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 244 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
675.1.c.a	$675$	$1$	675.c	3.b	$2$	$1$	$1$	$0.337$	$\Q$	$D_{3}$	$\Q(\sqrt{-3}) $	None	✓	✓			675.1.c.a	$2$	$0$	$0$	$0$	$0$	$-1$		$1$		$q+q^{4}-q^{7}+2q^{13}+q^{16}-q^{19}+\cdots$
675.1.c.b	$675$	$1$	675.c	3.b	$2$	$1$	$1$	$0.337$	$\Q$	$D_{3}$	$\Q(\sqrt{-3}) $	None	✓	✓			675.1.c.a	$2$	$0$	$0$	$0$	$0$	$1$		$1$		$q+q^{4}+q^{7}-2q^{13}+q^{16}-q^{19}+\cdots$
675.1.c.c	$675$	$1$	675.c	3.b	$2$	$2$	$2$	$0.337$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-15}) $	None			✓		135.1.d.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-i q^{2}-i q^{8}-q^{16}-i q^{17}+q^{19}+\cdots$
675.1.d.a	$675$	$1$	675.d	15.d	$2$	$2$	$2$	$0.337$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	675.1.c.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-q^{4}-i q^{7}-2 i q^{13}+q^{16}+q^{19}+\cdots$
675.1.g.a	$675$	$1$	675.g	5.c	$4$	$4$	$2$	$0.337$	$\Q(i, \sqrt{6})$	$D_{6}$	$\Q(\sqrt{-15}) $	None		✓			675.1.g.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta _{1}q^{2}+2\beta _{2}q^{4}-\beta _{3}q^{8}-q^{16}+\cdots$
675.1.g.b	$675$	$1$	675.g	5.c	$4$	$4$	$2$	$0.337$	$\Q(i, \sqrt{6})$	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓			675.1.g.b	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta _{2}q^{4}-\beta _{1}q^{7}-q^{16}-\beta _{2}q^{19}+\cdots$
675.1.o.a	$675$	$1$	675.o	75.j	$10$	$8$	$2$	$0.337$	$\Q(\zeta_{20})$	$A_{5}$	None	None		✓	✓	✓	675.1.o.a	$4$	$0$	$0$	$0$	$0$	$-4$		$1$		$q+(-\zeta_{20}-\zeta_{20}^{5})q^{2}+(-1+\zeta_{20}^{2}+\cdots)q^{4}+\cdots$
675.2.a.a	$675$	$2$	675.a	1.a	$1$	$1$	$1$	$5.390$	$\Q$	$_{}$	None	None	✓				135.2.a.a	$1$	$0$	$-2$	$0$	$0$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}+3q^{7}+2q^{11}+5q^{13}+\cdots$
675.2.a.b	$675$	$2$	675.a	1.a	$1$	$1$	$1$	$5.390$	$\Q$	$_{}$	None	None	✓	✓			675.2.a.b	$1$	$1$	$-1$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+3q^{8}-5q^{11}+5q^{13}+\cdots$
675.2.a.c	$675$	$2$	675.a	1.a	$1$	$1$	$1$	$5.390$	$\Q$	$_{}$	None	None	✓	✓			675.2.a.b	$1$	$0$	$-1$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+3q^{8}+5q^{11}-5q^{13}+\cdots$
675.2.a.d	$675$	$2$	675.a	1.a	$1$	$1$	$1$	$5.390$	$\Q$	$_{}$	$\Q(\sqrt{-3}) $	None	✓	✓			675.2.a.d	$2$	$0$	$0$	$0$	$0$	$-4$	$-$	$1$	$N(\mathrm{U}(1))$	$q-2q^{4}-4q^{7}+5q^{13}+4q^{16}+8q^{19}+\cdots$
675.2.a.e	$675$	$2$	675.a	1.a	$1$	$1$	$1$	$5.390$	$\Q$	$_{}$	$\Q(\sqrt{-3}) $	None	✓				27.2.a.a	$2$	$1$	$0$	$0$	$0$	$1$	$+$	$1$	$N(\mathrm{U}(1))$	$q-2q^{4}+q^{7}-5q^{13}+4q^{16}-7q^{19}+\cdots$
675.2.a.f	$675$	$2$	675.a	1.a	$1$	$1$	$1$	$5.390$	$\Q$	$_{}$	$\Q(\sqrt{-3}) $	None	✓	✓			675.2.a.d	$2$	$0$	$0$	$0$	$0$	$4$	$-$	$1$	$N(\mathrm{U}(1))$	$q-2q^{4}+4q^{7}-5q^{13}+4q^{16}+8q^{19}+\cdots$
