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 87 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
2900.1.e.a	$2900$	$1$	2900.e	580.e	$2$	$2$	$2$	$1.447$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-29}) $	None					116.1.d.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-i q^{2}-i q^{3}-q^{4}-q^{6}+i q^{8}+\cdots$
2900.1.e.b	$2900$	$1$	2900.e	580.e	$2$	$2$	$2$	$1.447$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-29}) $	None					116.1.d.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-i q^{2}-i q^{3}-q^{4}-q^{6}+i q^{8}+\cdots$
2900.1.g.a	$2900$	$1$	2900.g	116.d	$2$	$1$	$1$	$1.447$	$\Q$	$D_{3}$	$\Q(\sqrt{-29}) $	None	✓				116.1.d.a	$2$	$0$	$-1$	$1$	$0$	$0$		$1$		$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}-q^{11}+\cdots$
2900.1.g.b	$2900$	$1$	2900.g	116.d	$2$	$1$	$1$	$1.447$	$\Q$	$D_{2}$	$\Q(\sqrt{-5}) $, $\Q(\sqrt{-29}) $	$\Q(\sqrt{145}) $	✓				580.1.e.c	$4$	$0$	$-1$	$2$	$0$	$0$		$1$		$q-q^{2}+2q^{3}+q^{4}-2q^{6}-q^{8}+3q^{9}+\cdots$
2900.1.g.c	$2900$	$1$	2900.g	116.d	$2$	$1$	$1$	$1.447$	$\Q$	$D_{2}$	$\Q(\sqrt{-5}) $, $\Q(\sqrt{-29}) $	$\Q(\sqrt{145}) $	✓				580.1.e.c	$4$	$0$	$1$	$-2$	$0$	$0$		$1$		$q+q^{2}-2q^{3}+q^{4}-2q^{6}+q^{8}+3q^{9}+\cdots$
2900.1.g.d	$2900$	$1$	2900.g	116.d	$2$	$1$	$1$	$1.447$	$\Q$	$D_{3}$	$\Q(\sqrt{-29}) $	None	✓				116.1.d.a	$2$	$0$	$1$	$-1$	$0$	$0$		$1$		$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{11}+\cdots$
2900.1.g.e	$2900$	$1$	2900.g	116.d	$2$	$2$	$2$	$1.447$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-29}) $	None	✓				580.1.e.d	$4$	$0$	$-2$	$-2$	$0$	$0$		$1$		$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}-\beta q^{11}+\cdots$
2900.1.g.f	$2900$	$1$	2900.g	116.d	$2$	$2$	$2$	$1.447$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-145}) $	$\Q(\sqrt{145}) $					580.1.e.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-i q^{2}-q^{4}+i q^{8}-q^{9}+q^{16}+\cdots$
2900.1.g.g	$2900$	$1$	2900.g	116.d	$2$	$2$	$2$	$1.447$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-29}) $	None	✓				580.1.e.d	$4$	$0$	$2$	$2$	$0$	$0$		$1$		$q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}-\beta q^{11}+\cdots$
2900.1.i.a	$2900$	$1$	2900.i	580.i	$4$	$2$	$1$	$1.447$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-5}) $	None		✓			2900.1.i.a	$4$	$0$	$-2$	$0$	$0$	$2$		$1$		$q-q^{2}-2 i q^{3}+q^{4}+2 i q^{6}+(-i+1)q^{7}+\cdots$
2900.1.i.b	$2900$	$1$	2900.i	580.i	$4$	$2$	$1$	$1.447$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None					580.1.i.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-i q^{2}-q^{4}+i q^{8}+q^{9}+(-i-1)q^{13}+\cdots$
2900.1.i.c	$2900$	$1$	2900.i	580.i	$4$	$2$	$1$	$1.447$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-5}) $	None		✓			2900.1.i.a	$4$	$0$	$2$	$0$	$0$	$-2$		$1$		$q+q^{2}+2 i q^{3}+q^{4}+2 i q^{6}+(i-1)q^{7}+\cdots$
2900.1.t.a	$2900$	$1$	2900.t	580.t	$4$	$2$	$1$	$1.447$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None					580.1.i.a	$4$	$0$	$-2$	$0$	$0$	$0$		$1$		$q-q^{2}+q^{4}-q^{8}-q^{9}+(-i+1)q^{13}+\cdots$
