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 86 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	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	CM	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
6300.2.a.a	$6300$	$2$	6300.a	1.a	$1$	$1$	$1$	$50.306$	$\Q$	None	✓				420.2.a.c	$1$	$1$	$0$	$0$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{7}-6q^{11}+4q^{13}+6q^{17}+2q^{19}+\cdots$
6300.2.a.b	$6300$	$2$	6300.a	1.a	$1$	$1$	$1$	$50.306$	$\Q$	None	✓				420.2.k.b	$1$	$0$	$0$	$0$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{7}-4q^{11}-2q^{13}+2q^{17}-2q^{19}+\cdots$
6300.2.a.c	$6300$	$2$	6300.a	1.a	$1$	$1$	$1$	$50.306$	$\Q$	None	✓				140.2.e.a	$1$	$0$	$0$	$0$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{7}-3q^{11}-q^{13}-5q^{17}-8q^{19}+\cdots$
6300.2.a.d	$6300$	$2$	6300.a	1.a	$1$	$1$	$1$	$50.306$	$\Q$	None	✓				140.2.a.a	$1$	$1$	$0$	$0$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{7}-3q^{11}+q^{13}-3q^{17}+2q^{19}+\cdots$
6300.2.a.e	$6300$	$2$	6300.a	1.a	$1$	$1$	$1$	$50.306$	$\Q$	None	✓				700.2.a.c	$1$	$1$	$0$	$0$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{7}-3q^{11}+4q^{13}+2q^{19}-3q^{23}+\cdots$
6300.2.a.f	$6300$	$2$	6300.a	1.a	$1$	$1$	$1$	$50.306$	$\Q$	None	✓				2100.2.a.g	$1$	$1$	$0$	$0$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{7}-q^{11}-4q^{13}+2q^{17}-4q^{19}+\cdots$
6300.2.a.g	$6300$	$2$	6300.a	1.a	$1$	$1$	$1$	$50.306$	$\Q$	None	✓				140.2.e.b	$1$	$0$	$0$	$0$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{7}-4q^{13}+4q^{17}+4q^{19}+8q^{23}+\cdots$
6300.2.a.h	$6300$	$2$	6300.a	1.a	$1$	$1$	$1$	$50.306$	$\Q$	None	✓				1260.2.a.d	$1$	$0$	$0$	$0$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{7}+4q^{13}-6q^{17}+2q^{19}-6q^{23}+\cdots$
6300.2.a.i	$6300$	$2$	6300.a	1.a	$1$	$1$	$1$	$50.306$	$\Q$	None	✓				1260.2.a.d	$1$	$0$	$0$	$0$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{7}+4q^{13}+6q^{17}+2q^{19}+6q^{23}+\cdots$
6300.2.a.j	$6300$	$2$	6300.a	1.a	$1$	$1$	$1$	$50.306$	$\Q$	None	✓				2100.2.a.f	$1$	$0$	$0$	$0$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{7}+q^{11}-2q^{13}-8q^{17}-2q^{19}+\cdots$
6300.2.a.k	$6300$	$2$	6300.a	1.a	$1$	$1$	$1$	$50.306$	$\Q$	None	✓				2100.2.a.c	$1$	$0$	$0$	$0$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{7}+q^{11}-2q^{13}+6q^{19}-q^{23}+\cdots$
6300.2.a.l	$6300$	$2$	6300.a	1.a	$1$	$1$	$1$	$50.306$	$\Q$	None	✓				420.2.a.b	$1$	$1$	$0$	$0$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{7}+2q^{11}-4q^{13}+2q^{17}+2q^{19}+\cdots$
6300.2.a.m	$6300$	$2$	6300.a	1.a	$1$	$1$	$1$	$50.306$	$\Q$	None	✓				2100.2.a.b	$1$	$1$	$0$	$0$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{7}+3q^{11}+4q^{13}-6q^{17}-4q^{19}+\cdots$
