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 247 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
1200.1.c.a	$1200$	$1$	1200.c	15.d	$2$	$2$	$2$	$0.599$	$\Q(\sqrt{-1})$	$D_{3}$	$\Q(\sqrt{-3})$	None			✓	✓	300.1.g.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-i q^{3}-i q^{7}-q^{9}-i q^{13}-q^{19}+\cdots$
1200.1.l.a	$1200$	$1$	1200.l	3.b	$2$	$1$	$1$	$0.599$	$\Q$	$D_{3}$	$\Q(\sqrt{-3})$	None	✓				300.1.g.a	$2$	$0$	$0$	$-1$	$0$	$1$		$1$		$q-q^{3}+q^{7}+q^{9}-q^{13}+q^{19}-q^{21}+\cdots$
1200.1.l.b	$1200$	$1$	1200.l	3.b	$2$	$1$	$1$	$0.599$	$\Q$	$D_{3}$	$\Q(\sqrt{-3})$	None	✓				300.1.g.a	$2$	$0$	$0$	$1$	$0$	$-1$		$1$		$q+q^{3}-q^{7}+q^{9}+q^{13}+q^{19}-q^{21}+\cdots$
1200.1.r.a	$1200$	$1$	1200.r	48.i	$4$	$4$	$2$	$0.599$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-15})$	None			✓	✓	240.1.bm.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}q^{2}-\zeta_{8}q^{3}+\zeta_{8}^{2}q^{4}+\zeta_{8}^{2}q^{6}+\cdots$
1200.1.z.a	$1200$	$1$	1200.z	240.z	$4$	$2$	$1$	$0.599$	$\Q(\sqrt{-1})$	$D_{4}$	$\Q(\sqrt{-15})$	None		✓			1200.1.z.a	$4$	$0$	$-2$	$0$	$0$	$0$		$1$		$q-q^{2}+i q^{3}+q^{4}-i q^{6}-q^{8}+\cdots$
1200.1.z.b	$1200$	$1$	1200.z	240.z	$4$	$2$	$1$	$0.599$	$\Q(\sqrt{-1})$	$D_{4}$	$\Q(\sqrt{-15})$	None		✓			1200.1.z.a	$4$	$0$	$2$	$0$	$0$	$0$		$1$		$q+q^{2}-i q^{3}+q^{4}-i q^{6}+q^{8}+\cdots$
1200.1.bd.a	$1200$	$1$	1200.bd	240.ad	$4$	$2$	$1$	$0.599$	$\Q(\sqrt{-1})$	$D_{4}$	$\Q(\sqrt{-15})$	None		✓			1200.1.z.a	$4$	$0$	$0$	$-2$	$0$	$0$		$1$		$q-i q^{2}-q^{3}-q^{4}+i q^{6}+i q^{8}+\cdots$
1200.1.bd.b	$1200$	$1$	1200.bd	240.ad	$4$	$2$	$1$	$0.599$	$\Q(\sqrt{-1})$	$D_{4}$	$\Q(\sqrt{-15})$	None		✓			1200.1.z.a	$4$	$0$	$0$	$2$	$0$	$0$		$1$		$q+i q^{2}+q^{3}-q^{4}+i q^{6}-i q^{8}+\cdots$
1200.1.bj.a	$1200$	$1$	1200.bj	60.l	$4$	$4$	$2$	$0.599$	$\Q(\zeta_{8})$	$D_{2}$	$\Q(\sqrt{-3})$ , $\Q(\sqrt{-5})$	$\Q(\sqrt{15})$		✓			1200.1.bj.a	$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}q^{3}-\zeta_{8}^{3}q^{7}+\zeta_{8}^{2}q^{9}-2q^{21}+\cdots$
1200.1.bj.b	$1200$	$1$	1200.bj	60.l	$4$	$8$	$4$	$0.599$	$\Q(\zeta_{24})$	$D_{6}$	$\Q(\sqrt{-3})$	None		✓	✓		1200.1.bj.b	$16$	$0$	$0$	$0$	$0$	$0$		$2^{4}$		$q-\zeta_{24}^{3}q^{3}+\zeta_{24}^{9}q^{7}+\zeta_{24}^{6}q^{9}+\cdots$
1200.2.a.a	$1200$	$2$	1200.a	1.a	$1$	$1$	$1$	$9.582$	$\Q$	$_{}$	None	None	✓				60.2.d.a	$1$	$1$	$0$	$-1$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-4q^{7}+q^{9}+4q^{11}+4q^{17}+\cdots$
1200.2.a.b	$1200$	$2$	1200.a	1.a	$1$	$1$	$1$	$9.582$	$\Q$	$_{}$	None	None	✓				600.2.a.b	$1$	$0$	$0$	$-1$	$0$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-3q^{7}+q^{9}-2q^{11}-3q^{13}+\cdots$
