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 185 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
363.1.b.a	$363$	$1$	363.b	3.b	$2$	$1$	$1$	$0.181$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-11}) $	$\Q(\sqrt{33}) $	✓	✓	✓	✓	363.1.b.a	$4$	$0$	$0$	$-1$	$0$	$0$		$1$		$q-q^{3}+q^{4}+q^{9}-q^{12}+q^{16}+q^{25}+\cdots$
363.1.h.a	$363$	$1$	363.h	33.h	$10$	$4$	$1$	$0.181$	$\Q(\zeta_{10})$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-11}) $	$\Q(\sqrt{33}) $		✓	✓	✓	363.1.b.a	$16$	$0$	$0$	$1$	$0$	$0$		$1$		$q-\zeta_{10}^{4}q^{3}-\zeta_{10}q^{4}-\zeta_{10}^{3}q^{9}-q^{12}+\cdots$
363.2.a.a	$363$	$2$	363.a	1.a	$1$	$1$	$1$	$2.899$	$\Q$	$_{}$	None	None	✓	✓			363.2.a.a	$1$	$0$	$-2$	$-1$	$4$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-q^{3}+2q^{4}+4q^{5}+2q^{6}+\cdots$
363.2.a.b	$363$	$2$	363.a	1.a	$1$	$1$	$1$	$2.899$	$\Q$	$_{}$	None	None	✓				33.2.a.a	$1$	$0$	$-1$	$-1$	$-2$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}-q^{4}-2q^{5}+q^{6}-4q^{7}+\cdots$
363.2.a.c	$363$	$2$	363.a	1.a	$1$	$1$	$1$	$2.899$	$\Q$	$_{}$	None	None	✓	✓			363.2.a.a	$1$	$0$	$2$	$-1$	$4$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-q^{3}+2q^{4}+4q^{5}-2q^{6}+\cdots$
363.2.a.d	$363$	$2$	363.a	1.a	$1$	$2$	$2$	$2.899$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				33.2.e.b	$1$	$1$	$-3$	$-2$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{2}-q^{3}+3\beta q^{4}+(1-\beta )q^{5}+\cdots$
363.2.a.e	$363$	$2$	363.a	1.a	$1$	$2$	$2$	$2.899$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓		✓	✓	33.2.e.a	$1$	$1$	$-1$	$2$	$-3$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}+(-2+\beta )q^{5}+\cdots$
363.2.a.f	$363$	$2$	363.a	1.a	$1$	$2$	$2$	$2.899$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	✓			363.2.a.f	$2$	$1$	$0$	$-2$	$-6$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-q^{3}+q^{4}-3q^{5}-\beta q^{6}-2\beta q^{7}+\cdots$
363.2.a.g	$363$	$2$	363.a	1.a	$1$	$2$	$2$	$2.899$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	✓			363.2.a.g	$2$	$0$	$0$	$2$	$4$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta q^{2}+q^{3}+3q^{4}+2q^{5}-\beta q^{6}+\cdots$
363.2.a.h	$363$	$2$	363.a	1.a	$1$	$2$	$2$	$2.899$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				33.2.e.a	$1$	$0$	$1$	$2$	$-3$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{3}+(-1+\beta )q^{4}+(-2+\beta )q^{5}+\cdots$
363.2.a.i	$363$	$2$	363.a	1.a	$1$	$2$	$2$	$2.899$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓		✓		33.2.e.b	$1$	$0$	$3$	$-2$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}-q^{3}+3\beta q^{4}+(1-\beta )q^{5}+\cdots$
363.2.a.j	$363$	$2$	363.a	1.a	$1$	$4$	$4$	$2.899$	$\Q(\sqrt{3}, \sqrt{11})$	$_{}$	None	None	✓	✓	✓		363.2.a.j	$2$	$0$	$0$	$4$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(2+\beta _{3})q^{4}-\beta _{3}q^{5}+\cdots$
