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 321 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
441.1.b.a	$441$	$1$	441.b	3.b	$2$	$2$	$2$	$0.220$	$\Q(\sqrt{-2}) $	$D_{4}$	$\Q(\sqrt{-7}) $	None		✓	✓	✓	441.1.b.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta q^{2}-q^{4}-\beta q^{11}-q^{16}-2q^{22}+\cdots$
441.1.m.a	$441$	$1$	441.m	7.d	$6$	$2$	$1$	$0.220$	$\Q(\sqrt{-3}) $	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-7}) $	$\Q(\sqrt{21}) $			✓	✓	63.1.d.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{6}^{2}q^{4}-\zeta_{6}q^{16}+\zeta_{6}^{2}q^{25}+\zeta_{6}q^{37}+\cdots$
441.1.q.a	$441$	$1$	441.q	21.h	$6$	$4$	$2$	$0.220$	$\Q(\sqrt{-2}, \sqrt{-3})$	$D_{4}$	$\Q(\sqrt{-7}) $	None		✓	✓	✓	441.1.b.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(-\beta _{1}+\beta _{3})q^{11}+\cdots$
441.1.v.a	$441$	$1$	441.v	49.f	$14$	$6$	$1$	$0.220$	$\Q(\zeta_{14})$	$D_{14}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	441.1.v.a	$4$	$0$	$0$	$0$	$0$	$1$		$1$		$q-\zeta_{14}^{4}q^{4}-\zeta_{14}^{2}q^{7}+(\zeta_{14}-\zeta_{14}^{3}+\cdots)q^{13}+\cdots$
441.2.a.a	$441$	$2$	441.a	1.a	$1$	$1$	$1$	$3.521$	$\Q$	$_{}$	None	None	✓				21.2.e.a	$1$	$1$	$-2$	$0$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}-2q^{5}+4q^{10}+2q^{11}+\cdots$
441.2.a.b	$441$	$2$	441.a	1.a	$1$	$1$	$1$	$3.521$	$\Q$	$_{}$	None	None	✓				21.2.e.a	$1$	$0$	$-2$	$0$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}+2q^{5}-4q^{10}+2q^{11}+\cdots$
441.2.a.c	$441$	$2$	441.a	1.a	$1$	$1$	$1$	$3.521$	$\Q$	$_{}$	$\Q(\sqrt{-7}) $	None	✓				49.2.a.a	$2$	$1$	$-1$	$0$	$0$	$0$	$+$	$1$	$N(\mathrm{U}(1))$	$q-q^{2}-q^{4}+3q^{8}-4q^{11}-q^{16}+\cdots$
441.2.a.d	$441$	$2$	441.a	1.a	$1$	$1$	$1$	$3.521$	$\Q$	$_{}$	$\Q(\sqrt{-3}) $	None	✓		✓	✓	63.2.e.a	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$1$	$N(\mathrm{U}(1))$	$q-2q^{4}-7q^{13}+4q^{16}-7q^{19}-5q^{25}+\cdots$
441.2.a.e	$441$	$2$	441.a	1.a	$1$	$1$	$1$	$3.521$	$\Q$	$_{}$	$\Q(\sqrt{-3}) $	None	✓				63.2.e.a	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$1$	$N(\mathrm{U}(1))$	$q-2q^{4}+7q^{13}+4q^{16}+7q^{19}-5q^{25}+\cdots$
441.2.a.f	$441$	$2$	441.a	1.a	$1$	$1$	$1$	$3.521$	$\Q$	$_{}$	None	None	✓				21.2.a.a	$1$	$1$	$1$	$0$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-2q^{5}-3q^{8}-2q^{10}+\cdots$
441.2.a.g	$441$	$2$	441.a	1.a	$1$	$2$	$2$	$3.521$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓				63.2.a.b	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{4}+2\beta q^{5}-\beta q^{8}+6q^{10}+\cdots$
441.2.a.h	$441$	$2$	441.a	1.a	$1$	$2$	$2$	$3.521$	$\Q(\sqrt{7}) $	$_{}$	$\Q(\sqrt{-7}) $	None	✓	✓			441.2.a.h	$4$	$0$	$0$	$0$	$0$	$0$	$-$	$1$	$N(\mathrm{U}(1))$	$q+\beta q^{2}+5q^{4}+3\beta q^{8}-2\beta q^{11}+11q^{16}+\cdots$
441.2.a.i	$441$	$2$	441.a	1.a	$1$	$2$	$2$	$3.521$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				147.2.a.d	$1$	$0$	$2$	$0$	$-4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+(1+2\beta )q^{4}+(-2+\beta )q^{5}+\cdots$
