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 208 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
1260.1.p.a	$1260$	$1$	1260.p	35.c	$2$	$1$	$1$	$0.629$	$\Q$	$D_{3}$	$\Q(\sqrt{-35}) $	None	✓				140.1.h.a	$2$	$0$	$0$	$0$	$-1$	$1$		$1$		$q-q^{5}+q^{7}+q^{11}-q^{13}+q^{17}+q^{25}+\cdots$
1260.1.p.b	$1260$	$1$	1260.p	35.c	$2$	$1$	$1$	$0.629$	$\Q$	$D_{3}$	$\Q(\sqrt{-35}) $	None	✓				140.1.h.a	$2$	$0$	$0$	$0$	$1$	$-1$		$1$		$q+q^{5}-q^{7}+q^{11}+q^{13}-q^{17}+q^{25}+\cdots$
1260.1.u.a	$1260$	$1$	1260.u	140.j	$4$	$4$	$2$	$0.629$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-21}) $	None		✓			1260.1.u.a	$8$	$0$	$0$	$0$	$-4$	$0$		$1$		$q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}-q^{5}+\zeta_{8}q^{7}+\cdots$
1260.1.u.b	$1260$	$1$	1260.u	140.j	$4$	$4$	$2$	$0.629$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-21}) $	None		✓			1260.1.u.a	$8$	$0$	$0$	$0$	$4$	$0$		$1$		$q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+q^{5}-\zeta_{8}q^{7}+\cdots$
1260.1.bj.a	$1260$	$1$	1260.bj	1260.aj	$6$	$2$	$1$	$0.629$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-5}) $	None		✓			1260.1.bj.a	$4$	$0$	$-1$	$-1$	$2$	$-1$		$1$		$q-\zeta_{6}q^{2}-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}+q^{5}+\zeta_{6}^{2}q^{6}+\cdots$
1260.1.bj.b	$1260$	$1$	1260.bj	1260.aj	$6$	$2$	$1$	$0.629$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-5}) $	None		✓			1260.1.bj.b	$4$	$0$	$-1$	$2$	$2$	$-1$		$1$		$q-\zeta_{6}q^{2}+q^{3}+\zeta_{6}^{2}q^{4}+q^{5}-\zeta_{6}q^{6}+\cdots$
1260.1.bj.c	$1260$	$1$	1260.bj	1260.aj	$6$	$2$	$1$	$0.629$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-5}) $	None		✓			1260.1.bj.b	$4$	$0$	$1$	$-2$	$2$	$1$		$1$		$q+\zeta_{6}q^{2}-q^{3}+\zeta_{6}^{2}q^{4}+q^{5}-\zeta_{6}q^{6}+\cdots$
1260.1.bj.d	$1260$	$1$	1260.bj	1260.aj	$6$	$2$	$1$	$0.629$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-5}) $	None		✓			1260.1.bj.a	$4$	$0$	$1$	$1$	$2$	$1$		$1$		$q+\zeta_{6}q^{2}+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}+q^{5}+\zeta_{6}^{2}q^{6}+\cdots$
1260.1.bp.a	$1260$	$1$	1260.bp	1260.ap	$6$	$4$	$2$	$0.629$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-5}) $	None		✓			1260.1.bp.a	$8$	$0$	$0$	$0$	$-2$	$0$		$1$		$q-\zeta_{12}^{5}q^{2}+\zeta_{12}q^{3}-\zeta_{12}^{4}q^{4}+\zeta_{12}^{4}q^{5}+\cdots$
1260.1.bp.b	$1260$	$1$	1260.bp	1260.ap	$6$	$4$	$2$	$0.629$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-5}) $	None		✓			1260.1.bp.a	$8$	$0$	$0$	$0$	$2$	$0$		$1$		$q-\zeta_{12}^{5}q^{2}-\zeta_{12}q^{3}-\zeta_{12}^{4}q^{4}-\zeta_{12}^{4}q^{5}+\cdots$
1260.1.br.a	$1260$	$1$	1260.br	1260.ar	$6$	$4$	$2$	$0.629$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-5}) $	None		✓			1260.1.br.a	$8$	$0$	$0$	$0$	$-2$	$0$		$1$		$q+\zeta_{12}^{3}q^{2}+\zeta_{12}^{5}q^{3}-q^{4}-\zeta_{12}^{2}q^{5}+\cdots$
1260.1.br.b	$1260$	$1$	1260.br	1260.ar	$6$	$4$	$2$	$0.629$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-5}) $	None		✓			1260.1.br.b	$8$	$0$	$0$	$0$	$2$	$0$		$1$		$q+\zeta_{12}^{3}q^{2}-\zeta_{12}q^{3}-q^{4}+\zeta_{12}^{2}q^{5}+\cdots$