1200.2.a.c	$1200$	$2$	1200.a	1.a	$1$	$1$	$1$	$9.582$	$\Q$	$_{}$	None	None	✓				75.2.a.a	$1$	$0$	$0$	$-1$	$0$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-3q^{7}+q^{9}-2q^{11}-q^{13}+\cdots$
1200.2.a.d	$1200$	$2$	1200.a	1.a	$1$	$1$	$1$	$9.582$	$\Q$	$_{}$	None	None	✓		✓	✓	24.2.a.a	$1$	$1$	$0$	$-1$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{9}-4q^{11}+2q^{13}-2q^{17}+\cdots$
1200.2.a.e	$1200$	$2$	1200.a	1.a	$1$	$1$	$1$	$9.582$	$\Q$	$_{}$	None	None	✓				15.2.a.a	$1$	$0$	$0$	$-1$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{9}+4q^{11}+2q^{13}-2q^{17}+\cdots$
1200.2.a.f	$1200$	$2$	1200.a	1.a	$1$	$1$	$1$	$9.582$	$\Q$	$_{}$	None	None	✓				300.2.a.b	$1$	$1$	$0$	$-1$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}-6q^{11}+5q^{13}+\cdots$
1200.2.a.g	$1200$	$2$	1200.a	1.a	$1$	$1$	$1$	$9.582$	$\Q$	$_{}$	None	None	✓				30.2.c.a	$1$	$1$	$0$	$-1$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{7}+q^{9}-2q^{11}-6q^{13}+\cdots$
1200.2.a.h	$1200$	$2$	1200.a	1.a	$1$	$1$	$1$	$9.582$	$\Q$	$_{}$	None	None	✓				120.2.f.a	$1$	$0$	$0$	$-1$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{7}+q^{9}-2q^{11}+2q^{13}+\cdots$
1200.2.a.i	$1200$	$2$	1200.a	1.a	$1$	$1$	$1$	$9.582$	$\Q$	$_{}$	None	None	✓				600.2.a.e	$1$	$0$	$0$	$-1$	$0$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+5q^{7}+q^{9}+6q^{11}-3q^{13}+\cdots$
1200.2.a.j	$1200$	$2$	1200.a	1.a	$1$	$1$	$1$	$9.582$	$\Q$	$_{}$	None	None	✓				600.2.a.e	$1$	$0$	$0$	$1$	$0$	$-5$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-5q^{7}+q^{9}+6q^{11}+3q^{13}+\cdots$
1200.2.a.k	$1200$	$2$	1200.a	1.a	$1$	$1$	$1$	$9.582$	$\Q$	$_{}$	None	None	✓				30.2.a.a	$1$	$1$	$0$	$1$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-4q^{7}+q^{9}-2q^{13}-6q^{17}+\cdots$
1200.2.a.l	$1200$	$2$	1200.a	1.a	$1$	$1$	$1$	$9.582$	$\Q$	$_{}$	None	None	✓		✓	✓	120.2.f.a	$1$	$1$	$0$	$1$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{7}+q^{9}-2q^{11}-2q^{13}+\cdots$
1200.2.a.m	$1200$	$2$	1200.a	1.a	$1$	$1$	$1$	$9.582$	$\Q$	$_{}$	None	None	✓				30.2.c.a	$1$	$0$	$0$	$1$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{7}+q^{9}-2q^{11}+6q^{13}+\cdots$
1200.2.a.n	$1200$	$2$	1200.a	1.a	$1$	$1$	$1$	$9.582$	$\Q$	$_{}$	None	None	✓				300.2.a.b	$1$	$1$	$0$	$1$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}-6q^{11}-5q^{13}+\cdots$
1200.2.a.o	$1200$	$2$	1200.a	1.a	$1$	$1$	$1$	$9.582$	$\Q$	$_{}$	None	None	✓				120.2.a.b	$1$	$0$	$0$	$1$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{9}+4q^{11}-6q^{13}+6q^{17}+\cdots$
1200.2.a.p	$1200$	$2$	1200.a	1.a	$1$	$1$	$1$	$9.582$	$\Q$	$_{}$	None	None	✓				75.2.a.a	$1$	$0$	$0$	$1$	$0$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+3q^{7}+q^{9}-2q^{11}+q^{13}+\cdots$