363.2.d.a	$363$	$2$	363.d	33.d	$2$	$2$	$2$	$2.899$	$\Q(\sqrt{-2}) $	$_{}$	None	None		✓			363.2.d.a	$2$	$0$	$-2$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+(1+\beta )q^{3}-q^{4}+2\beta q^{5}+(-1+\cdots)q^{6}+\cdots$
363.2.d.b	$363$	$2$	363.d	33.d	$2$	$2$	$2$	$2.899$	$\Q(\sqrt{-2}) $	$_{}$	None	None		✓			363.2.d.a	$2$	$0$	$2$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+(1+\beta )q^{3}-q^{4}+2\beta q^{5}+(1+\cdots)q^{6}+\cdots$
363.2.d.c	$363$	$2$	363.d	33.d	$2$	$4$	$4$	$2.899$	$\Q(\sqrt{-2}, \sqrt{-3})$	$_{}$	None	None		✓			363.2.d.c	$4$	$0$	$0$	$-6$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-2\beta _{1}+\beta _{3})q^{2}+(-1-\beta _{2})q^{3}+\cdots$
363.2.d.d	$363$	$2$	363.d	33.d	$2$	$4$	$4$	$2.899$	$\Q(\sqrt{-2}, \sqrt{3})$	$_{}$	$\Q(\sqrt{-3}) $	None		✓			363.2.d.d	$4$	$0$	$0$	$0$	$0$	$0$		$11$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{1}q^{3}-2q^{4}-\beta _{2}q^{7}+3q^{9}+2\beta _{1}q^{12}+\cdots$
363.2.d.e	$363$	$2$	363.d	33.d	$2$	$8$	$8$	$2.899$	8.0.3588489216.5	$_{}$	None	None		✓			363.2.d.e	$4$	$0$	$0$	$-4$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{2}+(-1-\beta _{7})q^{3}+(2-\beta _{4}-\beta _{7})q^{4}+\cdots$
363.2.d.f	$363$	$2$	363.d	33.d	$2$	$8$	$8$	$2.899$	$\Q(\zeta_{20})$	$_{}$	None	None					33.2.f.a	$4$	$0$	$0$	$4$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta_{6} q^{2}+(\beta_{5}+\beta_{3}-\beta_1+1)q^{3}+\cdots$
363.2.e.a	$363$	$2$	363.e	11.c	$5$	$4$	$1$	$2.899$	$\Q(\zeta_{10})$	$_{}$	None	None		✓			363.2.a.g	$4$	$1$	$-5$	$-1$	$-2$	$-10$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1-\zeta_{10}+\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots$
363.2.e.b	$363$	$2$	363.e	11.c	$5$	$4$	$1$	$2.899$	$\Q(\zeta_{10})$	$_{}$	None	None					33.2.e.b	$2$	$0$	$-4$	$1$	$2$	$-1$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-2+\zeta_{10}-\zeta_{10}^{2}+2\zeta_{10}^{3})q^{2}+\cdots$
363.2.e.c	$363$	$2$	363.e	11.c	$5$	$4$	$1$	$2.899$	$\Q(\zeta_{10})$	$_{}$	None	None					33.2.e.a	$2$	$0$	$-2$	$-1$	$4$	$3$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\zeta_{10}+\zeta_{10}^{2})q^{2}+\zeta_{10}^{2}q^{3}+(-1+\cdots)q^{4}+\cdots$
363.2.e.d	$363$	$2$	363.e	11.c	$5$	$4$	$1$	$2.899$	$\Q(\zeta_{10})$	$_{}$	None	None		✓			363.2.a.a	$4$	$0$	$-2$	$1$	$-4$	$1$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-2+2\zeta_{10}-2\zeta_{10}^{2}+2\zeta_{10}^{3})q^{2}+\cdots$
363.2.e.e	$363$	$2$	363.e	11.c	$5$	$4$	$1$	$2.899$	$\Q(\zeta_{10})$	$_{}$	None	None					33.2.a.a	$4$	$0$	$-1$	$1$	$2$	$-4$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots$
363.2.e.f	$363$	$2$	363.e	11.c	$5$	$4$	$1$	$2.899$	$\Q(\zeta_{10})$	$_{}$	None	None					33.2.e.b	$2$	$0$	$1$	$1$	$-3$	$-1$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+2\zeta_{10}-2\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots$