1260.1.bt.a	$1260$	$1$	1260.bt	315.ag	$6$	$2$	$1$	$0.629$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-35}) $	None		✓			1260.1.bt.a	$4$	$0$	$0$	$-1$	$-1$	$-1$		$1$		$q-\zeta_{6}q^{3}-\zeta_{6}q^{5}+\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}+\cdots$
1260.1.bt.b	$1260$	$1$	1260.bt	315.ag	$6$	$2$	$1$	$0.629$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-35}) $	None		✓			1260.1.bt.b	$4$	$0$	$0$	$-1$	$-1$	$-1$		$1$		$q+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{5}+\zeta_{6}^{2}q^{7}-\zeta_{6}q^{9}+\cdots$
1260.1.bt.c	$1260$	$1$	1260.bt	315.ag	$6$	$2$	$1$	$0.629$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-35}) $	None		✓			1260.1.bt.a	$4$	$0$	$0$	$1$	$1$	$1$		$1$		$q+\zeta_{6}q^{3}+\zeta_{6}q^{5}-\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}+\cdots$
1260.1.bt.d	$1260$	$1$	1260.bt	315.ag	$6$	$2$	$1$	$0.629$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-35}) $	None		✓			1260.1.bt.b	$4$	$0$	$0$	$1$	$1$	$1$		$1$		$q-\zeta_{6}^{2}q^{3}+\zeta_{6}q^{5}-\zeta_{6}^{2}q^{7}-\zeta_{6}q^{9}+\cdots$
1260.1.cf.a	$1260$	$1$	1260.cf	105.o	$6$	$8$	$4$	$0.629$	$\Q(\zeta_{24})$	$S_{4}$	None	None		✓	✓	✓	1260.1.cf.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}^{7}q^{5}-\zeta_{24}^{10}q^{7}-\zeta_{24}^{6}q^{13}+\cdots$
1260.1.ci.a	$1260$	$1$	1260.ci	140.p	$6$	$2$	$1$	$0.629$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-5}) $	None					140.1.p.a	$4$	$0$	$-1$	$0$	$1$	$1$		$1$		$q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+\zeta_{6}q^{7}+\cdots$
1260.1.ci.b	$1260$	$1$	1260.ci	140.p	$6$	$2$	$1$	$0.629$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-5}) $	None					140.1.p.a	$4$	$0$	$1$	$0$	$1$	$-1$		$1$		$q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}-\zeta_{6}q^{7}+\cdots$
1260.1.cw.a	$1260$	$1$	1260.cw	1260.bw	$6$	$2$	$1$	$0.629$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-5}) $	None		✓			1260.1.bj.b	$4$	$0$	$-2$	$1$	$-1$	$-2$		$1$		$q-q^{2}+\zeta_{6}q^{3}+q^{4}+\zeta_{6}^{2}q^{5}-\zeta_{6}q^{6}+\cdots$
1260.1.cw.b	$1260$	$1$	1260.cw	1260.bw	$6$	$2$	$1$	$0.629$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-5}) $	None		✓			1260.1.bj.a	$4$	$0$	$-2$	$1$	$-1$	$1$		$1$		$q-q^{2}-\zeta_{6}^{2}q^{3}+q^{4}+\zeta_{6}^{2}q^{5}+\zeta_{6}^{2}q^{6}+\cdots$
1260.1.cw.c	$1260$	$1$	1260.cw	1260.bw	$6$	$2$	$1$	$0.629$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-5}) $	None		✓			1260.1.bj.a	$4$	$0$	$2$	$-1$	$-1$	$-1$		$1$		$q+q^{2}+\zeta_{6}^{2}q^{3}+q^{4}+\zeta_{6}^{2}q^{5}+\zeta_{6}^{2}q^{6}+\cdots$
1260.1.cw.d	$1260$	$1$	1260.cw	1260.bw	$6$	$2$	$1$	$0.629$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-5}) $	None		✓			1260.1.bj.b	$4$	$0$	$2$	$-1$	$-1$	$2$		$1$		$q+q^{2}-\zeta_{6}q^{3}+q^{4}+\zeta_{6}^{2}q^{5}-\zeta_{6}q^{6}+\cdots$
1260.1.de.a	$1260$	$1$	1260.de	1260.ce	$6$	$4$	$2$	$0.629$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-5}) $	None		✓			1260.1.br.a	$8$	$0$	$0$	$0$	$-4$	$0$		$1$		$q+\zeta_{12}^{5}q^{2}+\zeta_{12}^{5}q^{3}-\zeta_{12}^{4}q^{4}+\cdots$