441.2.a.j	$441$	$2$	441.a	1.a	$1$	$2$	$2$	$3.521$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				147.2.a.d	$1$	$0$	$2$	$0$	$4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+(1+2\beta )q^{4}+(2-\beta )q^{5}+\cdots$
441.2.c.a	$441$	$2$	441.c	21.c	$2$	$4$	$4$	$3.521$	$\Q(\sqrt{-2}, \sqrt{-3})$	$_{}$	None	None					63.2.p.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+\beta _{3}q^{5}-2\beta _{1}q^{8}-2\beta _{2}q^{10}+\cdots$
441.2.c.b	$441$	$2$	441.c	21.c	$2$	$8$	$8$	$3.521$	$\Q(\zeta_{16})$	$_{}$	None	None		✓	✓		441.2.c.b	$4$	$0$	$0$	$0$	$0$	$0$		$2^{3}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta_{2}+\beta_1)q^{2}+(2\beta_{3}-1)q^{4}+\cdots$
441.2.e.a	$441$	$2$	441.e	7.c	$3$	$2$	$1$	$3.521$	$\Q(\sqrt{-3}) $	$_{}$	None	None					21.2.a.a	$2$	$0$	$-1$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}-2\zeta_{6}q^{5}-3q^{8}+\cdots$
441.2.e.b	$441$	$2$	441.e	7.c	$3$	$2$	$1$	$3.521$	$\Q(\sqrt{-3}) $	$_{}$	None	None					21.2.a.a	$2$	$0$	$-1$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}+2\zeta_{6}q^{5}-3q^{8}+\cdots$
441.2.e.c	$441$	$2$	441.e	7.c	$3$	$2$	$1$	$3.521$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None					63.2.e.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{3}]$	$q+(2-2\zeta_{6})q^{4}+7q^{13}-4\zeta_{6}q^{16}+\cdots$
441.2.e.d	$441$	$2$	441.e	7.c	$3$	$2$	$1$	$3.521$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-7}) $	None					49.2.a.a	$4$	$0$	$1$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{3}]$	$q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}+3q^{8}+(4-4\zeta_{6})q^{11}+\cdots$
441.2.e.e	$441$	$2$	441.e	7.c	$3$	$2$	$1$	$3.521$	$\Q(\sqrt{-3}) $	$_{}$	None	None					21.2.e.a	$2$	$0$	$2$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+2\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{4}+2\zeta_{6}q^{5}+\cdots$
441.2.e.f	$441$	$2$	441.e	7.c	$3$	$4$	$2$	$3.521$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None					147.2.a.d	$2$	$0$	$-2$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{1}-\beta _{2})q^{2}+(-2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
441.2.e.g	$441$	$2$	441.e	7.c	$3$	$4$	$2$	$3.521$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None					147.2.a.d	$2$	$0$	$-2$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{1}-\beta _{2})q^{2}+(-2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
441.2.e.h	$441$	$2$	441.e	7.c	$3$	$4$	$2$	$3.521$	$\Q(\sqrt{-3}, \sqrt{7})$	$_{}$	$\Q(\sqrt{-7}) $	None		✓			441.2.a.h	$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{3}]$	$q+\beta _{1}q^{2}+5\beta _{2}q^{4}+3\beta _{3}q^{8}+(2\beta _{1}+\cdots)q^{11}+\cdots$
441.2.e.i	$441$	$2$	441.e	7.c	$3$	$4$	$2$	$3.521$	$\Q(\zeta_{12})$	$_{}$	None	None					63.2.a.b	$4$	$0$	$0$	$0$	$0$	$0$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta_{2} q^{2}+(\beta_1-1)q^{4}-2\beta_{2} q^{5}+\cdots$