1200.2.a.q	$1200$	$2$	1200.a	1.a	$1$	$1$	$1$	$9.582$	$\Q$	$_{}$	None	None	✓				600.2.a.b	$1$	$0$	$0$	$1$	$0$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+3q^{7}+q^{9}-2q^{11}+3q^{13}+\cdots$
1200.2.a.r	$1200$	$2$	1200.a	1.a	$1$	$1$	$1$	$9.582$	$\Q$	$_{}$	None	None	✓				120.2.a.a	$1$	$0$	$0$	$1$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+4q^{7}+q^{9}+6q^{13}+2q^{17}+\cdots$
1200.2.a.s	$1200$	$2$	1200.a	1.a	$1$	$1$	$1$	$9.582$	$\Q$	$_{}$	None	None	✓				60.2.d.a	$1$	$0$	$0$	$1$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+4q^{7}+q^{9}+4q^{11}-4q^{17}+\cdots$
1200.2.f.a	$1200$	$2$	1200.f	5.b	$2$	$2$	$2$	$9.582$	$\Q(\sqrt{-1})$	$_{}$	None	None					300.2.a.b	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{3}+i q^{7}-q^{9}-6 q^{11}-5 i q^{13}+\cdots$
1200.2.f.b	$1200$	$2$	1200.f	5.b	$2$	$2$	$2$	$9.582$	$\Q(\sqrt{-1})$	$_{}$	None	None					24.2.a.a	$2$	$1$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{3}-q^{9}-4 q^{11}+2 i q^{13}+2 i q^{17}+\cdots$
1200.2.f.c	$1200$	$2$	1200.f	5.b	$2$	$2$	$2$	$9.582$	$\Q(\sqrt{-1})$	$_{}$	None	None					600.2.a.b	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{3}+3 i q^{7}-q^{9}-2 q^{11}-3 i q^{13}+\cdots$
1200.2.f.d	$1200$	$2$	1200.f	5.b	$2$	$2$	$2$	$9.582$	$\Q(\sqrt{-1})$	$_{}$	None	None					75.2.a.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{3}+3 i q^{7}-q^{9}-2 q^{11}-i q^{13}+\cdots$
1200.2.f.e	$1200$	$2$	1200.f	5.b	$2$	$2$	$2$	$9.582$	$\Q(\sqrt{-1})$	$_{}$	None	None					30.2.a.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{3}+4 i q^{7}-q^{9}-2 i q^{13}+\cdots$
1200.2.f.f	$1200$	$2$	1200.f	5.b	$2$	$2$	$2$	$9.582$	$\Q(\sqrt{-1})$	$_{}$	None	None					120.2.a.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{3}+4 i q^{7}-q^{9}-6 i q^{13}+\cdots$
1200.2.f.g	$1200$	$2$	1200.f	5.b	$2$	$2$	$2$	$9.582$	$\Q(\sqrt{-1})$	$_{}$	None	None					120.2.a.b	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{3}-q^{9}+4 q^{11}-6 i q^{13}-6 i q^{17}+\cdots$
1200.2.f.h	$1200$	$2$	1200.f	5.b	$2$	$2$	$2$	$9.582$	$\Q(\sqrt{-1})$	$_{}$	None	None					15.2.a.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{3}-q^{9}+4 q^{11}-2 i q^{13}-2 i q^{17}+\cdots$
1200.2.f.i	$1200$	$2$	1200.f	5.b	$2$	$2$	$2$	$9.582$	$\Q(\sqrt{-1})$	$_{}$	None	None					600.2.a.e	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{3}+5 i q^{7}-q^{9}+6 q^{11}+3 i q^{13}+\cdots$
1200.2.h.a	$1200$	$2$	1200.h	12.b	$2$	$2$	$2$	$9.582$	$\Q(\sqrt{-3})$	$_{}$	None	None		✓			1200.2.h.a	$2$	$0$	$0$	$-3$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1-\zeta_{6})q^{3}+3\zeta_{6}q^{9}-3q^{11}+\cdots$