6300.2.a.n	$6300$	$2$	6300.a	1.a	$1$	$1$	$1$	$50.306$	$\Q$	None	✓				420.2.k.a	$1$	$0$	$0$	$0$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{7}+4q^{11}+6q^{13}+2q^{17}+6q^{19}+\cdots$
6300.2.a.o	$6300$	$2$	6300.a	1.a	$1$	$1$	$1$	$50.306$	$\Q$	None	✓				700.2.a.e	$1$	$0$	$0$	$0$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{7}+5q^{11}+6q^{13}+4q^{17}-6q^{19}+\cdots$
6300.2.a.p	$6300$	$2$	6300.a	1.a	$1$	$1$	$1$	$50.306$	$\Q$	None	✓				84.2.a.b	$1$	$1$	$0$	$0$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{7}+6q^{11}-2q^{13}-4q^{19}-6q^{23}+\cdots$
6300.2.a.q	$6300$	$2$	6300.a	1.a	$1$	$1$	$1$	$50.306$	$\Q$	None	✓				1260.2.a.b	$1$	$1$	$0$	$0$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{7}-4q^{11}+2q^{17}-6q^{19}+6q^{23}+\cdots$
6300.2.a.r	$6300$	$2$	6300.a	1.a	$1$	$1$	$1$	$50.306$	$\Q$	None	✓				420.2.k.b	$1$	$1$	$0$	$0$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{7}-4q^{11}+2q^{13}-2q^{17}-2q^{19}+\cdots$
6300.2.a.s	$6300$	$2$	6300.a	1.a	$1$	$1$	$1$	$50.306$	$\Q$	None	✓				700.2.a.c	$1$	$1$	$0$	$0$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{7}-3q^{11}-4q^{13}+2q^{19}+3q^{23}+\cdots$
6300.2.a.t	$6300$	$2$	6300.a	1.a	$1$	$1$	$1$	$50.306$	$\Q$	None	✓				140.2.e.a	$1$	$1$	$0$	$0$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{7}-3q^{11}+q^{13}+5q^{17}-8q^{19}+\cdots$
6300.2.a.u	$6300$	$2$	6300.a	1.a	$1$	$1$	$1$	$50.306$	$\Q$	None	✓				420.2.a.d	$1$	$0$	$0$	$0$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{7}-2q^{11}-4q^{13}+2q^{17}-2q^{19}+\cdots$
6300.2.a.v	$6300$	$2$	6300.a	1.a	$1$	$1$	$1$	$50.306$	$\Q$	None	✓				420.2.a.a	$1$	$0$	$0$	$0$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{7}-2q^{11}-4q^{13}+6q^{17}+6q^{19}+\cdots$
6300.2.a.w	$6300$	$2$	6300.a	1.a	$1$	$1$	$1$	$50.306$	$\Q$	None	✓				84.2.a.a	$1$	$0$	$0$	$0$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{7}-2q^{11}+6q^{13}-4q^{17}-4q^{19}+\cdots$
6300.2.a.x	$6300$	$2$	6300.a	1.a	$1$	$1$	$1$	$50.306$	$\Q$	None	✓				2100.2.a.g	$1$	$1$	$0$	$0$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{7}-q^{11}+4q^{13}-2q^{17}-4q^{19}+\cdots$
6300.2.a.y	$6300$	$2$	6300.a	1.a	$1$	$1$	$1$	$50.306$	$\Q$	None	✓				140.2.e.b	$1$	$1$	$0$	$0$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{7}+4q^{13}-4q^{17}+4q^{19}-8q^{23}+\cdots$
6300.2.a.z	$6300$	$2$	6300.a	1.a	$1$	$1$	$1$	$50.306$	$\Q$	None	✓				2100.2.a.c	$1$	$0$	$0$	$0$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{7}+q^{11}+2q^{13}+6q^{19}+q^{23}+\cdots$
