	$2$	2232.a	1.a	$1$	$2$	$2$	$17.823$	$\Q(\sqrt{33}) $	$_{}$	None	None	✓	✓			2232.2.a.p	$1$	$0$	$0$	$0$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{5}+(4-\beta )q^{11}+(2+\beta )q^{13}+(-2+\cdots)q^{17}+\cdots$
2232.2.a.t	$2232$	$2$	2232.a	1.a	$1$	$3$	$3$	$17.823$	3.3.892.1	$_{}$	None	None	✓	✓	✓		2232.2.a.t	$1$	$1$	$0$	$0$	$-3$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{5}+(1-\beta _{1}+\beta _{2})q^{7}+\cdots$
2232.2.a.u	$2232$	$2$	2232.a	1.a	$1$	$3$	$3$	$17.823$	3.3.1849.1	$_{}$	None	None	✓				744.2.a.j	$1$	$0$	$0$	$0$	$-2$	$-5$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{5}+(-2-\beta _{2})q^{7}+(-1+\cdots)q^{11}+\cdots$
2232.2.a.v	$2232$	$2$	2232.a	1.a	$1$	$3$	$3$	$17.823$	3.3.892.1	$_{}$	None	None	✓	✓	✓		2232.2.a.t	$1$	$0$	$0$	$0$	$3$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{5}+(1-\beta _{1}+\beta _{2})q^{7}+(-\beta _{1}+\cdots)q^{11}+\cdots$
2232.2.a.w	$2232$	$2$	2232.a	1.a	$1$	$3$	$3$	$17.823$	3.3.316.1	$_{}$	None	None	✓				248.2.a.e	$1$	$0$	$0$	$0$	$3$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{2})q^{5}+(1+2\beta _{1}-\beta _{2})q^{7}+(-3+\cdots)q^{11}+\cdots$
2232.2.h.a	$2232$	$2$	2232.h	93.c	$2$	$32$	$32$	$17.823$		$_{}$	None	None		✓	✓	✓	2232.2.h.a	$4$	$0$	$0$	$0$	$0$	$-16$			$\mathrm{SU}(2)[C_{2}]$
2232.2.q.a	$2232$	$2$	2232.q	31.c	$3$	$2$	$1$	$17.823$	$\Q(\sqrt{-3}) $	$_{}$	None	None					248.2.i.e	$2$	$0$	$0$	$0$	$-3$	$-5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-3\zeta_{6}q^{5}+(-5+5\zeta_{6})q^{7}+\zeta_{6}q^{11}+\cdots$
2232.2.q.b	$2232$	$2$	2232.q	31.c	$3$	$2$	$1$	$17.823$	$\Q(\sqrt{-3}) $	$_{}$	None	None					248.2.i.c	$2$	$0$	$0$	$0$	$-1$	$3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{5}+(3-3\zeta_{6})q^{7}-\zeta_{6}q^{11}+5\zeta_{6}q^{13}+\cdots$
2232.2.q.c	$2232$	$2$	2232.q	31.c	$3$	$2$	$1$	$17.823$	$\Q(\sqrt{-3}) $	$_{}$	None	None					248.2.i.b	$2$	$0$	$0$	$0$	$1$	$-3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{5}+(-3+3\zeta_{6})q^{7}-5\zeta_{6}q^{11}+\cdots$
2232.2.q.d	$2232$	$2$	2232.q	31.c	$3$	$2$	$1$	$17.823$	$\Q(\sqrt{-3}) $	$_{}$	None	None					744.2.q.b	$2$	$0$	$0$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+2\zeta_{6}q^{5}-4\zeta_{6}q^{11}-\zeta_{6}q^{13}+(5+\cdots)q^{19}+\cdots$
2232.2.q.e	$2232$	$2$	2232.q	31.c	$3$	$2$	$1$	$17.823$	$\Q(\sqrt{-3}) $	$_{}$	None	None					744.2.q.c	$2$	$0$	$0$	$0$	$2$	$5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+2\zeta_{6}q^{5}+(5-5\zeta_{6})q^{7}+3\zeta_{6}q^{11}+\cdots$
2232.2.q.f	$2232$	$2$	2232.q	31.c	$3$	$2$	$1$	$17.823$	$\Q(\sqrt{-3}) $	$_{}$	None	None					248.2.i.a	$2$	$0$	$0$	$0$	$3$	$-3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+3\zeta_{6}q^{5}+(-3+3\zeta_{6})q^{7}+5\zeta_{6}q^{11}+\cdots$
2232.2.q.g	$2232$	$2$	2232.q	31.c	$3$	$2$	$1$	$17.823$	$\Q(\sqrt{-3}) $	$_{}$	None	None					248.2.i.d	$2$	$0$	$0$	$0$	$3$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+3\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+\zeta_{6}q^{11}-7\zeta_{6}q^{13}+\cdots$
2232.2.q.h	$2232$	$2$	2232.q	31.c	$3$	$2$	$1$	$17.823$	$\Q(\sqrt{-3}) $	$_{}$	None	None					744.2.q.a	$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+4\zeta_{6}q^{5}-2\zeta_{6}q^{11}-\zeta_{6}q^{13}+(-7+\cdots)q^{19}+\cdots$
2232.2.q.i	$2232$	$2$	2232.q	31.c	$3$	$4$	$2$	$17.823$	$\Q(\sqrt{-3}, \sqrt{41})$	$_{}$	None	None					744.2.q.d	$2$	$0$	$0$	$0$	$-4$	$3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2+2\beta _{2})q^{5}+(-\beta _{1}+2\beta _{2})q^{7}+\cdots$
2232.2.q.j	$2232$	$2$	2232.q	31.c	$3$	$6$	$3$	$17.823$	6.0.591408.1	$_{}$	None	None					744.2.q.f	$2$	$0$	$0$	$0$	$-4$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}-\beta _{4})q^{5}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots$
2232.2.q.k	$2232$	$2$	2232.q	31.c	$3$	$6$	$3$	$17.823$	6.0.591408.1	$_{}$	None	None					248.2.i.f	$2$	$0$	$0$	$0$	$-3$	$1$		$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}-\beta _{3}+\beta _{4}-\beta _{5})q^{5}-\beta _{5}q^{7}+\cdots$

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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.