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 253 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
1440.1.c.a	$1440$	$1$	1440.c	15.d	$2$	$4$	$4$	$0.719$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	1440.1.c.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}q^{5}-\zeta_{8}^{2}q^{13}+(-\zeta_{8}+\zeta_{8}^{3}+\cdots)q^{17}+\cdots$
1440.1.p.a	$1440$	$1$	1440.p	40.e	$2$	$1$	$1$	$0.719$	$\Q$	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-10}) $	$\Q(\sqrt{6}) $	✓				360.1.p.a	$4$	$0$	$0$	$0$	$-1$	$0$		$1$		$q-q^{5}+2q^{19}+2q^{23}+q^{25}-2q^{47}+\cdots$
1440.1.p.b	$1440$	$1$	1440.p	40.e	$2$	$1$	$1$	$0.719$	$\Q$	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-10}) $	$\Q(\sqrt{6}) $	✓				360.1.p.a	$4$	$0$	$0$	$0$	$1$	$0$		$1$		$q+q^{5}+2q^{19}-2q^{23}+q^{25}+2q^{47}+\cdots$
1440.1.y.a	$1440$	$1$	1440.y	40.i	$4$	$4$	$2$	$0.719$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-6}) $	None			✓	✓	360.1.u.a	$8$	$0$	$0$	$0$	$0$	$4$		$1$		$q+\zeta_{8}^{3}q^{5}+(1-\zeta_{8}^{2})q^{7}+(-\zeta_{8}-\zeta_{8}^{3}+\cdots)q^{11}+\cdots$
1440.1.bh.a	$1440$	$1$	1440.bh	5.c	$4$	$2$	$1$	$0.719$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		✓			1440.1.bh.a	$4$	$0$	$0$	$0$	$-2$	$0$		$1$		$q-q^{5}+(1+i)q^{13}+(1-i)q^{17}+q^{25}+\cdots$
1440.1.bh.b	$1440$	$1$	1440.bh	5.c	$4$	$2$	$1$	$0.719$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None					160.1.p.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-iq^{5}+(-1-i)q^{13}+(1-i)q^{17}+\cdots$
1440.1.bh.c	$1440$	$1$	1440.bh	5.c	$4$	$2$	$1$	$0.719$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		✓			1440.1.bh.a	$4$	$0$	$0$	$0$	$2$	$0$		$1$		$q+q^{5}+(1+i)q^{13}+(-1+i)q^{17}+\cdots$
1440.1.cd.a	$1440$	$1$	1440.cd	45.h	$6$	$8$	$4$	$0.719$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-5}) $	None		✓	✓	✓	1440.1.cd.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}^{7}q^{3}-\zeta_{24}^{10}q^{5}+(-\zeta_{24}-\zeta_{24}^{3}+\cdots)q^{7}+\cdots$
1440.1.cm.a	$1440$	$1$	1440.cm	160.y	$8$	$8$	$2$	$0.719$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-15}) $	None		✓	✓	✓	1440.1.cm.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{16}^{3}q^{2}+\zeta_{16}^{6}q^{4}-\zeta_{16}^{5}q^{5}+\cdots$
1440.2.a.a	$1440$	$2$	1440.a	1.a	$1$	$1$	$1$	$11.498$	$\Q$	$_{}$	None	None	✓				480.2.a.c	$1$	$0$	$0$	$0$	$-1$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-4q^{7}-2q^{13}+6q^{17}+4q^{23}+\cdots$
1440.2.a.b	$1440$	$2$	1440.a	1.a	$1$	$1$	$1$	$11.498$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	1440.2.a.b	$1$	$1$	$0$	$0$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-2q^{7}+2q^{11}+2q^{17}-4q^{19}+\cdots$
1440.2.a.c	$1440$	$2$	1440.a	1.a	$1$	$1$	$1$	$11.498$	$\Q$	$_{}$	None	None	✓				480.2.a.d	$1$	$1$	$0$	$0$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+2q^{13}-6q^{17}-4q^{19}-8q^{23}+\cdots$