2900.1.t.b	$2900$	$1$	2900.t	580.t	$4$	$2$	$1$	$1.447$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-5}) $	None		✓			2900.1.i.a	$4$	$0$	$0$	$-4$	$0$	$2$		$1$		$q-i q^{2}-2 q^{3}-q^{4}+2 i q^{6}+(i+1)q^{7}+\cdots$
2900.1.t.c	$2900$	$1$	2900.t	580.t	$4$	$2$	$1$	$1.447$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-5}) $	None		✓			2900.1.i.a	$4$	$0$	$0$	$4$	$0$	$-2$		$1$		$q+i q^{2}+2 q^{3}-q^{4}+2 i q^{6}+(-i-1)q^{7}+\cdots$
2900.1.w.a	$2900$	$1$	2900.w	2900.w	$10$	$4$	$1$	$1.447$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-29}) $	None		✓			2900.1.w.a	$4$	$0$	$-1$	$3$	$-1$	$0$		$1$		$q+\zeta_{10}^{2}q^{2}+(1-\zeta_{10}^{3})q^{3}+\zeta_{10}^{4}q^{4}+\cdots$
2900.1.w.b	$2900$	$1$	2900.w	2900.w	$10$	$4$	$1$	$1.447$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-29}) $	None		✓			2900.1.w.a	$4$	$0$	$1$	$-3$	$-1$	$0$		$1$		$q-\zeta_{10}^{2}q^{2}+(-1+\zeta_{10}^{3})q^{3}+\zeta_{10}^{4}q^{4}+\cdots$
2900.1.w.c	$2900$	$1$	2900.w	2900.w	$10$	$8$	$2$	$1.447$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-29}) $	None		✓			2900.1.w.c	$4$	$0$	$-2$	$-3$	$1$	$0$		$1$		$q+\zeta_{30}^{6}q^{2}+(\zeta_{30}^{4}-\zeta_{30}^{5})q^{3}+\zeta_{30}^{12}q^{4}+\cdots$
2900.1.w.d	$2900$	$1$	2900.w	2900.w	$10$	$8$	$2$	$1.447$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-29}) $	None		✓			2900.1.w.c	$4$	$0$	$2$	$3$	$1$	$0$		$1$		$q-\zeta_{30}^{6}q^{2}+(-\zeta_{30}^{10}-\zeta_{30}^{14})q^{3}+\cdots$
2900.1.bb.a	$2900$	$1$	2900.bb	2900.ab	$10$	$4$	$1$	$1.447$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-1}) $	None		✓			2900.1.bb.a	$4$	$0$	$-1$	$0$	$1$	$0$		$1$		$q+\zeta_{10}^{4}q^{2}-\zeta_{10}^{3}q^{4}-\zeta_{10}^{2}q^{5}+\cdots$
2900.1.bb.b	$2900$	$1$	2900.bb	2900.ab	$10$	$4$	$1$	$1.447$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-1}) $	None		✓			2900.1.bb.a	$4$	$0$	$1$	$0$	$1$	$0$		$1$		$q-\zeta_{10}^{4}q^{2}-\zeta_{10}^{3}q^{4}-\zeta_{10}^{2}q^{5}+\cdots$
2900.1.bb.c	$2900$	$1$	2900.bb	2900.ab	$10$	$8$	$2$	$1.447$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-29}) $	None		✓			2900.1.bb.c	$8$	$0$	$0$	$0$	$-2$	$0$		$1$		$q-\zeta_{20}^{3}q^{2}+(\zeta_{20}^{5}-\zeta_{20}^{7})q^{3}+\zeta_{20}^{6}q^{4}+\cdots$
2900.1.bb.d	$2900$	$1$	2900.bb	2900.ab	$10$	$16$	$4$	$1.447$	$\Q(\zeta_{60})$	$D_{30}$	$\Q(\sqrt{-29}) $	None		✓	✓		2900.1.bb.d	$8$	$0$	$0$	$0$	$2$	$0$		$1$		$q-\zeta_{60}^{21}q^{2}+(-\zeta_{60}^{5}+\zeta_{60}^{19})q^{3}+\cdots$
2900.1.bd.a	$2900$	$1$	2900.bd	580.v	$14$	$12$	$2$	$1.447$	$\Q(\zeta_{28})$	$D_{7}$	$\Q(\sqrt{-1}) $	None			✓	✓	116.1.j.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{28}q^{2}+\zeta_{28}^{2}q^{4}+\zeta_{28}^{3}q^{8}+\zeta_{28}^{10}q^{9}+\cdots$
2900.1.be.a	$2900$	$1$	2900.be	116.h	$14$	$6$	$1$	$1.447$	$\Q(\zeta_{14})$	$D_{14}$	$\Q(\sqrt{-5}) $	None					580.1.y.c	$4$	$0$	$-1$	$2$	$0$	$-7$		$1$		$q+\zeta_{14}^{6}q^{2}+(\zeta_{14}+\zeta_{14}^{3})q^{3}-\zeta_{14}^{5}q^{4}+\cdots$