1200.2.h.b	$1200$	$2$	1200.h	12.b	$2$	$2$	$2$	$9.582$	$\Q(\sqrt{-3})$	$_{}$	None	None		✓			1200.2.h.a	$2$	$0$	$0$	$-3$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1-\zeta_{6})q^{3}+3\zeta_{6}q^{9}+3q^{11}+\cdots$
1200.2.h.c	$1200$	$2$	1200.h	12.b	$2$	$2$	$2$	$9.582$	$\Q(\sqrt{-3})$	$_{}$	$\Q(\sqrt{-3})$	None		✓			1200.2.h.c	$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q-\beta q^{3}-3\beta q^{7}-3 q^{9}-7 q^{13}+\cdots$
1200.2.h.d	$1200$	$2$	1200.h	12.b	$2$	$2$	$2$	$9.582$	$\Q(\sqrt{-3})$	$_{}$	$\Q(\sqrt{-3})$	None		✓			1200.2.h.d	$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+\beta q^{3}-\beta q^{7}-3 q^{9}-5 q^{13}-5\beta q^{19}+\cdots$
1200.2.h.e	$1200$	$2$	1200.h	12.b	$2$	$2$	$2$	$9.582$	$\Q(\sqrt{-3})$	$_{}$	$\Q(\sqrt{-3})$	None					48.2.c.a	$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+\beta q^{3}-2\beta q^{7}-3 q^{9}+2 q^{13}+\cdots$
1200.2.h.f	$1200$	$2$	1200.h	12.b	$2$	$2$	$2$	$9.582$	$\Q(\sqrt{-3})$	$_{}$	$\Q(\sqrt{-3})$	None		✓			1200.2.h.d	$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+\beta q^{3}-\beta q^{7}-3 q^{9}+5 q^{13}+5\beta q^{19}+\cdots$
1200.2.h.g	$1200$	$2$	1200.h	12.b	$2$	$2$	$2$	$9.582$	$\Q(\sqrt{-3})$	$_{}$	$\Q(\sqrt{-3})$	None		✓			1200.2.h.c	$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q-\beta q^{3}-3\beta q^{7}-3 q^{9}+7 q^{13}+\cdots$
1200.2.h.h	$1200$	$2$	1200.h	12.b	$2$	$2$	$2$	$9.582$	$\Q(\sqrt{-3})$	$_{}$	None	None		✓			1200.2.h.a	$2$	$0$	$0$	$3$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+\zeta_{6})q^{3}+3\zeta_{6}q^{9}-3q^{11}-2q^{13}+\cdots$
1200.2.h.i	$1200$	$2$	1200.h	12.b	$2$	$2$	$2$	$9.582$	$\Q(\sqrt{-3})$	$_{}$	None	None		✓			1200.2.h.a	$2$	$0$	$0$	$3$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(2-\zeta_{6})q^{3}+(3-3\zeta_{6})q^{9}+3q^{11}+\cdots$
1200.2.h.j	$1200$	$2$	1200.h	12.b	$2$	$4$	$4$	$9.582$	$\Q(\sqrt{-2}, \sqrt{-3})$	$_{}$	None	None					240.2.o.b	$4$	$0$	$0$	$-4$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1+\beta _{1})q^{3}+(-1-2\beta _{1})q^{9}+\beta _{3}q^{11}+\cdots$
1200.2.h.k	$1200$	$2$	1200.h	12.b	$2$	$4$	$4$	$9.582$	$\Q(i, \sqrt{6})$	$_{}$	None	None					240.2.h.a	$4$	$0$	$0$	$0$	$0$	$0$		$3$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+(\beta _{1}+\beta _{3})q^{7}+\beta _{2}q^{9}+(-2\beta _{1}+\cdots)q^{11}+\cdots$
1200.2.h.l	$1200$	$2$	1200.h	12.b	$2$	$4$	$4$	$9.582$	$\Q(\sqrt{-2}, \sqrt{-5})$	$_{}$	$\Q(\sqrt{-5})$	None					240.2.o.a	$8$	$0$	$0$	$0$	$0$	$0$		$3$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{1}q^{3}+(\beta _{1}+\beta _{3})q^{7}+(2+\beta _{2})q^{9}+\cdots$

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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.