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 89 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
3675.1.c.a	$3675$	$1$	3675.c	3.b	$2$	$1$	$1$	$1.834$	$\Q$	$D_{3}$	$\Q(\sqrt{-3}) $	None	✓				525.1.u.a	$2$	$0$	$0$	$-1$	$0$	$0$		$1$		$q-q^{3}+q^{4}+q^{9}-q^{12}+q^{13}+q^{16}+\cdots$
3675.1.c.b	$3675$	$1$	3675.c	3.b	$2$	$1$	$1$	$1.834$	$\Q$	$D_{3}$	$\Q(\sqrt{-3}) $	None	✓				525.1.u.a	$2$	$0$	$0$	$-1$	$0$	$0$		$1$		$q-q^{3}+q^{4}+q^{9}-q^{12}+q^{13}+q^{16}+\cdots$
3675.1.c.c	$3675$	$1$	3675.c	3.b	$2$	$1$	$1$	$1.834$	$\Q$	$D_{3}$	$\Q(\sqrt{-3}) $	None	✓				525.1.u.a	$2$	$0$	$0$	$1$	$0$	$0$		$1$		$q+q^{3}+q^{4}+q^{9}+q^{12}-q^{13}+q^{16}+\cdots$
3675.1.c.d	$3675$	$1$	3675.c	3.b	$2$	$1$	$1$	$1.834$	$\Q$	$D_{3}$	$\Q(\sqrt{-3}) $	None	✓				525.1.u.a	$2$	$0$	$0$	$1$	$0$	$0$		$1$		$q+q^{3}+q^{4}+q^{9}+q^{12}-q^{13}+q^{16}+\cdots$
3675.1.c.e	$3675$	$1$	3675.c	3.b	$2$	$2$	$2$	$1.834$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-35}) $	$\Q(\sqrt{21}) $					735.1.f.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-i q^{3}+q^{4}-q^{9}-i q^{12}+q^{16}+\cdots$
3675.1.c.f	$3675$	$1$	3675.c	3.b	$2$	$4$	$4$	$1.834$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-15}) $	None					735.1.f.c	$8$	$0$	$0$	$0$	$0$	$0$		$2$		$q+(-\zeta_{8}-\zeta_{8}^{3})q^{2}+\zeta_{8}^{2}q^{3}-q^{4}+\cdots$
3675.1.c.g	$3675$	$1$	3675.c	3.b	$2$	$4$	$4$	$1.834$	$\Q(\zeta_{8})$	$S_{4}$	None	None		✓			3675.1.c.g	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{8}^{2}q^{2}-\zeta_{8}q^{3}-\zeta_{8}^{3}q^{6}+\zeta_{8}^{2}q^{8}+\cdots$
3675.1.c.h	$3675$	$1$	3675.c	3.b	$2$	$4$	$4$	$1.834$	$\Q(\zeta_{8})$	$S_{4}$	None	None		✓			3675.1.c.g	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{8}^{2}q^{2}+\zeta_{8}^{3}q^{3}-\zeta_{8}q^{6}+\zeta_{8}^{2}q^{8}+\cdots$
3675.1.f.a	$3675$	$1$	3675.f	15.d	$2$	$2$	$2$	$1.834$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None					525.1.u.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+i q^{3}-q^{4}-q^{9}-i q^{12}-i q^{13}+\cdots$
3675.1.f.b	$3675$	$1$	3675.f	15.d	$2$	$2$	$2$	$1.834$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None					525.1.u.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+i q^{3}-q^{4}-q^{9}-i q^{12}-i q^{13}+\cdots$
3675.1.f.c	$3675$	$1$	3675.f	15.d	$2$	$4$	$4$	$1.834$	$\Q(\zeta_{8})$	$S_{4}$	None	None		✓			3675.1.c.g	$4$	$0$	$-4$	$0$	$0$	$0$		$1$		$q-q^{2}-\zeta_{8}q^{3}+\zeta_{8}q^{6}+q^{8}+\zeta_{8}^{2}q^{9}+\cdots$
3675.1.f.d	$3675$	$1$	3675.f	15.d	$2$	$4$	$4$	$1.834$	$\Q(\zeta_{8})$	$S_{4}$	None	None		✓			3675.1.c.g	$4$	$0$	$4$	$0$	$0$	$0$		$1$		$q+q^{2}-\zeta_{8}q^{3}-\zeta_{8}q^{6}-q^{8}+\zeta_{8}^{2}q^{9}+\cdots$
3675.1.k.a	$3675$	$1$	3675.k	105.k	$4$	$8$	$4$	$1.834$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-15}) $	None		✓			3675.1.k.a	$8$	$0$	$0$	$0$	$0$	$0$		$2$		$q+(\zeta_{16}+\zeta_{16}^{3})q^{2}+\zeta_{16}^{2}q^{3}+(\zeta_{16}^{2}+\cdots)q^{4}+\cdots$
