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 94 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
484.1.b.a	$484$	$1$	484.b	4.b	$2$	$1$	$1$	$0.242$	$\Q$	$D_{3}$	$\Q(\sqrt{-1}) $	None	✓	✓			484.1.b.a	$2$	$0$	$-1$	$0$	$-1$	$0$		$1$		$q-q^{2}+q^{4}-q^{5}-q^{8}+q^{9}+q^{10}+\cdots$
484.1.b.b	$484$	$1$	484.b	4.b	$2$	$1$	$1$	$0.242$	$\Q$	$D_{3}$	$\Q(\sqrt{-1}) $	None	✓	✓			484.1.b.a	$2$	$0$	$1$	$0$	$-1$	$0$		$1$		$q+q^{2}+q^{4}-q^{5}+q^{8}+q^{9}-q^{10}+\cdots$
484.1.f.a	$484$	$1$	484.f	11.d	$10$	$4$	$1$	$0.242$	$\Q(\zeta_{10})$	$D_{3}$	$\Q(\sqrt{-11}) $	None			✓	✓	44.1.d.a	$8$	$0$	$0$	$1$	$1$	$0$		$1$		$q-\zeta_{10}^{4}q^{3}-\zeta_{10}^{2}q^{5}-\zeta_{10}q^{15}+\cdots$
484.1.h.a	$484$	$1$	484.h	44.h	$10$	$4$	$1$	$0.242$	$\Q(\zeta_{10})$	$D_{3}$	$\Q(\sqrt{-1}) $	None		✓			484.1.b.a	$8$	$0$	$-1$	$0$	$1$	$0$		$1$		$q-\zeta_{10}q^{2}+\zeta_{10}^{2}q^{4}-\zeta_{10}^{4}q^{5}-\zeta_{10}^{3}q^{8}+\cdots$
484.1.h.b	$484$	$1$	484.h	44.h	$10$	$4$	$1$	$0.242$	$\Q(\zeta_{10})$	$D_{3}$	$\Q(\sqrt{-1}) $	None		✓			484.1.b.a	$8$	$0$	$1$	$0$	$1$	$0$		$1$		$q+\zeta_{10}q^{2}+\zeta_{10}^{2}q^{4}-\zeta_{10}^{4}q^{5}+\zeta_{10}^{3}q^{8}+\cdots$
484.2.a.a	$484$	$2$	484.a	1.a	$1$	$1$	$1$	$3.865$	$\Q$	$_{}$	None	None	✓				44.2.a.a	$1$	$1$	$0$	$1$	$-3$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-3q^{5}-2q^{7}-2q^{9}+4q^{13}+\cdots$
484.2.a.b	$484$	$2$	484.a	1.a	$1$	$2$	$2$	$3.865$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				44.2.e.a	$1$	$0$	$0$	$-3$	$-1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{3}-\beta q^{5}+(1-3\beta )q^{7}+\cdots$
484.2.a.c	$484$	$2$	484.a	1.a	$1$	$2$	$2$	$3.865$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓		✓		44.2.e.a	$1$	$1$	$0$	$-3$	$-1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{3}-\beta q^{5}+(-1+3\beta )q^{7}+\cdots$
484.2.a.d	$484$	$2$	484.a	1.a	$1$	$2$	$2$	$3.865$	$\Q(\sqrt{33}) $	$_{}$	$\Q(\sqrt{-11}) $	None	✓	✓			484.2.a.d	$2$	$0$	$0$	$1$	$3$	$0$	$-$	$1$	$N(\mathrm{U}(1))$	$q+\beta q^{3}+(2-\beta )q^{5}+(5+\beta )q^{9}+(-8+\cdots)q^{15}+\cdots$
484.2.a.e	$484$	$2$	484.a	1.a	$1$	$2$	$2$	$3.865$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	✓			484.2.a.e	$2$	$0$	$0$	$4$	$6$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+3q^{5}+2\beta q^{7}+q^{9}-3\beta q^{13}+\cdots$
484.2.c.a	$484$	$2$	484.c	44.c	$2$	$2$	$2$	$3.865$	$\Q(\sqrt{-2}) $	$_{}$	$\Q(\sqrt{-1}) $	None		✓			484.2.c.a	$4$	$0$	$0$	$0$	$-8$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+\beta q^{2}-2q^{4}-4q^{5}-2\beta q^{8}+3q^{9}+\cdots$
484.2.c.b	$484$	$2$	484.c	44.c	$2$	$4$	$4$	$3.865$	$\Q(\sqrt{-2}, \sqrt{3})$	$_{}$	$\Q(\sqrt{-1}) $	None		✓			484.2.c.b	$4$	$0$	$0$	$0$	$8$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+(\beta _{1}-\beta _{3})q^{2}-2q^{4}+(2-\beta _{2})q^{5}+\cdots$
484.2.c.c	$484$	$2$	484.c	44.c	$2$	$8$	$8$	$3.865$	8.0.64000000.1	$_{}$	None	None		✓			484.2.c.c	$4$	$0$	$0$	$0$	$8$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-1+\beta _{2}+\beta _{4})q^{3}+\beta _{2}q^{4}+\cdots$