675.2.a.g	$675$	$2$	675.a	1.a	$1$	$1$	$1$	$5.390$	$\Q$	$_{}$	None	None	✓	✓			675.2.a.b	$1$	$1$	$1$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-3q^{8}-5q^{11}-5q^{13}+\cdots$
675.2.a.h	$675$	$2$	675.a	1.a	$1$	$1$	$1$	$5.390$	$\Q$	$_{}$	None	None	✓	✓			675.2.a.b	$1$	$0$	$1$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-3q^{8}+5q^{11}+5q^{13}+\cdots$
675.2.a.i	$675$	$2$	675.a	1.a	$1$	$1$	$1$	$5.390$	$\Q$	$_{}$	None	None	✓				135.2.a.a	$1$	$0$	$2$	$0$	$0$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}+3q^{7}-2q^{11}+5q^{13}+\cdots$
675.2.a.j	$675$	$2$	675.a	1.a	$1$	$2$	$2$	$5.390$	$\Q(\sqrt{5}) $	$_{}$	$\Q(\sqrt{-15}) $	None	✓				135.2.b.a	$2$	$1$	$-3$	$0$	$0$	$0$	$+$	$1$	$N(\mathrm{U}(1))$	$q+(-1-\beta )q^{2}+3\beta q^{4}+(-1-4\beta )q^{8}+\cdots$
675.2.a.k	$675$	$2$	675.a	1.a	$1$	$2$	$2$	$5.390$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓		✓		135.2.a.c	$1$	$1$	$-1$	$0$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(1+\beta )q^{4}+(-2+2\beta )q^{7}+\cdots$
675.2.a.l	$675$	$2$	675.a	1.a	$1$	$2$	$2$	$5.390$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				135.2.b.b	$2$	$1$	$0$	$0$	$0$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-3q^{7}-2\beta q^{8}-3\beta q^{11}-3q^{13}+\cdots$
675.2.a.m	$675$	$2$	675.a	1.a	$1$	$2$	$2$	$5.390$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				135.2.b.b	$2$	$0$	$0$	$0$	$0$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+3q^{7}-2\beta q^{8}+3\beta q^{11}+3q^{13}+\cdots$
675.2.a.n	$675$	$2$	675.a	1.a	$1$	$2$	$2$	$5.390$	$\Q(\sqrt{7}) $	$_{}$	None	None	✓	✓			675.2.a.n	$2$	$0$	$0$	$0$	$0$	$-6$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+5q^{4}-3q^{7}+3\beta q^{8}+2\beta q^{11}+\cdots$
675.2.a.o	$675$	$2$	675.a	1.a	$1$	$2$	$2$	$5.390$	$\Q(\sqrt{7}) $	$_{}$	None	None	✓	✓			675.2.a.n	$2$	$0$	$0$	$0$	$0$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+5q^{4}+3q^{7}+3\beta q^{8}-2\beta q^{11}+\cdots$
675.2.a.p	$675$	$2$	675.a	1.a	$1$	$2$	$2$	$5.390$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓				135.2.a.c	$1$	$0$	$1$	$0$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(1+\beta )q^{4}+(-2+2\beta )q^{7}+\cdots$
675.2.a.q	$675$	$2$	675.a	1.a	$1$	$2$	$2$	$5.390$	$\Q(\sqrt{5}) $	$_{}$	$\Q(\sqrt{-15}) $	None	✓				135.2.b.a	$2$	$0$	$3$	$0$	$0$	$0$	$-$	$1$	$N(\mathrm{U}(1))$	$q+(1+\beta )q^{2}+3\beta q^{4}+(1+4\beta )q^{8}+(5+\cdots)q^{16}+\cdots$
675.2.b.a	$675$	$2$	675.b	5.b	$2$	$2$	$2$	$5.390$	$\Q(\sqrt{-1}) $	$_{}$	None	None					135.2.a.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2 i q^{2}-2 q^{4}+3 i q^{7}-2 q^{11}+\cdots$