441.2.e.j	$441$	$2$	441.e	7.c	$3$	$4$	$2$	$3.521$	$\Q(\zeta_{12})$	$_{}$	None	None					63.2.a.b	$4$	$0$	$0$	$0$	$0$	$0$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta_{2} q^{2}+(\beta_1-1)q^{4}+2\beta_{2} q^{5}+\cdots$
441.2.f.a	$441$	$2$	441.f	9.c	$3$	$2$	$1$	$3.521$	$\Q(\sqrt{-3}) $	$_{}$	None	None					63.2.g.a	$2$	$1$	$-1$	$-3$	$-1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots$
441.2.f.b	$441$	$2$	441.f	9.c	$3$	$2$	$1$	$3.521$	$\Q(\sqrt{-3}) $	$_{}$	None	None					63.2.g.a	$2$	$0$	$-1$	$3$	$1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+(2-\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots$
441.2.f.c	$441$	$2$	441.f	9.c	$3$	$6$	$3$	$3.521$	$\Q(\zeta_{18})$	$_{}$	None	None					63.2.f.a	$2$	$0$	$-3$	$0$	$3$	$0$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta_{5}+\beta_1-1)q^{2}+(-\beta_{5}+\beta_{3})q^{3}+\cdots$
441.2.f.d	$441$	$2$	441.f	9.c	$3$	$6$	$3$	$3.521$	6.0.309123.1	$_{}$	None	None					63.2.f.b	$2$	$0$	$1$	$4$	$-5$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}-\beta _{2}-\beta _{3}+\beta _{5})q^{2}+(-\beta _{2}+\cdots)q^{3}+\cdots$
441.2.f.e	$441$	$2$	441.f	9.c	$3$	$10$	$5$	$3.521$	10.0.$\cdots$.1	$_{}$	None	None					63.2.g.b	$2$	$0$	$2$	$-1$	$4$	$0$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}-\beta _{4}q^{3}+(-1-\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots$
441.2.f.f	$441$	$2$	441.f	9.c	$3$	$10$	$5$	$3.521$	10.0.$\cdots$.1	$_{}$	None	None					63.2.g.b	$2$	$0$	$2$	$1$	$-4$	$0$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+\beta _{4}q^{3}+(-1-\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots$
441.2.f.g	$441$	$2$	441.f	9.c	$3$	$12$	$6$	$3.521$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		✓			441.2.f.g	$4$	$0$	$-2$	$0$	$0$	$0$		$3^{3}$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}+\beta _{6})q^{2}+\beta _{10}q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots$
441.2.f.h	$441$	$2$	441.f	9.c	$3$	$24$	$12$	$3.521$		$_{}$	None	None		✓	✓		441.2.f.h	$4$	$0$	$4$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{3}]$
441.2.g.a	$441$	$2$	441.g	63.g	$3$	$2$	$1$	$3.521$	$\Q(\sqrt{-3}) $	$_{}$	None	None					63.2.g.a	$2$	$0$	$-1$	$3$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+(2-\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots$
441.2.g.b	$441$	$2$	441.g	63.g	$3$	$6$	$3$	$3.521$	$\Q(\zeta_{18})$	$_{}$	None	None					63.2.f.a	$2$	$0$	$-3$	$0$	$-6$	$0$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta_{5}+\beta_1-1)q^{2}+(\beta_{4}+\beta_{2})q^{3}+\cdots$
441.2.g.c	$441$	$2$	441.g	63.g	$3$	$6$	$3$	$3.521$	$\Q(\zeta_{18})$	$_{}$	None	None					63.2.f.a	$2$	$0$	$-3$	$0$	$6$	$0$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta_{5}+\beta_1-1)q^{2}+(-\beta_{4}-\beta_{2})q^{3}+\cdots$
441.2.g.d	$441$	$2$	441.g	63.g	$3$	$6$	$3$	$3.521$	6.0.309123.1	$_{}$	None	None					63.2.f.b	$2$	$0$	$1$	$-2$	$10$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}-\beta _{2}-\beta _{3}+\beta _{5})q^{2}+(-1+\cdots)q^{3}+\cdots$
