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 57 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
2299.1.b.a	$2299$	$1$	2299.b	19.b	$2$	$2$	$2$	$1.147$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-19}) $	None	✓				209.1.m.a	$2$	$0$	$0$	$0$	$-1$	$-1$		$1$		$q+q^{4}+(-1+\beta )q^{5}+(-1+\beta )q^{7}+\cdots$
2299.1.b.b	$2299$	$1$	2299.b	19.b	$2$	$2$	$2$	$1.147$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-19}) $	None	✓				209.1.m.a	$2$	$0$	$0$	$0$	$-1$	$1$		$1$		$q+q^{4}+(-1+\beta )q^{5}+(1-\beta )q^{7}+q^{9}+\cdots$
2299.1.m.a	$2299$	$1$	2299.m	209.m	$10$	$4$	$1$	$1.147$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-19}) $	None					209.1.m.a	$4$	$0$	$0$	$0$	$-2$	$-3$		$1$		$q+\zeta_{10}^{4}q^{4}+(\zeta_{10}^{2}+\zeta_{10}^{4})q^{5}+(-1+\cdots)q^{7}+\cdots$
2299.1.m.b	$2299$	$1$	2299.m	209.m	$10$	$4$	$1$	$1.147$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-19}) $	None					209.1.m.a	$4$	$0$	$0$	$0$	$3$	$-2$		$1$		$q+\zeta_{10}^{4}q^{4}+(1-\zeta_{10})q^{5}+(-\zeta_{10}+\cdots)q^{7}+\cdots$
2299.1.m.c	$2299$	$1$	2299.m	209.m	$10$	$4$	$1$	$1.147$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-19}) $	None					209.1.m.a	$4$	$0$	$0$	$0$	$3$	$2$		$1$		$q+\zeta_{10}^{4}q^{4}+(1-\zeta_{10})q^{5}+(\zeta_{10}-\zeta_{10}^{2}+\cdots)q^{7}+\cdots$
2299.1.t.a	$2299$	$1$	2299.t	2299.t	$22$	$10$	$1$	$1.147$	$\Q(\zeta_{22})$	$D_{11}$	$\Q(\sqrt{-19}) $	None		✓	✓	✓	2299.1.t.a	$4$	$0$	$0$	$0$	$-2$	$-2$		$1$		$q+\zeta_{22}^{8}q^{4}+(\zeta_{22}^{2}-\zeta_{22}^{7})q^{5}+(\zeta_{22}^{2}+\cdots)q^{7}+\cdots$
2299.1.w.a	$2299$	$1$	2299.w	209.s	$30$	$16$	$2$	$1.147$	$\Q(\zeta_{60})$	$A_{4}$	None	None			✓	✓	209.1.h.a	$16$	$0$	$0$	$2$	$2$	$0$		$1$		$q-\zeta_{60}^{17}q^{2}-\zeta_{60}^{26}q^{3}+\zeta_{60}^{8}q^{5}+\cdots$
2299.1.bj.a	$2299$	$1$	2299.bj	2299.aj	$110$	$40$	$1$	$1.147$	$\Q(\zeta_{55})$	$D_{55}$	$\Q(\sqrt{-19}) $	None		✓	✓	✓	2299.1.bj.a	$4$	$0$	$0$	$0$	$2$	$-3$		$1$		$q-\zeta_{110}^{13}q^{4}+(\zeta_{110}^{28}+\zeta_{110}^{54})q^{5}+\cdots$
2299.2.a.a	$2299$	$2$	2299.a	1.a	$1$	$1$	$1$	$18.358$	$\Q$	$_{}$	None	None	✓	✓			2299.2.a.a	$1$	$2$	$-2$	$-3$	$-3$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-3q^{3}+2q^{4}-3q^{5}+6q^{6}+\cdots$
2299.2.a.b	$2299$	$2$	2299.a	1.a	$1$	$1$	$1$	$18.358$	$\Q$	$_{}$	None	None	✓				19.2.a.a	$1$	$0$	$0$	$-2$	$3$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-2q^{4}+3q^{5}+q^{7}+q^{9}+4q^{12}+\cdots$
2299.2.a.c	$2299$	$2$	2299.a	1.a	$1$	$1$	$1$	$18.358$	$\Q$	$_{}$	None	None	✓				209.2.a.a	$1$	$0$	$0$	$1$	$-3$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}-3q^{5}+4q^{7}-2q^{9}+\cdots$
2299.2.a.d	$2299$	$2$	2299.a	1.a	$1$	$1$	$1$	$18.358$	$\Q$	$_{}$	None	None	✓	✓			2299.2.a.a	$1$	$1$	$2$	$-3$	$-3$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-3q^{3}+2q^{4}-3q^{5}-6q^{6}+\cdots$
2299.2.a.e	$2299$	$2$	2299.a	1.a	$1$	$2$	$2$	$18.358$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	✓			2299.2.a.e	$1$	$1$	$-2$	$0$	$6$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+\beta q^{3}+(2-2\beta )q^{4}+\cdots$