363.2.e.g	$363$	$2$	363.e	11.c	$5$	$4$	$1$	$2.899$	$\Q(\zeta_{10})$	$_{}$	None	None					33.2.a.a	$4$	$0$	$1$	$1$	$2$	$4$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}-\zeta_{10}^{2}q^{3}+\cdots$
363.2.e.h	$363$	$2$	363.e	11.c	$5$	$4$	$1$	$2.899$	$\Q(\zeta_{10})$	$_{}$	None	None					33.2.e.a	$2$	$0$	$2$	$-1$	$4$	$-3$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(\zeta_{10}-\zeta_{10}^{2})q^{2}+\zeta_{10}^{2}q^{3}+(-1+\cdots)q^{4}+\cdots$
363.2.e.i	$363$	$2$	363.e	11.c	$5$	$4$	$1$	$2.899$	$\Q(\zeta_{10})$	$_{}$	None	None		✓			363.2.a.a	$4$	$0$	$2$	$1$	$-4$	$-1$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(2-2\zeta_{10}+2\zeta_{10}^{2}-2\zeta_{10}^{3})q^{2}+\cdots$
363.2.e.j	$363$	$2$	363.e	11.c	$5$	$4$	$1$	$2.899$	$\Q(\zeta_{10})$	$_{}$	None	None					33.2.e.a	$2$	$0$	$3$	$-1$	$-1$	$3$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\zeta_{10}^{3})q^{2}+\zeta_{10}^{2}q^{3}+(1-\zeta_{10}+\cdots)q^{4}+\cdots$
363.2.e.k	$363$	$2$	363.e	11.c	$5$	$4$	$1$	$2.899$	$\Q(\zeta_{10})$	$_{}$	None	None					33.2.e.b	$2$	$0$	$4$	$1$	$2$	$1$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(2-\zeta_{10}+\zeta_{10}^{2}-2\zeta_{10}^{3})q^{2}-\zeta_{10}^{2}q^{3}+\cdots$
363.2.e.l	$363$	$2$	363.e	11.c	$5$	$4$	$1$	$2.899$	$\Q(\zeta_{10})$	$_{}$	None	None		✓			363.2.a.g	$4$	$0$	$5$	$-1$	$-2$	$10$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1+\zeta_{10}-\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+\zeta_{10}^{2}q^{3}+\cdots$
363.2.e.m	$363$	$2$	363.e	11.c	$5$	$8$	$2$	$2.899$	8.0.324000000.3	$_{}$	None	None		✓			363.2.a.f	$8$	$0$	$0$	$2$	$6$	$0$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{7}q^{2}-\beta _{6}q^{3}+\beta _{4}q^{4}+(3+3\beta _{2}+\cdots)q^{5}+\cdots$
363.2.e.n	$363$	$2$	363.e	11.c	$5$	$16$	$4$	$2.899$	16.0.$\cdots$.3	$_{}$	None	None		✓	✓		363.2.a.j	$8$	$0$	$0$	$-4$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{12}q^{2}+\beta _{4}q^{3}+(\beta _{3}-\beta _{6}+\beta _{8}+\cdots)q^{4}+\cdots$
363.2.f.a	$363$	$2$	363.f	33.f	$10$	$8$	$2$	$2.899$	8.0.64000000.1	$_{}$	None	None		✓			363.2.d.a	$8$	$0$	$-2$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q-\beta _{6}q^{2}+(-1+\beta _{2}-\beta _{3}-\beta _{4}+\beta _{6}+\cdots)q^{3}+\cdots$
363.2.f.b	$363$	$2$	363.f	33.f	$10$	$8$	$2$	$2.899$	$\Q(\zeta_{20})$	$_{}$	None	None					33.2.f.a	$4$	$0$	$0$	$-6$	$0$	$10$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(-\zeta_{20}^{5}-\zeta_{20}^{7})q^{2}+(-1-\zeta_{20}+\cdots)q^{3}+\cdots$
363.2.f.c	$363$	$2$	363.f	33.f	$10$	$8$	$2$	$2.899$	8.0.228765625.1	$_{}$	$\Q(\sqrt{-11}) $	None					33.2.d.a	$16$	$0$	$0$	$-1$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{10}]$	$q-\beta _{1}q^{3}-2\beta _{7}q^{4}+(-\beta _{4}-2\beta _{5})q^{5}+\cdots$
363.2.f.d	$363$	$2$	363.f	33.f	$10$	$8$	$2$	$2.899$	$\Q(\zeta_{20})$	$_{}$	None	None					33.2.f.a	$4$	$0$	$0$	$4$	$0$	$10$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(-\zeta_{20}-\zeta_{20}^{7})q^{2}+(1+\zeta_{20}-\zeta_{20}^{2}+\cdots)q^{3}+\cdots$