1440.2.a.d	$1440$	$2$	1440.a	1.a	$1$	$1$	$1$	$11.498$	$\Q$	$_{}$	None	None	✓				480.2.a.d	$1$	$0$	$0$	$0$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+2q^{13}-6q^{17}+4q^{19}+8q^{23}+\cdots$
1440.2.a.e	$1440$	$2$	1440.a	1.a	$1$	$1$	$1$	$11.498$	$\Q$	$_{}$	None	None	✓	✓			1440.2.a.b	$1$	$0$	$0$	$0$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+2q^{7}-2q^{11}+2q^{17}+4q^{19}+\cdots$
1440.2.a.f	$1440$	$2$	1440.a	1.a	$1$	$1$	$1$	$11.498$	$\Q$	$_{}$	None	None	✓				480.2.a.c	$1$	$0$	$0$	$0$	$-1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+4q^{7}-2q^{13}+6q^{17}-4q^{23}+\cdots$
1440.2.a.g	$1440$	$2$	1440.a	1.a	$1$	$1$	$1$	$11.498$	$\Q$	$_{}$	None	None	✓				480.2.a.a	$1$	$1$	$0$	$0$	$1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-4q^{7}-4q^{11}+6q^{13}-2q^{17}+\cdots$
1440.2.a.h	$1440$	$2$	1440.a	1.a	$1$	$1$	$1$	$11.498$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	1440.2.a.b	$1$	$1$	$0$	$0$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-2q^{7}-2q^{11}-2q^{17}-4q^{19}+\cdots$
1440.2.a.i	$1440$	$2$	1440.a	1.a	$1$	$1$	$1$	$11.498$	$\Q$	$_{}$	None	None	✓				160.2.a.a	$1$	$0$	$0$	$0$	$1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-2q^{7}+4q^{11}-6q^{13}-2q^{17}+\cdots$
1440.2.a.j	$1440$	$2$	1440.a	1.a	$1$	$1$	$1$	$11.498$	$\Q$	$_{}$	None	None	✓				480.2.a.b	$1$	$0$	$0$	$0$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-4q^{11}+2q^{13}+2q^{17}+8q^{19}+\cdots$
1440.2.a.k	$1440$	$2$	1440.a	1.a	$1$	$1$	$1$	$11.498$	$\Q$	$_{}$	None	None	✓				480.2.a.b	$1$	$0$	$0$	$0$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+4q^{11}+2q^{13}+2q^{17}-8q^{19}+\cdots$
1440.2.a.l	$1440$	$2$	1440.a	1.a	$1$	$1$	$1$	$11.498$	$\Q$	$_{}$	None	None	✓				160.2.a.a	$1$	$1$	$0$	$0$	$1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+2q^{7}-4q^{11}-6q^{13}-2q^{17}+\cdots$
1440.2.a.m	$1440$	$2$	1440.a	1.a	$1$	$1$	$1$	$11.498$	$\Q$	$_{}$	None	None	✓	✓			1440.2.a.b	$1$	$0$	$0$	$0$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+2q^{7}+2q^{11}-2q^{17}+4q^{19}+\cdots$
1440.2.a.n	$1440$	$2$	1440.a	1.a	$1$	$1$	$1$	$11.498$	$\Q$	$_{}$	None	None	✓				480.2.a.a	$1$	$0$	$0$	$0$	$1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+4q^{7}+4q^{11}+6q^{13}-2q^{17}+\cdots$
1440.2.a.o	$1440$	$2$	1440.a	1.a	$1$	$2$	$2$	$11.498$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓		✓		160.2.a.c	$2$	$1$	$0$	$0$	$-2$	$0$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{5}+\beta q^{7}-2\beta q^{11}-2q^{13}-2q^{17}+\cdots$
1440.2.a.p	$1440$	$2$	1440.a	1.a	$1$	$2$	$2$	$11.498$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	✓	✓		1440.2.a.p	$2$	$0$	$0$	$0$	$-2$	$0$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{5}-\beta q^{7}-\beta q^{11}+4q^{13}-2q^{17}+\cdots$
1440.2.a.q	$1440$	$2$	1440.a	1.a	$1$	$2$	$2$	$11.498$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	✓	✓		1440.2.a.p	$2$	$0$	$0$	$0$	$2$	$0$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+q^{5}-\beta q^{7}+\beta q^{11}+4q^{13}+2q^{17}+\cdots$