2299.2.a.f	$2299$	$2$	2299.a	1.a	$1$	$2$	$2$	$18.358$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				209.2.a.b	$1$	$1$	$0$	$-2$	$-2$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(-1+\beta )q^{3}-q^{5}+(2-\beta )q^{6}+\cdots$
2299.2.a.g	$2299$	$2$	2299.a	1.a	$1$	$2$	$2$	$18.358$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				209.2.f.a	$1$	$0$	$0$	$2$	$-1$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-2\beta )q^{2}+2\beta q^{3}+3q^{4}-\beta q^{5}+\cdots$
2299.2.a.h	$2299$	$2$	2299.a	1.a	$1$	$2$	$2$	$18.358$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				209.2.f.a	$1$	$0$	$0$	$2$	$-1$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-2\beta )q^{2}+(2-2\beta )q^{3}+3q^{4}+(-1+\cdots)q^{5}+\cdots$
2299.2.a.i	$2299$	$2$	2299.a	1.a	$1$	$2$	$2$	$18.358$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	✓			2299.2.a.i	$1$	$1$	$0$	$3$	$-1$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-2\beta )q^{2}+(1+\beta )q^{3}+3q^{4}+(-1+\cdots)q^{5}+\cdots$
2299.2.a.j	$2299$	$2$	2299.a	1.a	$1$	$2$	$2$	$18.358$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	✓			2299.2.a.i	$1$	$0$	$0$	$3$	$-1$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-2\beta )q^{2}+(2-\beta )q^{3}+3q^{4}-\beta q^{5}+\cdots$
2299.2.a.k	$2299$	$2$	2299.a	1.a	$1$	$2$	$2$	$18.358$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	✓			2299.2.a.e	$1$	$0$	$2$	$0$	$6$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}-\beta q^{3}+(2+2\beta )q^{4}+3q^{5}+\cdots$
2299.2.a.l	$2299$	$2$	2299.a	1.a	$1$	$3$	$3$	$18.358$	3.3.1229.1	$_{}$	None	None	✓	✓			2299.2.a.l	$1$	$1$	$-3$	$-1$	$1$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta _{1}q^{3}-q^{4}+\beta _{1}q^{5}+\beta _{1}q^{6}+\cdots$
2299.2.a.m	$2299$	$2$	2299.a	1.a	$1$	$3$	$3$	$18.358$	3.3.1229.1	$_{}$	None	None	✓	✓			2299.2.a.l	$1$	$0$	$3$	$-1$	$1$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta _{1}q^{3}-q^{4}+\beta _{1}q^{5}-\beta _{1}q^{6}+\cdots$
2299.2.a.n	$2299$	$2$	2299.a	1.a	$1$	$5$	$5$	$18.358$	5.5.246832.1	$_{}$	None	None	✓				209.2.a.c	$1$	$1$	$-2$	$1$	$-5$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}+\beta _{3}q^{3}+(\beta _{1}+\beta _{2}+\beta _{3}+\beta _{4})q^{4}+\cdots$
2299.2.a.o	$2299$	$2$	2299.a	1.a	$1$	$7$	$7$	$18.358$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	✓			2299.2.a.o	$1$	$1$	$-4$	$-1$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}-\beta _{5}q^{3}+(1-\beta _{5}+\beta _{6})q^{4}+\cdots$
2299.2.a.p	$2299$	$2$	2299.a	1.a	$1$	$7$	$7$	$18.358$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	✓			2299.2.a.p	$1$	$1$	$-2$	$-1$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{1}+\beta _{4}+\beta _{6})q^{4}+\cdots$
2299.2.a.q	$2299$	$2$	2299.a	1.a	$1$	$7$	$7$	$18.358$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓				209.2.a.d	$1$	$0$	$1$	$2$	$2$	$-10$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{2}q^{3}+(2+\beta _{2}+\beta _{3})q^{4}+\cdots$