484.2.c.d	$484$	$2$	484.c	44.c	$2$	$16$	$16$	$3.865$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None					44.2.g.a	$4$	$0$	$0$	$0$	$4$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{13}q^{2}-\beta _{14}q^{3}+(-\beta _{1}-\beta _{14}+\cdots)q^{4}+\cdots$
484.2.c.e	$484$	$2$	484.c	44.c	$2$	$16$	$16$	$3.865$	16.0.$\cdots$.2	$_{}$	None	None		✓			484.2.c.e	$4$	$0$	$0$	$0$	$-8$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(\beta _{2}-\beta _{5})q^{3}+(1+\beta _{3}+\beta _{5}+\cdots)q^{4}+\cdots$
484.2.e.a	$484$	$2$	484.e	11.c	$5$	$4$	$1$	$3.865$	$\Q(\zeta_{10})$	$_{}$	None	None					44.2.a.a	$4$	$0$	$0$	$-1$	$3$	$-2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\zeta_{10}^{2}q^{3}+3\zeta_{10}q^{5}-2\zeta_{10}^{3}q^{7}+\cdots$
484.2.e.b	$484$	$2$	484.e	11.c	$5$	$4$	$1$	$3.865$	$\Q(\zeta_{10})$	$_{}$	None	None					44.2.a.a	$4$	$0$	$0$	$-1$	$3$	$2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\zeta_{10}^{2}q^{3}+3\zeta_{10}q^{5}+2\zeta_{10}^{3}q^{7}+\cdots$
484.2.e.c	$484$	$2$	484.e	11.c	$5$	$4$	$1$	$3.865$	$\Q(\zeta_{10})$	$_{}$	None	None					44.2.e.a	$2$	$0$	$0$	$-1$	$3$	$7$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\zeta_{10}-\zeta_{10}^{2}-\zeta_{10}^{3})q^{3}+(1+\zeta_{10}^{2}+\cdots)q^{5}+\cdots$
484.2.e.d	$484$	$2$	484.e	11.c	$5$	$4$	$1$	$3.865$	$\Q(\zeta_{10})$	$_{}$	None	None					44.2.e.a	$2$	$0$	$0$	$4$	$-2$	$-8$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(\zeta_{10}-2\zeta_{10}^{2}+\zeta_{10}^{3})q^{3}+(-1+\cdots)q^{5}+\cdots$
484.2.e.e	$484$	$2$	484.e	11.c	$5$	$4$	$1$	$3.865$	$\Q(\zeta_{10})$	$_{}$	None	None					44.2.e.a	$2$	$0$	$0$	$4$	$-2$	$8$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(\zeta_{10}-2\zeta_{10}^{2}+\zeta_{10}^{3})q^{3}+(-1+\cdots)q^{5}+\cdots$
484.2.e.f	$484$	$2$	484.e	11.c	$5$	$8$	$2$	$3.865$	8.0.324000000.3	$_{}$	None	None		✓			484.2.a.e	$8$	$0$	$0$	$-4$	$-6$	$0$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+2\beta _{6}q^{3}+(-3-3\beta _{2}-3\beta _{4}-3\beta _{6}+\cdots)q^{5}+\cdots$
484.2.e.g	$484$	$2$	484.e	11.c	$5$	$8$	$2$	$3.865$	8.0.$\cdots$.3	$_{}$	$\Q(\sqrt{-11}) $	None		✓			484.2.a.d	$8$	$0$	$0$	$-1$	$-3$	$0$		$1$	$\mathrm{U}(1)[D_{5}]$	$q-\beta _{1}q^{3}+(-2-2\beta _{2}-2\beta _{4}+\beta _{5}+\cdots)q^{5}+\cdots$
484.2.g.a	$484$	$2$	484.g	44.g	$10$	$8$	$2$	$3.865$	8.0.64000000.1	$_{}$	None	None		✓			484.2.c.c	$4$	$0$	$0$	$-10$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+\beta _{1}q^{2}+(-2+2\beta _{2}-\beta _{4})q^{3}+2\beta _{2}q^{4}+\cdots$
484.2.g.b	$484$	$2$	484.g	44.g	$10$	$8$	$2$	$3.865$	8.0.64000000.1	$_{}$	None	None		✓			484.2.c.c	$4$	$0$	$0$	$-10$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+\beta _{1}q^{2}+(-2-2\beta _{4}+\beta _{6})q^{3}+2\beta _{2}q^{4}+\cdots$
484.2.g.c	$484$	$2$	484.g	44.g	$10$	$8$	$2$	$3.865$	8.0.64000000.1	$_{}$	$\Q(\sqrt{-1}) $	None		✓			484.2.c.a	$16$	$0$	$0$	$0$	$8$	$0$		$1$	$\mathrm{U}(1)[D_{10}]$	$q+\beta _{1}q^{2}+2\beta _{2}q^{4}-4\beta _{4}q^{5}+2\beta _{3}q^{8}+\cdots$