6300.2.a.ba	$6300$	$2$	6300.a	1.a	$1$	$1$	$1$	$50.306$	$\Q$	None	✓				2100.2.a.f	$1$	$0$	$0$	$0$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{7}+q^{11}+2q^{13}+8q^{17}-2q^{19}+\cdots$
6300.2.a.bb	$6300$	$2$	6300.a	1.a	$1$	$1$	$1$	$50.306$	$\Q$	None	✓				2100.2.a.b	$1$	$1$	$0$	$0$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{7}+3q^{11}-4q^{13}+6q^{17}-4q^{19}+\cdots$
6300.2.a.bc	$6300$	$2$	6300.a	1.a	$1$	$1$	$1$	$50.306$	$\Q$	None	✓				420.2.k.a	$1$	$1$	$0$	$0$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{7}+4q^{11}-6q^{13}-2q^{17}+6q^{19}+\cdots$
6300.2.a.bd	$6300$	$2$	6300.a	1.a	$1$	$1$	$1$	$50.306$	$\Q$	None	✓				1260.2.a.b	$1$	$1$	$0$	$0$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{7}+4q^{11}-2q^{17}-6q^{19}-6q^{23}+\cdots$
6300.2.a.be	$6300$	$2$	6300.a	1.a	$1$	$1$	$1$	$50.306$	$\Q$	None	✓				700.2.a.e	$1$	$0$	$0$	$0$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{7}+5q^{11}-6q^{13}-4q^{17}-6q^{19}+\cdots$
6300.2.a.bf	$6300$	$2$	6300.a	1.a	$1$	$1$	$1$	$50.306$	$\Q$	None	✓				140.2.a.b	$1$	$0$	$0$	$0$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{7}+5q^{11}+3q^{13}-q^{17}+6q^{19}+\cdots$
6300.2.a.bg	$6300$	$2$	6300.a	1.a	$1$	$2$	$2$	$50.306$	$\Q(\sqrt{3}) $	None	✓	✓	✓		6300.2.a.bg	$2$	$0$	$0$	$0$	$0$	$-2$	$-$	$3$	$\mathrm{SU}(2)$	$q-q^{7}+\beta q^{11}-2q^{13}+2q^{19}-\beta q^{23}+\cdots$
6300.2.a.bh	$6300$	$2$	6300.a	1.a	$1$	$2$	$2$	$50.306$	$\Q(\sqrt{7}) $	None	✓	✓			6300.2.a.bh	$2$	$1$	$0$	$0$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{7}+\beta q^{11}+2\beta q^{17}-3\beta q^{23}+\cdots$
6300.2.a.bi	$6300$	$2$	6300.a	1.a	$1$	$2$	$2$	$50.306$	$\Q(\sqrt{7}) $	None	✓	✓	✓		6300.2.a.bh	$2$	$1$	$0$	$0$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{7}+\beta q^{11}-2\beta q^{17}+3\beta q^{23}+\cdots$
6300.2.a.bj	$6300$	$2$	6300.a	1.a	$1$	$2$	$2$	$50.306$	$\Q(\sqrt{3}) $	None	✓	✓			6300.2.a.bg	$2$	$0$	$0$	$0$	$0$	$2$	$-$	$3$	$\mathrm{SU}(2)$	$q+q^{7}+\beta q^{11}+2q^{13}+2q^{19}+\beta q^{23}+\cdots$
6300.2.a.bk	$6300$	$2$	6300.a	1.a	$1$	$4$	$4$	$50.306$	$\Q(\sqrt{3}, \sqrt{7})$	None	✓		✓		1260.2.k.e	$2$	$1$	$0$	$0$	$0$	$-4$	$+$	$2^{3}$	$\mathrm{SU}(2)$	$q-q^{7}+(-\beta _{1}-\beta _{3})q^{11}+(-1+\beta _{2}+\cdots)q^{13}+\cdots$
6300.2.a.bl	$6300$	$2$	6300.a	1.a	$1$	$4$	$4$	$50.306$	$\Q(\sqrt{3}, \sqrt{7})$	None	✓		✓		1260.2.k.e	$2$	$0$	$0$	$0$	$0$	$4$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+q^{7}+(-\beta _{1}-\beta _{3})q^{11}+(1-\beta _{2})q^{13}+\cdots$
6300.2.d.a	$6300$	$2$	6300.d	21.c	$2$	$4$	$4$	$50.306$	$\Q(\sqrt{-2}, \sqrt{5})$	None					1260.2.d.a	$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{1}-\beta _{3})q^{7}-\beta _{1}q^{11}+(\beta _{1}-\beta _{2}+\cdots)q^{13}+\cdots$