2299.2.a.r	$2299$	$2$	2299.a	1.a	$1$	$7$	$7$	$18.358$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	✓			2299.2.a.p	$1$	$0$	$2$	$-1$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{1}+\beta _{4}+\beta _{6})q^{4}+\cdots$
2299.2.a.s	$2299$	$2$	2299.a	1.a	$1$	$7$	$7$	$18.358$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	✓			2299.2.a.o	$1$	$0$	$4$	$-1$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}-\beta _{5}q^{3}+(1-\beta _{5}+\beta _{6})q^{4}+\cdots$
2299.2.a.t	$2299$	$2$	2299.a	1.a	$1$	$14$	$14$	$18.358$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None	✓				209.2.f.b	$1$	$1$	$-1$	$-2$	$-14$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{2}q^{3}+(\beta _{4}-\beta _{5})q^{4}+(-1+\cdots)q^{5}+\cdots$
2299.2.a.u	$2299$	$2$	2299.a	1.a	$1$	$14$	$14$	$18.358$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None	✓		✓		209.2.f.b	$1$	$1$	$1$	$-2$	$-14$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{2}q^{3}+(\beta _{4}-\beta _{5})q^{4}+(-1+\cdots)q^{5}+\cdots$
2299.2.a.v	$2299$	$2$	2299.a	1.a	$1$	$16$	$16$	$18.358$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None	✓	✓	✓		2299.2.a.v	$1$	$1$	$-6$	$-2$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{4}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots$
2299.2.a.w	$2299$	$2$	2299.a	1.a	$1$	$16$	$16$	$18.358$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None	✓	✓			2299.2.a.v	$1$	$0$	$6$	$-2$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{4}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots$
2299.2.a.x	$2299$	$2$	2299.a	1.a	$1$	$20$	$20$	$18.358$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None	✓		✓		209.2.f.c	$1$	$0$	$-1$	$4$	$18$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{6}q^{3}+(1+\beta _{2})q^{4}+(1-\beta _{3}+\cdots)q^{5}+\cdots$
2299.2.a.y	$2299$	$2$	2299.a	1.a	$1$	$20$	$20$	$18.358$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None	✓		✓		209.2.f.c	$1$	$0$	$1$	$4$	$18$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{6}q^{3}+(1+\beta _{2})q^{4}+(1-\beta _{3}+\cdots)q^{5}+\cdots$
2299.4.a.a	$2299$	$4$	2299.a	1.a	$1$	$1$	$1$	$135.645$	$\Q$	$_{}$	None	None	✓	✓			2299.4.a.a	$1$	$2$	$-3$	$-5$	$10$	$-11$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{2}-5q^{3}+q^{4}+10q^{5}+15q^{6}+\cdots$
2299.4.a.b	$2299$	$4$	2299.a	1.a	$1$	$1$	$1$	$135.645$	$\Q$	$_{}$	None	None	✓				19.4.a.a	$1$	$1$	$3$	$-5$	$-12$	$-11$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{2}-5q^{3}+q^{4}-12q^{5}-15q^{6}+\cdots$
2299.4.a.c	$2299$	$4$	2299.a	1.a	$1$	$1$	$1$	$135.645$	$\Q$	$_{}$	None	None	✓	✓			2299.4.a.a	$1$	$1$	$3$	$-5$	$10$	$11$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{2}-5q^{3}+q^{4}+10q^{5}-15q^{6}+\cdots$
2299.4.a.d	$2299$	$4$	2299.a	1.a	$1$	$2$	$2$	$135.645$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	✓			2299.4.a.d	$1$	$0$	$-2$	$5$	$-5$	$-23$	$+$	$5$	$\mathrm{SU}(2)$	$q-q^{2}+(3+\beta )q^{3}-7q^{4}+(-3-\beta )q^{5}+\cdots$
2299.4.a.e	$2299$	$4$	2299.a	1.a	$1$	$2$	$2$	$135.645$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	✓			2299.4.a.e	$1$	$1$	$-2$	$5$	$35$	$7$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-4\beta )q^{2}+(1+3\beta )q^{3}+(9+8\beta )q^{4}+\cdots$