1440.2.b.a	$1440$	$2$	1440.b	24.f	$2$	$2$	$2$	$11.498$	$\Q(\sqrt{-2}) $	$_{}$	None	None					360.2.b.a	$2$	$0$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{5}+3\beta q^{7}+\beta q^{11}-3\beta q^{13}+2\beta q^{17}+\cdots$
1440.2.b.b	$1440$	$2$	1440.b	24.f	$2$	$2$	$2$	$11.498$	$\Q(\sqrt{-2}) $	$_{}$	None	None					360.2.b.a	$2$	$0$	$0$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{5}+3\beta q^{7}-\beta q^{11}-3\beta q^{13}-2\beta q^{17}+\cdots$
1440.2.b.c	$1440$	$2$	1440.b	24.f	$2$	$6$	$6$	$11.498$	6.0.2580992.1	$_{}$	None	None					360.2.b.c	$2$	$0$	$0$	$0$	$-6$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{5}-\beta _{1}q^{7}+(\beta _{1}+\beta _{3})q^{11}+(\beta _{1}+\cdots)q^{13}+\cdots$
1440.2.b.d	$1440$	$2$	1440.b	24.f	$2$	$6$	$6$	$11.498$	6.0.2580992.1	$_{}$	None	None					360.2.b.c	$2$	$0$	$0$	$0$	$6$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{5}-\beta _{1}q^{7}+(-\beta _{1}-\beta _{3})q^{11}+(\beta _{1}+\cdots)q^{13}+\cdots$
1440.2.d.a	$1440$	$2$	1440.d	40.f	$2$	$4$	$4$	$11.498$	$\Q(\sqrt{-2}, \sqrt{-5})$	$_{}$	$\Q(\sqrt{-30}) $	None					360.2.d.a	$8$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{2}q^{5}-2\beta _{2}q^{11}-\beta _{3}q^{13}+\beta _{1}q^{17}+\cdots$
1440.2.d.b	$1440$	$2$	1440.d	40.f	$2$	$4$	$4$	$11.498$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	$\Q(\sqrt{-6}) $	None					360.2.d.d	$8$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{5}-\beta _{3}q^{7}+(\beta _{1}+\beta _{2})q^{11}+(-1+\cdots)q^{25}+\cdots$
1440.2.d.c	$1440$	$2$	1440.d	40.f	$2$	$4$	$4$	$11.498$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None					40.2.f.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}-\beta _{2})q^{5}-\beta _{3}q^{7}-2\beta _{2}q^{11}+\cdots$
1440.2.d.d	$1440$	$2$	1440.d	40.f	$2$	$4$	$4$	$11.498$	$\Q(\sqrt{-3}, \sqrt{5})$	$_{}$	$\Q(\sqrt{-15}) $	None					360.2.d.c	$8$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{5}+2\beta _{2}q^{17}-\beta _{3}q^{19}-\beta _{2}q^{23}+\cdots$
1440.2.d.e	$1440$	$2$	1440.d	40.f	$2$	$6$	$6$	$11.498$	6.0.839056.1	$_{}$	None	None					120.2.d.a	$2$	$0$	$0$	$0$	$0$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{5}-\beta _{1}q^{7}+(-\beta _{1}-\beta _{5})q^{11}+\cdots$
1440.2.d.f	$1440$	$2$	1440.d	40.f	$2$	$6$	$6$	$11.498$	6.0.839056.1	$_{}$	None	None					120.2.d.a	$2$	$0$	$0$	$0$	$0$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{5}-\beta _{1}q^{7}+(\beta _{1}+\beta _{5})q^{11}+(1+\cdots)q^{13}+\cdots$
1440.2.f.a	$1440$	$2$	1440.f	5.b	$2$	$2$	$2$	$11.498$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None		✓			1440.2.f.a	$4$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+(-2-i)q^{5}+4iq^{13}-2iq^{17}+\cdots$
1440.2.f.b	$1440$	$2$	1440.f	5.b	$2$	$2$	$2$	$11.498$	$\Q(\sqrt{-1}) $	$_{}$	None	None					480.2.f.c	$2$	$0$	$0$	$0$	$-2$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1-i)q^{5}+2iq^{7}-2iq^{13}-8q^{19}+\cdots$