675.2.b.b	$675$	$2$	675.b	5.b	$2$	$2$	$2$	$5.390$	$\Q(\sqrt{-1}) $	$_{}$	None	None					135.2.a.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2 i q^{2}-2 q^{4}-3 i q^{7}+2 q^{11}+\cdots$
675.2.b.c	$675$	$2$	675.b	5.b	$2$	$2$	$2$	$5.390$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			675.2.a.b	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}+q^{4}+3 i q^{8}-5 q^{11}+5 i q^{13}+\cdots$
675.2.b.d	$675$	$2$	675.b	5.b	$2$	$2$	$2$	$5.390$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			675.2.a.b	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}+q^{4}+3 i q^{8}+5 q^{11}-5 i q^{13}+\cdots$
675.2.b.e	$675$	$2$	675.b	5.b	$2$	$2$	$2$	$5.390$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-3}) $	None		✓			675.2.a.d	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2 q^{4}+4 i q^{7}+5 i q^{13}+4 q^{16}+\cdots$
675.2.b.f	$675$	$2$	675.b	5.b	$2$	$2$	$2$	$5.390$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-3}) $	None					27.2.a.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2 q^{4}+i q^{7}+5 i q^{13}+4 q^{16}+\cdots$
675.2.b.g	$675$	$2$	675.b	5.b	$2$	$4$	$4$	$5.390$	$\Q(i, \sqrt{7})$	$_{}$	None	None		✓			675.2.a.n	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{2}-5q^{4}+3\beta _{1}q^{7}-3\beta _{3}q^{8}+\cdots$
675.2.b.h	$675$	$2$	675.b	5.b	$2$	$4$	$4$	$5.390$	$\Q(i, \sqrt{13})$	$_{}$	None	None					135.2.a.c	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-2+\beta _{3})q^{4}+(-2\beta _{1}-2\beta _{2}+\cdots)q^{7}+\cdots$
675.2.b.i	$675$	$2$	675.b	5.b	$2$	$4$	$4$	$5.390$	$\Q(i, \sqrt{13})$	$_{}$	None	None					135.2.a.c	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-2+\beta _{3})q^{4}+(2\beta _{1}+2\beta _{2}+\cdots)q^{7}+\cdots$
675.2.e.a	$675$	$2$	675.e	9.c	$3$	$2$	$1$	$5.390$	$\Q(\sqrt{-3}) $	$_{}$	None	None					45.2.e.a	$2$	$0$	$-1$	$0$	$0$	$-3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}+(-3+3\zeta_{6})q^{7}+\cdots$
675.2.e.b	$675$	$2$	675.e	9.c	$3$	$6$	$3$	$5.390$	6.0.954288.1	$_{}$	None	None					45.2.e.b	$2$	$0$	$-1$	$0$	$0$	$5$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{4}-\beta _{5})q^{2}+(-2-\beta _{1}-\beta _{2}+2\beta _{3}+\cdots)q^{4}+\cdots$
675.2.e.c	$675$	$2$	675.e	9.c	$3$	$8$	$4$	$5.390$	8.0.1223810289.2	$_{}$	None	None					225.2.e.c	$2$	$0$	$-2$	$0$	$0$	$-1$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{2}+(\beta _{1}-\beta _{2}-\beta _{3}+\beta _{6})q^{4}+\cdots$
675.2.e.d	$675$	$2$	675.e	9.c	$3$	$8$	$4$	$5.390$	$\Q(\zeta_{24})$	$_{}$	None	None					45.2.j.a	$4$	$0$	$0$	$0$	$0$	$0$		$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta_{7} q^{2}-\beta_{2} q^{4}+(-\beta_{7}+2\beta_{5}-2\beta_{3})q^{7}+\cdots$