2299.4.a.f	$2299$	$4$	2299.a	1.a	$1$	$2$	$2$	$135.645$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	✓			2299.4.a.d	$1$	$1$	$2$	$5$	$-5$	$23$	$-$	$5$	$\mathrm{SU}(2)$	$q+q^{2}+(3+\beta )q^{3}-7q^{4}+(-3-\beta )q^{5}+\cdots$
2299.4.a.g	$2299$	$4$	2299.a	1.a	$1$	$2$	$2$	$135.645$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	✓			2299.4.a.e	$1$	$0$	$2$	$5$	$35$	$-7$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+4\beta )q^{2}+(1+3\beta )q^{3}+(9+8\beta )q^{4}+\cdots$
2299.4.a.h	$2299$	$4$	2299.a	1.a	$1$	$3$	$3$	$135.645$	3.3.3144.1	$_{}$	None	None	✓				19.4.a.b	$1$	$0$	$-3$	$1$	$14$	$35$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{1}+\beta _{2})q^{2}+(-\beta _{1}+2\beta _{2})q^{3}+\cdots$
2299.4.a.i	$2299$	$4$	2299.a	1.a	$1$	$8$	$8$	$135.645$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓				209.4.a.a	$1$	$1$	$0$	$-1$	$-12$	$59$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{3}q^{3}+(3+\beta _{2})q^{4}+(-2+\cdots)q^{5}+\cdots$
2299.4.a.j	$2299$	$4$	2299.a	1.a	$1$	$10$	$10$	$135.645$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None	✓				209.4.a.b	$1$	$0$	$6$	$-9$	$-10$	$53$	$+$	$2$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(-1+\beta _{4})q^{3}+(2-\beta _{1}+\cdots)q^{4}+\cdots$
2299.4.a.k	$2299$	$4$	2299.a	1.a	$1$	$13$	$13$	$135.645$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	$_{}$	None	None	✓				209.4.a.c	$1$	$0$	$2$	$11$	$8$	$-39$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{5})q^{3}+(6+\beta _{2})q^{4}+\cdots$
2299.4.a.l	$2299$	$4$	2299.a	1.a	$1$	$15$	$15$	$135.645$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	$_{}$	None	None	✓				209.4.a.d	$1$	$1$	$-4$	$3$	$10$	$-73$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{3}q^{3}+(5+\beta _{2})q^{4}+(1+\beta _{6}+\cdots)q^{5}+\cdots$
2299.4.a.m	$2299$	$4$	2299.a	1.a	$1$	$18$	$18$	$135.645$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	$_{}$	None	None	✓	✓			2299.4.a.m	$1$	$1$	$-6$	$-8$	$-58$	$-44$	$-$	$2^{6}\cdot 3$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{4}q^{3}+(4+\beta _{2})q^{4}+(-3+\cdots)q^{5}+\cdots$
2299.4.a.n	$2299$	$4$	2299.a	1.a	$1$	$18$	$18$	$135.645$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	$_{}$	None	None	✓	✓			2299.4.a.m	$1$	$0$	$6$	$-8$	$-58$	$44$	$+$	$2^{6}\cdot 3$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{4}q^{3}+(4+\beta _{2})q^{4}+(-3+\cdots)q^{5}+\cdots$
2299.4.a.o	$2299$	$4$	2299.a	1.a	$1$	$22$	$22$	$135.645$		$_{}$	None	None	✓	✓			2299.4.a.o	$1$	$1$	$-11$	$7$	$0$	$-25$	$-$		$\mathrm{SU}(2)$
2299.4.a.p	$2299$	$4$	2299.a	1.a	$1$	$22$	$22$	$135.645$		$_{}$	None	None	✓	✓			2299.4.a.o	$1$	$0$	$11$	$7$	$0$	$25$	$+$		$\mathrm{SU}(2)$
2299.4.a.q	$2299$	$4$	2299.a	1.a	$1$	$23$	$23$	$135.645$		$_{}$	None	None	✓	✓			2299.4.a.q	$1$	$1$	$-4$	$2$	$10$	$-14$	$-$		$\mathrm{SU}(2)$

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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.