1440.2.f.c	$1440$	$2$	1440.f	5.b	$2$	$2$	$2$	$11.498$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None					160.2.c.a	$4$	$0$	$0$	$0$	$-2$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+(-1-i)q^{5}+2iq^{13}+4iq^{17}+\cdots$
1440.2.f.d	$1440$	$2$	1440.f	5.b	$2$	$2$	$2$	$11.498$	$\Q(\sqrt{-1}) $	$_{}$	None	None					480.2.f.c	$2$	$0$	$0$	$0$	$-2$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1+i)q^{5}+2iq^{7}+2iq^{13}+8q^{19}+\cdots$
1440.2.f.e	$1440$	$2$	1440.f	5.b	$2$	$2$	$2$	$11.498$	$\Q(\sqrt{-1}) $	$_{}$	None	None					480.2.f.a	$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(2-i)q^{5}+2iq^{7}-6q^{11}-2iq^{13}+\cdots$
1440.2.f.f	$1440$	$2$	1440.f	5.b	$2$	$2$	$2$	$11.498$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None		✓			1440.2.f.a	$4$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+(2+i)q^{5}+4iq^{13}+2iq^{17}+(3+\cdots)q^{25}+\cdots$
1440.2.f.g	$1440$	$2$	1440.f	5.b	$2$	$2$	$2$	$11.498$	$\Q(\sqrt{-1}) $	$_{}$	None	None					480.2.f.a	$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(2+i)q^{5}+2iq^{7}+6q^{11}+2iq^{13}+\cdots$
1440.2.f.h	$1440$	$2$	1440.f	5.b	$2$	$4$	$4$	$11.498$	$\Q(i, \sqrt{5})$	$_{}$	None	None					480.2.f.e	$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{5}+\beta _{2}q^{7}-\beta _{3}q^{11}+2\beta _{1}q^{13}+\cdots$
1440.2.f.i	$1440$	$2$	1440.f	5.b	$2$	$4$	$4$	$11.498$	$\Q(i, \sqrt{5})$	$_{}$	$\Q(\sqrt{-5}) $	None					160.2.c.b	$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{3}q^{5}-\beta _{1}q^{7}+(-\beta _{1}+2\beta _{2})q^{23}+\cdots$
1440.2.f.j	$1440$	$2$	1440.f	5.b	$2$	$8$	$8$	$11.498$	$\Q(\zeta_{24})$	$_{}$	None	None		✓	✓		1440.2.f.j	$8$	$0$	$0$	$0$	$0$	$0$		$2^{14}$	$\mathrm{SU}(2)[C_{2}]$	$q-\zeta_{24}^{4}q^{5}+\zeta_{24}^{5}q^{7}-\zeta_{24}^{6}q^{11}+\cdots$
1440.2.h.a	$1440$	$2$	1440.h	12.b	$2$	$4$	$4$	$11.498$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			1440.2.h.a	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\zeta_{8}q^{5}+(2\zeta_{8}-\zeta_{8}^{2})q^{7}+(-4-\zeta_{8}^{3})q^{11}+\cdots$
1440.2.h.b	$1440$	$2$	1440.h	12.b	$2$	$4$	$4$	$11.498$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			1440.2.h.b	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\zeta_{8}q^{5}+(2\zeta_{8}-\zeta_{8}^{2})q^{7}-\zeta_{8}^{3}q^{11}+\cdots$
1440.2.h.c	$1440$	$2$	1440.h	12.b	$2$	$4$	$4$	$11.498$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			1440.2.h.b	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\zeta_{8}q^{5}+(2\zeta_{8}-\zeta_{8}^{2})q^{7}+\zeta_{8}^{3}q^{11}+\cdots$
1440.2.h.d	$1440$	$2$	1440.h	12.b	$2$	$4$	$4$	$11.498$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			1440.2.h.a	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\zeta_{8}q^{5}+(2\zeta_{8}-\zeta_{8}^{2})q^{7}+(4+\zeta_{8}^{3})q^{11}+\cdots$

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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.