2900.1.be.b	$2900$	$1$	2900.be	116.h	$14$	$6$	$1$	$1.447$	$\Q(\zeta_{14})$	$D_{14}$	$\Q(\sqrt{-5}) $	None					580.1.y.c	$4$	$0$	$1$	$-2$	$0$	$7$		$1$		$q-\zeta_{14}^{6}q^{2}+(-\zeta_{14}-\zeta_{14}^{3})q^{3}-\zeta_{14}^{5}q^{4}+\cdots$
2900.1.be.c	$2900$	$1$	2900.be	116.h	$14$	$12$	$2$	$1.447$	$\Q(\zeta_{28})$	$D_{14}$	$\Q(\sqrt{-1}) $	None			✓		580.1.y.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{28}^{5}q^{2}+\zeta_{28}^{10}q^{4}-\zeta_{28}q^{8}+\cdots$
2900.1.bj.a	$2900$	$1$	2900.bj	116.j	$14$	$6$	$1$	$1.447$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-1}) $	None					116.1.j.a	$4$	$0$	$1$	$0$	$0$	$0$		$1$		$q-\zeta_{14}^{2}q^{2}+\zeta_{14}^{4}q^{4}-\zeta_{14}^{6}q^{8}+\cdots$
2900.1.bj.b	$2900$	$1$	2900.bj	116.j	$14$	$12$	$2$	$1.447$	$\Q(\zeta_{28})$	$D_{7}$	$\Q(\sqrt{-5}) $	None			✓		580.1.v.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{28}^{11}q^{2}+(-\zeta_{28}^{3}+\zeta_{28}^{9})q^{3}+\cdots$
2900.1.bk.a	$2900$	$1$	2900.bk	2900.ak	$20$	$8$	$1$	$1.447$	$\Q(\zeta_{20})$	$D_{20}$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	2900.1.bk.a	$4$	$0$	$-2$	$0$	$0$	$0$		$1$		$q+\zeta_{20}^{4}q^{2}+\zeta_{20}^{8}q^{4}-\zeta_{20}^{7}q^{5}+\cdots$
2900.1.bv.a	$2900$	$1$	2900.bv	2900.av	$20$	$8$	$1$	$1.447$	$\Q(\zeta_{20})$	$D_{20}$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	2900.1.bk.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{20}^{3}q^{2}+\zeta_{20}^{6}q^{4}+\zeta_{20}^{9}q^{5}+\cdots$
2900.1.bx.a	$2900$	$1$	2900.bx	580.ad	$28$	$12$	$1$	$1.447$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-5}) $	None		✓			2900.1.bx.a	$4$	$0$	$0$	$-4$	$0$	$-12$		$1$		$q-\zeta_{28}^{11}q^{2}+(-\zeta_{28}^{2}-\zeta_{28}^{10})q^{3}+\cdots$
2900.1.bx.b	$2900$	$1$	2900.bx	580.ad	$28$	$12$	$1$	$1.447$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-5}) $	None		✓			2900.1.bx.a	$4$	$0$	$0$	$4$	$0$	$12$		$1$		$q+\zeta_{28}^{11}q^{2}+(\zeta_{28}^{2}+\zeta_{28}^{10})q^{3}+\cdots$
2900.1.bx.c	$2900$	$1$	2900.bx	580.ad	$28$	$12$	$1$	$1.447$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-1}) $	None					580.1.bd.a	$4$	$0$	$2$	$0$	$0$	$0$		$1$		$q-\zeta_{28}^{4}q^{2}+\zeta_{28}^{8}q^{4}-\zeta_{28}^{12}q^{8}+\cdots$
2900.1.cg.a	$2900$	$1$	2900.cg	580.am	$28$	$12$	$1$	$1.447$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-5}) $	None		✓			2900.1.bx.a	$4$	$0$	$-2$	$0$	$0$	$2$		$1$		$q-\zeta_{28}^{6}q^{2}+(-\zeta_{28}+\zeta_{28}^{3})q^{3}+\zeta_{28}^{12}q^{4}+\cdots$
2900.1.cg.b	$2900$	$1$	2900.cg	580.am	$28$	$12$	$1$	$1.447$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-1}) $	None					580.1.bd.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{28}^{13}q^{2}-\zeta_{28}^{12}q^{4}+\zeta_{28}^{11}q^{8}+\cdots$
2900.1.cg.c	$2900$	$1$	2900.cg	580.am	$28$	$12$	$1$	$1.447$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-5}) $	None		✓			2900.1.bx.a	$4$	$0$	$2$	$0$	$0$	$-2$		$1$		$q+\zeta_{28}^{6}q^{2}+(\zeta_{28}-\zeta_{28}^{3})q^{3}+\zeta_{28}^{12}q^{4}+\cdots$