675.2.e.e	$675$	$2$	675.e	9.c	$3$	$8$	$4$	$5.390$	8.0.1223810289.2	$_{}$	None	None					225.2.e.c	$2$	$0$	$2$	$0$	$0$	$1$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+(\beta _{1}-\beta _{2}-\beta _{3}+\beta _{6})q^{4}+\cdots$
675.2.f.a	$675$	$2$	675.f	15.e	$4$	$4$	$2$	$5.390$	$\Q(i, \sqrt{6})$	$_{}$	None	None		✓			675.2.f.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}+2\beta _{3}q^{7}-\beta _{3}q^{8}+\cdots$
675.2.f.b	$675$	$2$	675.f	15.e	$4$	$4$	$2$	$5.390$	$\Q(i, \sqrt{6})$	$_{}$	None	None		✓			675.2.f.b	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}+\beta _{3}q^{7}-\beta _{3}q^{8}+\cdots$
675.2.f.c	$675$	$2$	675.f	15.e	$4$	$4$	$2$	$5.390$	$\Q(i, \sqrt{6})$	$_{}$	$\Q(\sqrt{-3}) $	None		✓			675.2.f.c	$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+2\beta _{2}q^{4}+2\beta _{1}q^{7}-3\beta _{3}q^{13}-4q^{16}+\cdots$
675.2.f.d	$675$	$2$	675.f	15.e	$4$	$4$	$2$	$5.390$	$\Q(i, \sqrt{6})$	$_{}$	$\Q(\sqrt{-3}) $	None		✓			675.2.f.d	$8$	$0$	$0$	$0$	$0$	$0$		$3^{2}$	$\mathrm{U}(1)[D_{4}]$	$q+2\beta _{2}q^{4}-\beta _{1}q^{7}-\beta _{3}q^{13}-4q^{16}+\cdots$
675.2.f.e	$675$	$2$	675.f	15.e	$4$	$4$	$2$	$5.390$	$\Q(i, \sqrt{6})$	$_{}$	None	None		✓			675.2.f.b	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}-\beta _{3}q^{7}-\beta _{3}q^{8}+\cdots$
675.2.f.f	$675$	$2$	675.f	15.e	$4$	$4$	$2$	$5.390$	$\Q(i, \sqrt{6})$	$_{}$	None	None		✓			675.2.f.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}-2\beta _{3}q^{7}-\beta _{3}q^{8}+\cdots$
675.2.f.g	$675$	$2$	675.f	15.e	$4$	$8$	$4$	$5.390$	8.0.$\cdots$.8	$_{}$	None	None					135.2.f.b	$4$	$0$	$0$	$0$	$0$	$-8$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{2}+(2\beta _{2}+\beta _{4}+\beta _{5})q^{4}+(-1+\cdots)q^{7}+\cdots$
675.2.f.h	$675$	$2$	675.f	15.e	$4$	$8$	$4$	$5.390$	8.0.3317760000.9	$_{}$	$\Q(\sqrt{-15}) $	None		✓			675.2.f.h	$8$	$0$	$0$	$0$	$0$	$0$		$3^{4}$	$\mathrm{U}(1)[D_{4}]$	$q+\beta _{4}q^{2}+(3\beta _{1}+\beta _{2})q^{4}+(-3\beta _{3}-\beta _{5}+\cdots)q^{8}+\cdots$
675.2.f.i	$675$	$2$	675.f	15.e	$4$	$8$	$4$	$5.390$	8.0.$\cdots$.1	$_{}$	None	None					135.2.f.a	$4$	$0$	$0$	$0$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{2}+(\beta _{4}+\beta _{6})q^{4}+(-\beta _{2}-\beta _{4}+\cdots)q^{7}+\cdots$
675.2.h.a	$675$	$2$	675.h	25.d	$5$	$40$	$10$	$5.390$		$_{}$	None	None		✓			675.2.h.a	$2$	$0$	$-2$	$0$	$-3$	$-2$			$\mathrm{SU}(2)[C_{5}]$
675.2.h.b	$675$	$2$	675.h	25.d	$5$	$40$	$10$	$5.390$		$_{}$	None	None		✓			675.2.h.b	$4$	$0$	$0$	$0$	$0$	$20$			$\mathrm{SU}(2)[C_{5}]$
675.2.h.c	$675$	$2$	675.h	25.d	$5$	$40$	$10$	$5.390$		$_{}$	None	None		✓			675.2.h.c	$4$	$0$	$0$	$0$	$0$	$-12$			$\mathrm{SU}(2)[C_{5}]$

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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.