6300.2.d.b	$6300$	$2$	6300.d	21.c	$2$	$4$	$4$	$50.306$	$\Q(\sqrt{-2}, \sqrt{5})$	None					1260.2.d.a	$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{1}+\beta _{3})q^{7}+\beta _{1}q^{11}+(\beta _{1}+\beta _{2}+\cdots)q^{13}+\cdots$
6300.2.d.c	$6300$	$2$	6300.d	21.c	$2$	$4$	$4$	$50.306$	$\Q(\sqrt{-2}, \sqrt{3})$	None					252.2.f.a	$4$	$0$	$0$	$0$	$0$	$4$		$2^{2}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+\beta _{1})q^{7}+\beta _{2}q^{11}+2\beta _{1}q^{13}+\cdots$
6300.2.d.d	$6300$	$2$	6300.d	21.c	$2$	$12$	$12$	$50.306$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		✓			6300.2.d.d	$4$	$0$	$0$	$0$	$0$	$-2$		$2^{8}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{5}q^{7}-\beta _{9}q^{11}+\beta _{8}q^{13}+\beta _{1}q^{17}+\cdots$
6300.2.d.e	$6300$	$2$	6300.d	21.c	$2$	$12$	$12$	$50.306$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		✓			6300.2.d.d	$4$	$0$	$0$	$0$	$0$	$2$		$2^{8}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{7}-\beta _{9}q^{11}-\beta _{8}q^{13}-\beta _{1}q^{17}+\cdots$
6300.2.d.f	$6300$	$2$	6300.d	21.c	$2$	$16$	$16$	$50.306$	16.0.$\cdots$.7	None			✓		1260.2.f.a	$8$	$0$	$0$	$0$	$0$	$0$		$2^{20}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{7}q^{7}-\beta _{1}q^{11}+\beta _{2}q^{13}-\beta _{4}q^{17}+\cdots$
6300.2.f.a	$6300$	$2$	6300.f	105.g	$2$	$8$	$8$	$50.306$	8.0.40960000.1	None					1260.2.d.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{2}+\beta _{3})q^{7}-\beta _{4}q^{11}+(\beta _{3}+\beta _{7})q^{13}+\cdots$
6300.2.f.b	$6300$	$2$	6300.f	105.g	$2$	$8$	$8$	$50.306$	$\Q(\zeta_{24})$	None					252.2.f.a	$8$	$0$	$0$	$0$	$0$	$0$		$2^{10}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta_{3} q^{7}+\beta_{5} q^{11}+(-2\beta_{3}-\beta_1)q^{13}+\cdots$
6300.2.f.c	$6300$	$2$	6300.f	105.g	$2$	$8$	$8$	$50.306$	8.0.40960000.1	None					1260.2.d.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{2}+\beta _{3})q^{7}-\beta _{4}q^{11}+(\beta _{3}+\beta _{7})q^{13}+\cdots$
6300.2.f.d	$6300$	$2$	6300.f	105.g	$2$	$24$	$24$	$50.306$		None		✓	✓		6300.2.d.d	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
6300.2.k.a	$6300$	$2$	6300.k	5.b	$2$	$2$	$2$	$50.306$	$\Q(\sqrt{-1}) $	None					420.2.a.c	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{7}-6 q^{11}-4 i q^{13}+6 i q^{17}+\cdots$
6300.2.k.b	$6300$	$2$	6300.k	5.b	$2$	$2$	$2$	$50.306$	$\Q(\sqrt{-1}) $	None					1260.2.a.b	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{7}-4 q^{11}+2 i q^{17}+6 q^{19}+\cdots$

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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.