3675.1.k.b	$3675$	$1$	3675.k	105.k	$4$	$8$	$4$	$1.834$	$\Q(\zeta_{24})$	$D_{6}$	$\Q(\sqrt{-3}) $	None					525.1.be.a	$16$	$0$	$0$	$0$	$0$	$0$		$2^{4}$		$q+\zeta_{24}^{9}q^{3}-\zeta_{24}^{6}q^{4}-\zeta_{24}^{6}q^{9}+\cdots$
3675.1.k.c	$3675$	$1$	3675.k	105.k	$4$	$8$	$4$	$1.834$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-15}) $	None		✓			3675.1.k.a	$8$	$0$	$0$	$0$	$0$	$0$		$2$		$q+(\zeta_{16}+\zeta_{16}^{3})q^{2}-\zeta_{16}^{2}q^{3}+(\zeta_{16}^{2}+\cdots)q^{4}+\cdots$
3675.1.p.a	$3675$	$1$	3675.p	105.o	$6$	$4$	$2$	$1.834$	$\Q(\zeta_{12})$	$D_{3}$	$\Q(\sqrt{-3}) $	None					525.1.u.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{12}q^{3}-\zeta_{12}^{4}q^{4}+\zeta_{12}^{2}q^{9}-\zeta_{12}^{5}q^{12}+\cdots$
3675.1.p.b	$3675$	$1$	3675.p	105.o	$6$	$8$	$4$	$1.834$	$\Q(\zeta_{24})$	$S_{4}$	None	None		✓			3675.1.c.g	$8$	$0$	$-4$	$0$	$0$	$0$		$1$		$q-\zeta_{24}^{4}q^{2}-\zeta_{24}^{5}q^{3}+\zeta_{24}^{9}q^{6}+\cdots$
3675.1.p.c	$3675$	$1$	3675.p	105.o	$6$	$8$	$4$	$1.834$	$\Q(\zeta_{24})$	$S_{4}$	None	None		✓			3675.1.c.g	$8$	$0$	$4$	$0$	$0$	$0$		$1$		$q+\zeta_{24}^{4}q^{2}-\zeta_{24}^{5}q^{3}-\zeta_{24}^{9}q^{6}+\cdots$
3675.1.u.a	$3675$	$1$	3675.u	21.h	$6$	$2$	$1$	$1.834$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None					525.1.u.a	$4$	$0$	$0$	$-1$	$0$	$0$		$1$		$q-\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}^{2}q^{9}+\zeta_{6}^{2}q^{12}+\cdots$
3675.1.u.b	$3675$	$1$	3675.u	21.h	$6$	$2$	$1$	$1.834$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None					525.1.u.a	$4$	$0$	$0$	$1$	$0$	$0$		$1$		$q+\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}^{2}q^{9}-\zeta_{6}^{2}q^{12}+\cdots$
3675.1.u.c	$3675$	$1$	3675.u	21.h	$6$	$4$	$2$	$1.834$	$\Q(\zeta_{12})$	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-35}) $	$\Q(\sqrt{21}) $					735.1.f.a	$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{12}q^{3}+\zeta_{12}^{4}q^{4}+\zeta_{12}^{2}q^{9}-\zeta_{12}^{5}q^{12}+\cdots$
3675.1.u.d	$3675$	$1$	3675.u	21.h	$6$	$8$	$4$	$1.834$	$\Q(\zeta_{24})$	$S_{4}$	None	None		✓			3675.1.c.g	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{24}^{10}q^{2}+\zeta_{24}^{11}q^{3}-\zeta_{24}^{9}q^{6}+\cdots$
3675.1.u.e	$3675$	$1$	3675.u	21.h	$6$	$8$	$4$	$1.834$	$\Q(\zeta_{24})$	$S_{4}$	None	None		✓			3675.1.c.g	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{24}^{10}q^{2}-\zeta_{24}^{5}q^{3}+\zeta_{24}^{3}q^{6}+\cdots$
3675.1.u.f	$3675$	$1$	3675.u	21.h	$6$	$8$	$4$	$1.834$	$\Q(\zeta_{24})$	$D_{4}$	$\Q(\sqrt{-15}) $	None					735.1.f.c	$16$	$0$	$0$	$0$	$0$	$0$		$2^{2}$		$q+(-\zeta_{24}+\zeta_{24}^{7})q^{2}-\zeta_{24}^{2}q^{3}-\zeta_{24}^{8}q^{4}+\cdots$
3675.1.bf.a	$3675$	$1$	3675.bf	105.w	$12$	$8$	$2$	$1.834$	$\Q(\zeta_{24})$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-35}) $	$\Q(\sqrt{105}) $					525.1.k.a	$32$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{24}^{7}q^{3}-\zeta_{24}^{10}q^{4}-\zeta_{24}^{2}q^{9}+\cdots$