363.2.f.e	$363$	$2$	363.f	33.f	$10$	$8$	$2$	$2.899$	$\Q(\zeta_{20})$	$_{}$	None	None					33.2.f.a	$4$	$0$	$0$	$4$	$0$	$-10$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(-\zeta_{20}-\zeta_{20}^{7})q^{2}+(1-\zeta_{20}-\zeta_{20}^{2}+\cdots)q^{3}+\cdots$
363.2.f.f	$363$	$2$	363.f	33.f	$10$	$8$	$2$	$2.899$	8.0.64000000.1	$_{}$	None	None		✓			363.2.d.a	$8$	$0$	$2$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(1-\beta _{2}+\beta _{4}-\beta _{6})q^{2}+(\beta _{1}-\beta _{3}+\cdots)q^{3}+\cdots$
363.2.f.g	$363$	$2$	363.f	33.f	$10$	$16$	$4$	$2.899$	16.0.$\cdots$.7	$_{}$	$\Q(\sqrt{-3}) $	None		✓			363.2.d.d	$16$	$0$	$0$	$0$	$0$	$0$		$11^{4}$	$\mathrm{U}(1)[D_{10}]$	$q+(\beta _{1}+\beta _{5}-\beta _{10}-\beta _{13})q^{3}+2\beta _{4}q^{4}+\cdots$
363.2.f.h	$363$	$2$	363.f	33.f	$10$	$16$	$4$	$2.899$	16.0.$\cdots$.1	$_{}$	None	None		✓			363.2.d.c	$16$	$0$	$0$	$6$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(\beta _{2}-2\beta _{6}-\beta _{8}+\beta _{12}+\beta _{13})q^{2}+\cdots$
363.2.f.i	$363$	$2$	363.f	33.f	$10$	$32$	$8$	$2.899$		$_{}$	None	None		✓	✓		363.2.d.e	$16$	$0$	$0$	$4$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
363.2.i.a	$363$	$2$	363.i	121.e	$11$	$110$	$11$	$2.899$		$_{}$	None	None		✓			363.2.i.a	$2$	$0$	$-3$	$110$	$-6$	$-8$			$\mathrm{SU}(2)[C_{11}]$
363.2.i.b	$363$	$2$	363.i	121.e	$11$	$110$	$11$	$2.899$		$_{}$	None	None		✓			363.2.i.b	$2$	$0$	$-1$	$-110$	$2$	$-4$			$\mathrm{SU}(2)[C_{11}]$
363.2.j.a	$363$	$2$	363.j	363.j	$22$	$420$	$42$	$2.899$		$_{}$	None	None		✓	✓	✓	363.2.j.a	$4$	$0$	$0$	$-22$	$0$	$-22$			$\mathrm{SU}(2)[C_{22}]$
363.2.m.a	$363$	$2$	363.m	121.g	$55$	$440$	$11$	$2.899$		$_{}$	None	None		✓			363.2.m.a	$2$	$0$	$1$	$110$	$3$	$-1$			$\mathrm{SU}(2)[C_{55}]$
363.2.m.b	$363$	$2$	363.m	121.g	$55$	$440$	$11$	$2.899$		$_{}$	None	None		✓			363.2.m.b	$2$	$0$	$3$	$-110$	$1$	$3$			$\mathrm{SU}(2)[C_{55}]$
363.2.p.a	$363$	$2$	363.p	363.p	$110$	$1680$	$42$	$2.899$		$_{}$	None	None		✓	✓	✓	363.2.p.a	$4$	$0$	$0$	$-28$	$0$	$-78$			$\mathrm{SU}(2)[C_{110}]$
363.3.b.a	$363$	$3$	363.b	3.b	$2$	$1$	$1$	$9.891$	$\Q$	$_{}$	$\Q(\sqrt{-3}) $	None	✓	✓			363.3.b.a	$2$	$0$	$0$	$-3$	$0$	$-11$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-3q^{3}+4q^{4}-11q^{7}+9q^{9}-12q^{12}+\cdots$
363.3.b.b	$363$	$3$	363.b	3.b	$2$	$1$	$1$	$9.891$	$\Q$	$_{}$	$\Q(\sqrt{-3}) $	None	✓	✓			363.3.b.a	$2$	$0$	$0$	$-3$	$0$	$11$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-3q^{3}+4q^{4}+11q^{7}+9q^{9}-12q^{12}+\cdots$
363.3.b.c	$363$	$3$	363.b	3.b	$2$	$2$	$2$	$9.891$	$\Q(\sqrt{-11}) $	$_{}$	$\Q(\sqrt{-11}) $	None		✓			363.3.b.c	$4$	$0$	$0$	$5$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+(3-\beta )q^{3}+4q^{4}+(-3+6\beta )q^{5}+\cdots$

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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.