484.2.g.d	$484$	$2$	484.g	44.g	$10$	$8$	$2$	$3.865$	8.0.64000000.1	$_{}$	None	None		✓			484.2.c.c	$4$	$0$	$0$	$10$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q-\beta _{5}q^{2}+(2-2\beta _{2}+\beta _{4})q^{3}-2q^{4}+\cdots$
484.2.g.e	$484$	$2$	484.g	44.g	$10$	$8$	$2$	$3.865$	8.0.64000000.1	$_{}$	None	None		✓			484.2.c.c	$4$	$0$	$0$	$10$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+\beta _{1}q^{2}+(\beta _{2}-2\beta _{4}+2\beta _{6})q^{3}+2\beta _{2}q^{4}+\cdots$
484.2.g.f	$484$	$2$	484.g	44.g	$10$	$16$	$4$	$3.865$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None					44.2.g.a	$4$	$0$	$-5$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+\beta _{15}q^{2}+(1-\beta _{1}-\beta _{3}-\beta _{4}+\beta _{6}+\cdots)q^{3}+\cdots$
484.2.g.g	$484$	$2$	484.g	44.g	$10$	$16$	$4$	$3.865$	16.0.$\cdots$.2	$_{}$	None	None					44.2.c.a	$16$	$0$	$0$	$0$	$4$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{10}]$	$q+\beta _{5}q^{2}-\beta _{11}q^{3}+(-\beta _{2}-\beta _{7}+\beta _{9}+\cdots)q^{4}+\cdots$
484.2.g.h	$484$	$2$	484.g	44.g	$10$	$16$	$4$	$3.865$	16.0.$\cdots$.7	$_{}$	$\Q(\sqrt{-1}) $	None		✓			484.2.c.b	$16$	$0$	$0$	$0$	$-8$	$0$		$1$	$\mathrm{U}(1)[D_{10}]$	$q+(-\beta _{1}+\beta _{3})q^{2}+2\beta _{4}q^{4}+(-2\beta _{8}+\cdots)q^{5}+\cdots$
484.2.g.i	$484$	$2$	484.g	44.g	$10$	$16$	$4$	$3.865$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None					44.2.g.a	$4$	$0$	$5$	$0$	$-6$	$0$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q-\beta _{2}q^{2}+(-1-\beta _{1}-\beta _{2}-\beta _{13}-\beta _{14}+\cdots)q^{3}+\cdots$
484.2.g.j	$484$	$2$	484.g	44.g	$10$	$16$	$4$	$3.865$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None					44.2.g.a	$4$	$0$	$5$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q-\beta _{15}q^{2}+(1-\beta _{1}-\beta _{3}-\beta _{4}+\beta _{6}+\cdots)q^{3}+\cdots$
484.2.g.k	$484$	$2$	484.g	44.g	$10$	$64$	$16$	$3.865$		$_{}$	None	None		✓	✓		484.2.c.e	$16$	$0$	$0$	$0$	$8$	$0$			$\mathrm{SU}(2)[C_{10}]$
484.2.i.a	$484$	$2$	484.i	121.e	$11$	$110$	$11$	$3.865$		$_{}$	None	None		✓	✓	✓	484.2.i.a	$2$	$0$	$0$	$-2$	$2$	$-2$			$\mathrm{SU}(2)[C_{11}]$
484.2.j.a	$484$	$2$	484.j	484.j	$22$	$640$	$64$	$3.865$		$_{}$	None	None		✓	✓	✓	484.2.j.a	$4$	$0$	$-11$	$0$	$-18$	$0$			$\mathrm{SU}(2)[C_{22}]$
484.2.m.a	$484$	$2$	484.m	121.g	$55$	$440$	$11$	$3.865$		$_{}$	None	None		✓	✓	✓	484.2.m.a	$2$	$0$	$0$	$2$	$-2$	$7$			$\mathrm{SU}(2)[C_{55}]$
484.2.p.a	$484$	$2$	484.p	484.p	$110$	$2560$	$64$	$3.865$		$_{}$	None	None		✓	✓	✓	484.2.p.a	$4$	$0$	$-39$	$0$	$-82$	$0$			$\mathrm{SU}(2)[C_{110}]$
484.3.b.a	$484$	$3$	484.b	4.b	$2$	$1$	$1$	$13.188$	$\Q$	$_{}$	$\Q(\sqrt{-1}) $	None	✓	✓			484.3.b.a	$2$	$0$	$-2$	$0$	$6$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-2q^{2}+4q^{4}+6q^{5}-8q^{8}+9q^{9}+\cdots$
484.3.b.b	$484$	$3$	484.b	4.b	$2$	$1$	$1$	$13.188$	$\Q$	$_{}$	$\Q(\sqrt{-1}) $	None	✓	✓			484.3.b.a	$2$	$0$	$2$	$0$	$6$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2q^{2}+4q^{4}+6q^{5}+8q^{8}+9q^{9}+\cdots$