3675.1.bf.b	$3675$	$1$	3675.bf	105.w	$12$	$8$	$2$	$1.834$	$\Q(\zeta_{24})$	$D_{6}$	$\Q(\sqrt{-3}) $	None					525.1.be.a	$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{24}^{7}q^{3}-\zeta_{24}^{10}q^{4}-\zeta_{24}^{2}q^{9}+\cdots$
3675.1.bf.c	$3675$	$1$	3675.bf	105.w	$12$	$16$	$4$	$1.834$	$\Q(\zeta_{48})$	$D_{8}$	$\Q(\sqrt{-15}) $	None		✓			3675.1.k.a	$16$	$0$	$0$	$0$	$0$	$0$		$2^{2}$		$q+(\zeta_{48}^{5}-\zeta_{48}^{23})q^{2}-\zeta_{48}^{10}q^{3}+\cdots$
3675.1.bf.d	$3675$	$1$	3675.bf	105.w	$12$	$16$	$4$	$1.834$	$\Q(\zeta_{48})$	$D_{8}$	$\Q(\sqrt{-15}) $	None		✓			3675.1.k.a	$16$	$0$	$0$	$0$	$0$	$0$		$2^{2}$		$q+(\zeta_{48}^{7}+\zeta_{48}^{13})q^{2}-\zeta_{48}^{2}q^{3}+(-\zeta_{48}^{2}+\cdots)q^{4}+\cdots$
3675.1.bj.a	$3675$	$1$	3675.bj	735.ab	$14$	$12$	$2$	$1.834$	$\Q(\zeta_{28})$	$D_{7}$	$\Q(\sqrt{-3}) $	None			✓	✓	147.1.l.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{28}^{5}q^{3}-\zeta_{28}^{8}q^{4}+\zeta_{28}^{11}q^{7}+\cdots$
3675.1.bm.a	$3675$	$1$	3675.bm	147.l	$14$	$6$	$1$	$1.834$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-3}) $	None			✓	✓	147.1.l.a	$4$	$0$	$0$	$1$	$0$	$1$		$1$		$q+\zeta_{14}^{3}q^{3}+\zeta_{14}^{2}q^{4}+\zeta_{14}q^{7}+\zeta_{14}^{6}q^{9}+\cdots$
3675.1.bx.a	$3675$	$1$	3675.bx	735.ak	$28$	$24$	$2$	$1.834$	$\Q(\zeta_{56})$	$D_{14}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	3675.1.bx.a	$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{56}^{5}q^{3}-\zeta_{56}^{22}q^{4}-\zeta_{56}^{11}q^{7}+\cdots$
3675.1.cg.a	$3675$	$1$	3675.cg	147.n	$42$	$12$	$1$	$1.834$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-3}) $	None		✓			3675.1.cg.a	$4$	$0$	$0$	$-1$	$0$	$-1$		$1$		$q-\zeta_{42}^{2}q^{3}+\zeta_{42}^{20}q^{4}+\zeta_{42}^{17}q^{7}+\cdots$
3675.1.cg.b	$3675$	$1$	3675.cg	147.n	$42$	$12$	$1$	$1.834$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-3}) $	None		✓			3675.1.cg.a	$4$	$0$	$0$	$1$	$0$	$1$		$1$		$q+\zeta_{42}^{2}q^{3}+\zeta_{42}^{20}q^{4}-\zeta_{42}^{17}q^{7}+\cdots$
3675.1.cl.a	$3675$	$1$	3675.cl	735.aq	$42$	$24$	$2$	$1.834$	$\Q(\zeta_{84})$	$D_{21}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	3675.1.cg.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{84}^{25}q^{3}-\zeta_{84}^{40}q^{4}-\zeta_{84}^{13}q^{7}+\cdots$
3675.1.cy.a	$3675$	$1$	3675.cy	735.as	$84$	$48$	$2$	$1.834$	$\Q(\zeta_{168})$	$D_{42}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	3675.1.cy.a	$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{168}^{59}q^{3}-\zeta_{168}^{2}q^{4}+\zeta_{168}^{29}q^{7}+\cdots$
3675.2.a.a	$3675$	$2$	3675.a	1.a	$1$	$1$	$1$	$29.345$	$\Q$	$_{}$	None	None	✓				21.2.e.a	$1$	$1$	$-2$	$-1$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-q^{3}+2q^{4}+2q^{6}+q^{9}-2q^{11}+\cdots$