1260.1.de.b	$1260$	$1$	1260.de	1260.ce	$6$	$4$	$2$	$0.629$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-5}) $	None		✓			1260.1.br.b	$8$	$0$	$0$	$0$	$4$	$0$		$1$		$q-\zeta_{12}^{5}q^{2}-\zeta_{12}^{3}q^{3}-\zeta_{12}^{4}q^{4}+\cdots$
1260.1.eb.a	$1260$	$1$	1260.eb	1260.db	$12$	$8$	$2$	$0.629$	$\Q(\zeta_{24})$	$S_{4}$	None	None		✓			1260.1.eb.a	$8$	$0$	$-4$	$0$	$0$	$0$		$1$		$q-\zeta_{24}^{4}q^{2}+\zeta_{24}^{3}q^{3}+\zeta_{24}^{8}q^{4}+\cdots$
1260.1.eb.b	$1260$	$1$	1260.eb	1260.db	$12$	$8$	$2$	$0.629$	$\Q(\zeta_{24})$	$S_{4}$	None	None		✓			1260.1.eb.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{24}^{10}q^{2}+\zeta_{24}^{3}q^{3}-\zeta_{24}^{8}q^{4}+\cdots$
1260.2.a.a	$1260$	$2$	1260.a	1.a	$1$	$1$	$1$	$10.061$	$\Q$	$_{}$	None	None	✓		✓	✓	420.2.a.d	$1$	$1$	$0$	$0$	$-1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-q^{7}-2q^{11}+4q^{13}-2q^{17}+\cdots$
1260.2.a.b	$1260$	$2$	1260.a	1.a	$1$	$1$	$1$	$10.061$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	1260.2.a.b	$1$	$0$	$0$	$0$	$-1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-q^{7}+4q^{11}+2q^{17}-6q^{19}+\cdots$
1260.2.a.c	$1260$	$2$	1260.a	1.a	$1$	$1$	$1$	$10.061$	$\Q$	$_{}$	None	None	✓				140.2.a.a	$1$	$0$	$0$	$0$	$-1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+q^{7}-3q^{11}-q^{13}+3q^{17}+\cdots$
1260.2.a.d	$1260$	$2$	1260.a	1.a	$1$	$1$	$1$	$10.061$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	1260.2.a.d	$1$	$1$	$0$	$0$	$-1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+q^{7}-4q^{13}-6q^{17}+2q^{19}+\cdots$
1260.2.a.e	$1260$	$2$	1260.a	1.a	$1$	$1$	$1$	$10.061$	$\Q$	$_{}$	None	None	✓				420.2.a.b	$1$	$0$	$0$	$0$	$-1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+q^{7}+2q^{11}+4q^{13}-2q^{17}+\cdots$
1260.2.a.f	$1260$	$2$	1260.a	1.a	$1$	$1$	$1$	$10.061$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	1260.2.a.b	$1$	$1$	$0$	$0$	$1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-q^{7}-4q^{11}-2q^{17}-6q^{19}+\cdots$
1260.2.a.g	$1260$	$2$	1260.a	1.a	$1$	$1$	$1$	$10.061$	$\Q$	$_{}$	None	None	✓				420.2.a.a	$1$	$0$	$0$	$0$	$1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-q^{7}-2q^{11}+4q^{13}-6q^{17}+\cdots$
1260.2.a.h	$1260$	$2$	1260.a	1.a	$1$	$1$	$1$	$10.061$	$\Q$	$_{}$	None	None	✓				140.2.a.b	$1$	$0$	$0$	$0$	$1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-q^{7}+5q^{11}-3q^{13}+q^{17}+\cdots$
1260.2.a.i	$1260$	$2$	1260.a	1.a	$1$	$1$	$1$	$10.061$	$\Q$	$_{}$	None	None	✓		✓	✓	420.2.a.c	$1$	$1$	$0$	$0$	$1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+q^{7}-6q^{11}-4q^{13}-6q^{17}+\cdots$
1260.2.a.j	$1260$	$2$	1260.a	1.a	$1$	$1$	$1$	$10.061$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	1260.2.a.d	$1$	$0$	$0$	$0$	$1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+q^{7}-4q^{13}+6q^{17}+2q^{19}+\cdots$
1260.2.c.a	$1260$	$2$	1260.c	28.d	$2$	$4$	$4$	$10.061$	$\Q(\zeta_{12})$	$_{}$	None	None					140.2.g.a	$2$	$0$	$2$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta_{3}+1)q^{2}+(\beta_{3}-2\beta_{2}+\beta_1)q^{4}+\cdots$