441.2.g.e	$441$	$2$	441.g	63.g	$3$	$6$	$3$	$3.521$	6.0.309123.1	$_{}$	None	None					63.2.f.b	$2$	$0$	$1$	$2$	$-10$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}-\beta _{2}-\beta _{3}+\beta _{5})q^{2}+(1-\beta _{1}+\cdots)q^{3}+\cdots$
441.2.g.f	$441$	$2$	441.g	63.g	$3$	$10$	$5$	$3.521$	10.0.$\cdots$.1	$_{}$	None	None					63.2.g.b	$2$	$0$	$2$	$-2$	$8$	$0$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+(-\beta _{2}+\beta _{7})q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots$
441.2.g.g	$441$	$2$	441.g	63.g	$3$	$12$	$6$	$3.521$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		✓			441.2.f.g	$4$	$0$	$-2$	$0$	$0$	$0$		$3^{3}$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{2}+\beta _{5})q^{2}+(-\beta _{8}-\beta _{10})q^{3}+\cdots$
441.2.g.h	$441$	$2$	441.g	63.g	$3$	$24$	$12$	$3.521$		$_{}$	None	None		✓	✓		441.2.f.h	$4$	$0$	$4$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{3}]$
441.2.h.a	$441$	$2$	441.h	63.h	$3$	$2$	$1$	$3.521$	$\Q(\sqrt{-3}) $	$_{}$	None	None					63.2.g.a	$2$	$0$	$2$	$0$	$-1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{2}+(1-2\zeta_{6})q^{3}-q^{4}+(-1+\zeta_{6})q^{5}+\cdots$
441.2.h.b	$441$	$2$	441.h	63.h	$3$	$6$	$3$	$3.521$	6.0.309123.1	$_{}$	None	None					63.2.f.b	$2$	$0$	$-2$	$-2$	$-5$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{2}+\beta _{3})q^{2}+(-\beta _{1}-\beta _{2}+\beta _{5})q^{3}+\cdots$
441.2.h.c	$441$	$2$	441.h	63.h	$3$	$6$	$3$	$3.521$	6.0.309123.1	$_{}$	None	None					63.2.f.b	$2$	$0$	$-2$	$2$	$5$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{2}+\beta _{3})q^{2}+(\beta _{1}+\beta _{2}-\beta _{5})q^{3}+\cdots$
441.2.h.d	$441$	$2$	441.h	63.h	$3$	$6$	$3$	$3.521$	$\Q(\zeta_{18})$	$_{}$	None	None					63.2.f.a	$2$	$0$	$6$	$0$	$-3$	$0$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta_{4}-\beta_{3}+1)q^{2}+(\beta_{5}+\beta_{2})q^{3}+\cdots$
441.2.h.e	$441$	$2$	441.h	63.h	$3$	$6$	$3$	$3.521$	$\Q(\zeta_{18})$	$_{}$	None	None					63.2.f.a	$2$	$0$	$6$	$0$	$3$	$0$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta_{4}-\beta_{3}+1)q^{2}+(-\beta_{5}-\beta_{2})q^{3}+\cdots$
441.2.h.f	$441$	$2$	441.h	63.h	$3$	$10$	$5$	$3.521$	10.0.$\cdots$.1	$_{}$	None	None					63.2.g.b	$2$	$0$	$-4$	$1$	$-4$	$0$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}+\beta _{5})q^{2}+\beta _{8}q^{3}+(1-\beta _{4}+\cdots)q^{4}+\cdots$
441.2.h.g	$441$	$2$	441.h	63.h	$3$	$12$	$6$	$3.521$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		✓			441.2.f.g	$4$	$0$	$4$	$0$	$0$	$0$		$3^{3}$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{2}q^{2}+\beta _{10}q^{3}+(1+\beta _{2}+\beta _{4})q^{4}+\cdots$
441.2.h.h	$441$	$2$	441.h	63.h	$3$	$24$	$12$	$3.521$		$_{}$	None	None		✓	✓		441.2.f.h	$4$	$0$	$-8$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{3}]$

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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.