3675.2.a.b	$3675$	$2$	3675.a	1.a	$1$	$1$	$1$	$29.345$	$\Q$	$_{}$	None	None	✓				75.2.a.a	$1$	$0$	$-2$	$-1$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-q^{3}+2q^{4}+2q^{6}+q^{9}+2q^{11}+\cdots$
3675.2.a.c	$3675$	$2$	3675.a	1.a	$1$	$1$	$1$	$29.345$	$\Q$	$_{}$	None	None	✓				21.2.e.a	$1$	$1$	$-2$	$1$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+q^{3}+2q^{4}-2q^{6}+q^{9}-2q^{11}+\cdots$
3675.2.a.d	$3675$	$2$	3675.a	1.a	$1$	$1$	$1$	$29.345$	$\Q$	$_{}$	None	None	✓				105.2.d.a	$1$	$1$	$-1$	$-1$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}-q^{4}+q^{6}+3q^{8}+q^{9}+\cdots$
3675.2.a.e	$3675$	$2$	3675.a	1.a	$1$	$1$	$1$	$29.345$	$\Q$	$_{}$	None	None	✓				525.2.i.b	$1$	$1$	$-1$	$-1$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}-q^{4}+q^{6}+3q^{8}+q^{9}+\cdots$
3675.2.a.f	$3675$	$2$	3675.a	1.a	$1$	$1$	$1$	$29.345$	$\Q$	$_{}$	None	None	✓				105.2.a.a	$1$	$1$	$-1$	$1$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}-q^{4}-q^{6}+3q^{8}+q^{9}+\cdots$
3675.2.a.g	$3675$	$2$	3675.a	1.a	$1$	$1$	$1$	$29.345$	$\Q$	$_{}$	None	None	✓				525.2.i.b	$1$	$1$	$-1$	$1$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}-q^{4}-q^{6}+3q^{8}+q^{9}+\cdots$
3675.2.a.h	$3675$	$2$	3675.a	1.a	$1$	$1$	$1$	$29.345$	$\Q$	$_{}$	None	None	✓				105.2.i.a	$1$	$1$	$0$	$-1$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{4}+q^{9}+2q^{12}+q^{13}+\cdots$
3675.2.a.i	$3675$	$2$	3675.a	1.a	$1$	$1$	$1$	$29.345$	$\Q$	$_{}$	None	None	✓				105.2.i.a	$1$	$1$	$0$	$1$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}+q^{9}-2q^{12}-q^{13}+\cdots$
3675.2.a.j	$3675$	$2$	3675.a	1.a	$1$	$1$	$1$	$29.345$	$\Q$	$_{}$	None	None	✓				15.2.a.a	$1$	$0$	$1$	$-1$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}-q^{4}-q^{6}-3q^{8}+q^{9}+\cdots$
3675.2.a.k	$3675$	$2$	3675.a	1.a	$1$	$1$	$1$	$29.345$	$\Q$	$_{}$	None	None	✓				525.2.i.b	$1$	$1$	$1$	$-1$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}-q^{4}-q^{6}-3q^{8}+q^{9}+\cdots$
3675.2.a.l	$3675$	$2$	3675.a	1.a	$1$	$1$	$1$	$29.345$	$\Q$	$_{}$	None	None	✓				105.2.d.a	$1$	$0$	$1$	$1$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}-q^{4}+q^{6}-3q^{8}+q^{9}+\cdots$
3675.2.a.m	$3675$	$2$	3675.a	1.a	$1$	$1$	$1$	$29.345$	$\Q$	$_{}$	None	None	✓				525.2.i.b	$1$	$1$	$1$	$1$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}-q^{4}+q^{6}-3q^{8}+q^{9}+\cdots$
3675.2.a.n	$3675$	$2$	3675.a	1.a	$1$	$1$	$1$	$29.345$	$\Q$	$_{}$	None	None	✓				21.2.a.a	$1$	$1$	$1$	$1$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}-q^{4}+q^{6}-3q^{8}+q^{9}+\cdots$
3675.2.a.o	$3675$	$2$	3675.a	1.a	$1$	$1$	$1$	$29.345$	$\Q$	$_{}$	None	None	✓				105.2.i.b	$1$	$1$	$2$	$-1$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-q^{3}+2q^{4}-2q^{6}+q^{9}-6q^{11}+\cdots$

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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.