1260.2.c.b	$1260$	$2$	1260.c	28.d	$2$	$4$	$4$	$10.061$	$\Q(\zeta_{12})$	$_{}$	None	None					140.2.g.a	$2$	$0$	$2$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta_{3}+1)q^{2}+(\beta_{3}-2\beta_{2}+\beta_1)q^{4}+\cdots$
1260.2.c.c	$1260$	$2$	1260.c	28.d	$2$	$8$	$8$	$10.061$	8.0.342102016.5	$_{}$	None	None					140.2.g.c	$4$	$0$	$-2$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{4}q^{2}+(-\beta _{3}-\beta _{4}-\beta _{5})q^{4}+\beta _{2}q^{5}+\cdots$
1260.2.c.d	$1260$	$2$	1260.c	28.d	$2$	$16$	$16$	$10.061$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None					420.2.c.a	$2$	$0$	$-2$	$0$	$0$	$-4$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{4}q^{2}+\beta _{8}q^{4}+\beta _{3}q^{5}+(-\beta _{9}-\beta _{10}+\cdots)q^{7}+\cdots$
1260.2.c.e	$1260$	$2$	1260.c	28.d	$2$	$16$	$16$	$10.061$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None					420.2.c.a	$2$	$0$	$-2$	$0$	$0$	$4$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{4}q^{2}+\beta _{8}q^{4}-\beta _{3}q^{5}-\beta _{15}q^{7}+\cdots$
1260.2.c.f	$1260$	$2$	1260.c	28.d	$2$	$32$	$32$	$10.061$		$_{}$	None	None		✓	✓		1260.2.c.f	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1260.2.d.a	$1260$	$2$	1260.d	21.c	$2$	$4$	$4$	$10.061$	$\Q(\sqrt{-2}, \sqrt{5})$	$_{}$	None	None		✓			1260.2.d.a	$2$	$0$	$0$	$0$	$-4$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{5}+(-\beta _{1}+\beta _{3})q^{7}-\beta _{1}q^{11}+(\beta _{1}+\cdots)q^{13}+\cdots$
1260.2.d.b	$1260$	$2$	1260.d	21.c	$2$	$4$	$4$	$10.061$	$\Q(\sqrt{-2}, \sqrt{5})$	$_{}$	None	None		✓			1260.2.d.a	$2$	$0$	$0$	$0$	$4$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{5}+(\beta _{1}+\beta _{3})q^{7}-\beta _{1}q^{11}+(-\beta _{1}+\cdots)q^{13}+\cdots$
1260.2.f.a	$1260$	$2$	1260.f	105.g	$2$	$8$	$8$	$10.061$	8.0.$\cdots$.11	$_{}$	None	None		✓			1260.2.f.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{5}+\beta _{5}q^{7}+(\beta _{5}+\beta _{6})q^{11}+(\beta _{1}+\cdots)q^{13}+\cdots$
1260.2.f.b	$1260$	$2$	1260.f	105.g	$2$	$8$	$8$	$10.061$	8.0.$\cdots$.11	$_{}$	None	None		✓			1260.2.f.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{1}-\beta _{2}-\beta _{3}+\beta _{5}-\beta _{6}+\beta _{7})q^{5}+\cdots$
1260.2.k.a	$1260$	$2$	1260.k	5.b	$2$	$2$	$2$	$10.061$	$\Q(\sqrt{-1}) $	$_{}$	None	None					420.2.k.b	$2$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-i-2)q^{5}-i q^{7}-4 q^{11}+2 i q^{13}+\cdots$
1260.2.k.b	$1260$	$2$	1260.k	5.b	$2$	$2$	$2$	$10.061$	$\Q(\sqrt{-1}) $	$_{}$	None	None					140.2.e.b	$2$	$0$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-2 i-1)q^{5}+i q^{7}-4 i q^{13}+\cdots$
1260.2.k.c	$1260$	$2$	1260.k	5.b	$2$	$2$	$2$	$10.061$	$\Q(\sqrt{-1}) $	$_{}$	None	None					140.2.e.a	$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(i+2)q^{5}+i q^{7}-3 q^{11}-i q^{13}+\cdots$

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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.