2900.1.ck.a	$2900$	$1$	2900.ck	2900.bk	$70$	$24$	$1$	$1.447$	$\Q(\zeta_{35})$	$D_{70}$	$\Q(\sqrt{-1}) $	None		✓			2900.1.ck.a	$4$	$0$	$-1$	$0$	$-1$	$0$		$1$		$q+\zeta_{70}^{19}q^{2}-\zeta_{70}^{3}q^{4}-\zeta_{70}^{32}q^{5}+\cdots$
2900.1.ck.b	$2900$	$1$	2900.ck	2900.bk	$70$	$24$	$1$	$1.447$	$\Q(\zeta_{35})$	$D_{70}$	$\Q(\sqrt{-1}) $	None		✓			2900.1.ck.a	$4$	$0$	$1$	$0$	$-1$	$0$		$1$		$q-\zeta_{70}^{19}q^{2}-\zeta_{70}^{3}q^{4}+\zeta_{70}^{27}q^{5}+\cdots$
2900.1.cl.a	$2900$	$1$	2900.cl	2900.bl	$70$	$24$	$1$	$1.447$	$\Q(\zeta_{35})$	$D_{35}$	$\Q(\sqrt{-1}) $	None		✓			2900.1.cl.a	$4$	$0$	$1$	$0$	$1$	$0$		$1$		$q+\zeta_{70}^{8}q^{2}+\zeta_{70}^{16}q^{4}+\zeta_{70}^{4}q^{5}+\cdots$
2900.1.cl.b	$2900$	$1$	2900.cl	2900.bl	$70$	$24$	$1$	$1.447$	$\Q(\zeta_{35})$	$D_{35}$	$\Q(\sqrt{-1}) $	None		✓			2900.1.cl.a	$4$	$0$	$1$	$0$	$1$	$0$		$1$		$q+\zeta_{70}^{8}q^{2}+\zeta_{70}^{16}q^{4}-\zeta_{70}^{19}q^{5}+\cdots$
2900.1.cr.a	$2900$	$1$	2900.cr	2900.br	$140$	$48$	$1$	$1.447$	$\Q(\zeta_{140})$	$D_{140}$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	2900.1.cr.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{140}^{53}q^{2}-\zeta_{140}^{36}q^{4}-\zeta_{140}^{69}q^{5}+\cdots$
2900.1.da.a	$2900$	$1$	2900.da	2900.ca	$140$	$48$	$1$	$1.447$	$\Q(\zeta_{140})$	$D_{140}$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	2900.1.cr.a	$4$	$0$	$2$	$0$	$0$	$0$		$1$		$q+\zeta_{140}^{8}q^{2}+\zeta_{140}^{16}q^{4}-\zeta_{140}^{39}q^{5}+\cdots$
2900.2.a.a	$2900$	$2$	2900.a	1.a	$1$	$1$	$1$	$23.157$	$\Q$	$_{}$	None	None	✓				116.2.a.c	$1$	$2$	$0$	$-2$	$0$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-4q^{7}+q^{9}-6q^{11}-2q^{13}+\cdots$
2900.2.a.b	$2900$	$2$	2900.a	1.a	$1$	$1$	$1$	$23.157$	$\Q$	$_{}$	None	None	✓				116.2.a.b	$1$	$0$	$0$	$-1$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+4q^{7}-2q^{9}+3q^{11}-5q^{13}+\cdots$
2900.2.a.c	$2900$	$2$	2900.a	1.a	$1$	$1$	$1$	$23.157$	$\Q$	$_{}$	None	None	✓				580.2.a.a	$1$	$1$	$0$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{9}-2q^{11}+2q^{13}-2q^{19}+8q^{23}+\cdots$
2900.2.a.d	$2900$	$2$	2900.a	1.a	$1$	$1$	$1$	$23.157$	$\Q$	$_{}$	None	None	✓				580.2.a.b	$1$	$0$	$0$	$0$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{7}-3q^{9}-4q^{11}+6q^{13}+4q^{17}+\cdots$
2900.2.a.e	$2900$	$2$	2900.a	1.a	$1$	$1$	$1$	$23.157$	$\Q$	$_{}$	None	None	✓				116.2.a.a	$1$	$0$	$0$	$3$	$0$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}-4q^{7}+6q^{9}-q^{11}+3q^{13}+\cdots$
2900.2.a.f	$2900$	$2$	2900.a	1.a	$1$	$3$	$3$	$23.157$	3.3.148.1	$_{}$	None	None	✓				580.2.a.d	$1$	$1$	$0$	$-2$	$0$	$-2$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+(-1+\beta _{2})q^{7}+(1+\cdots)q^{9}+\cdots$
2900.2.a.g	$2900$	$2$	2900.a	1.a	$1$	$3$	$3$	$23.157$	3.3.564.1	$_{}$	None	None	✓				580.2.a.c	$1$	$0$	$0$	$-2$	$0$	$4$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{3}+(1-\beta _{2})q^{7}+(4+\beta _{1}+\cdots)q^{9}+\cdots$

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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.