484.3.b.c	$484$	$3$	484.b	4.b	$2$	$2$	$2$	$13.188$	$\Q(\sqrt{3}) $	$_{}$	$\Q(\sqrt{-1}) $	None	✓	✓			484.3.b.c	$2$	$0$	$-4$	$0$	$-6$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-2q^{2}+4q^{4}+(-3-4\beta )q^{5}-8q^{8}+\cdots$
484.3.b.d	$484$	$3$	484.b	4.b	$2$	$2$	$2$	$13.188$	$\Q(\sqrt{3}) $	$_{}$	$\Q(\sqrt{-1}) $	None	✓	✓			484.3.b.c	$2$	$0$	$4$	$0$	$-6$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2q^{2}+4q^{4}+(-3+4\beta )q^{5}+8q^{8}+\cdots$
484.3.b.e	$484$	$3$	484.b	4.b	$2$	$8$	$8$	$13.188$	8.0.$\cdots$.2	$_{}$	None	None		✓			484.3.b.e	$4$	$0$	$0$	$0$	$-8$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}+\beta _{4}q^{3}+(-1-\beta _{6})q^{4}+(-1+\cdots)q^{5}+\cdots$
484.3.b.f	$484$	$3$	484.b	4.b	$2$	$10$	$10$	$13.188$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	$_{}$	None	None		✓			484.3.b.f	$2$	$0$	$0$	$0$	$2$	$0$		$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{5}q^{2}-\beta _{3}q^{3}-\beta _{2}q^{4}+(\beta _{5}+\beta _{9})q^{5}+\cdots$
484.3.b.g	$484$	$3$	484.b	4.b	$2$	$10$	$10$	$13.188$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	$_{}$	None	None		✓			484.3.b.f	$2$	$0$	$0$	$0$	$2$	$0$		$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{2}-\beta _{3}q^{3}-\beta _{2}q^{4}+(\beta _{5}+\beta _{9})q^{5}+\cdots$
484.3.b.h	$484$	$3$	484.b	4.b	$2$	$10$	$10$	$13.188$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None					44.3.b.a	$2$	$0$	$0$	$0$	$-4$	$0$		$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}-\beta _{5}q^{3}-\beta _{1}q^{4}-\beta _{6}q^{5}+\cdots$
484.3.b.i	$484$	$3$	484.b	4.b	$2$	$16$	$16$	$13.188$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		✓			484.3.b.i	$4$	$0$	$0$	$0$	$8$	$0$		$2^{16}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-\beta _{6}q^{3}+(-1+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots$
484.3.b.j	$484$	$3$	484.b	4.b	$2$	$20$	$20$	$13.188$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None					44.3.h.a	$2$	$0$	$0$	$0$	$2$	$0$		$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{9}q^{2}-\beta _{4}q^{3}-\beta _{11}q^{4}+\beta _{18}q^{5}+\cdots$
484.3.b.k	$484$	$3$	484.b	4.b	$2$	$20$	$20$	$13.188$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None					44.3.h.a	$2$	$0$	$0$	$0$	$2$	$0$		$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{9}q^{2}-\beta _{4}q^{3}-\beta _{11}q^{4}+\beta _{18}q^{5}+\cdots$
484.3.d.a	$484$	$3$	484.d	11.b	$2$	$2$	$2$	$13.188$	$\Q(\sqrt{-2}) $	$_{}$	None	None		✓			484.3.d.a	$2$	$0$	$0$	$-2$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}+q^{5}-3\beta q^{7}-8q^{9}-4\beta q^{13}+\cdots$
484.3.d.b	$484$	$3$	484.d	11.b	$2$	$8$	$8$	$13.188$	8.0.$\cdots$.1	$_{}$	None	None		✓			484.3.d.b	$2$	$0$	$0$	$-4$	$-20$	$0$		$2\cdot 11^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{3}+(-2-\beta _{3}+\beta _{6})q^{5}+(-\beta _{4}+\cdots)q^{7}+\cdots$

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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.