LMFDB - Newform search results

Refine search

Level	Weight	Analytic conductor	$Nk^2$	Dim.

Bad $p$	Char.	Primitive character	Character order	Coefficient field

Self-twists	CM/RM discriminant	Inner twist count	Is self-dual	Analytic rank

Coefficient ring index	Coefficient ring gens.		Projective image	Projective image type
		Only for weight 1:

				Sort order	Select

Results (1-50 of 356 matches)

Next Download displayed columns for results to

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	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	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
225.1.g.a	$225$	$1$	225.g	5.c	$4$	$2$	$1$	$0.112$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-15}) $	$\Q(\sqrt{5}) $		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+iq^{4}-q^{16}-iq^{19}-q^{31}+iq^{49}+\cdots$
225.2.a.a	$225$	$2$	225.a	1.a	$1$	$1$	$1$	$1.797$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-2$	$0$	$0$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}-3q^{7}-2q^{11}+q^{13}+\cdots$
225.2.a.b	$225$	$2$	225.a	1.a	$1$	$1$	$1$	$1.797$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$-1$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+3q^{8}+4q^{11}+2q^{13}+\cdots$
225.2.a.c	$225$	$2$	225.a	1.a	$1$	$1$	$1$	$1.797$	$\Q$	$_{}$	$\Q(\sqrt{-3}) $	None	✓	$2$	$1$	$0$	$0$	$0$	$-5$	$+$	$1$	$N(\mathrm{U}(1))$	$q-2q^{4}-5q^{7}-5q^{13}+4q^{16}-q^{19}+\cdots$
225.2.a.d	$225$	$2$	225.a	1.a	$1$	$1$	$1$	$1.797$	$\Q$	$_{}$	$\Q(\sqrt{-3}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$5$	$-$	$1$	$N(\mathrm{U}(1))$	$q-2q^{4}+5q^{7}+5q^{13}+4q^{16}-q^{19}+\cdots$
225.2.a.e	$225$	$2$	225.a	1.a	$1$	$1$	$1$	$1.797$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$2$	$0$	$0$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}+3q^{7}-2q^{11}-q^{13}+\cdots$
225.2.a.f	$225$	$2$	225.a	1.a	$1$	$2$	$2$	$1.797$	$\Q(\sqrt{5}) $	$_{}$	$\Q(\sqrt{-15}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$-$	$2$	$N(\mathrm{U}(1))$	$q-\beta q^{2}+3q^{4}-\beta q^{8}-q^{16}+2\beta q^{17}+\cdots$
225.2.b.a	$225$	$2$	225.b	5.b	$2$	$2$	$2$	$1.797$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2iq^{2}-2q^{4}+3iq^{7}-2q^{11}+iq^{13}+\cdots$
225.2.b.b	$225$	$2$	225.b	5.b	$2$	$2$	$2$	$1.797$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}+q^{4}+3iq^{8}+4q^{11}+2iq^{13}+\cdots$
225.2.b.c	$225$	$2$	225.b	5.b	$2$	$2$	$2$	$1.797$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$5$	$\mathrm{U}(1)[D_{2}]$	$q+2q^{4}+iq^{7}-iq^{13}+4q^{16}+q^{19}+\cdots$
225.2.e.a	$225$	$2$	225.e	9.c	$3$	$2$	$1$	$1.797$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$1$	$3$	$0$	$-3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+(2-\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots$
225.2.e.b	$225$	$2$	225.e	9.c	$3$	$6$	$3$	$1.797$	6.0.954288.1	$_{}$	None	None		$2$	$0$	$1$	$-1$	$0$	$5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{1}-\beta _{2}+\beta _{4}+\beta _{5})q^{2}-\beta _{4}q^{3}+\cdots$
225.2.e.c	$225$	$2$	225.e	9.c	$3$	$8$	$4$	$1.797$	8.0.1223810289.2	$_{}$	None	None		$2$	$0$	$-2$	$1$	$0$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{2}+(-\beta _{4}+\beta _{7})q^{3}+(-1+\beta _{1}+\cdots)q^{4}+\cdots$
225.2.e.d	$225$	$2$	225.e	9.c	$3$	$8$	$4$	$1.797$	$\Q(\zeta_{24})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{24}^{7}q^{2}+(\zeta_{24}^{6}-\zeta_{24}^{7})q^{3}-\zeta_{24}^{2}q^{4}+\cdots$
225.2.e.e	$225$	$2$	225.e	9.c	$3$	$8$	$4$	$1.797$	8.0.1223810289.2	$_{}$	None	None		$2$	$0$	$2$	$-1$	$0$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+(\beta _{4}-\beta _{7})q^{3}+(-1+\beta _{1}+\cdots)q^{4}+\cdots$
225.2.f.a	$225$	$2$	225.f	15.e	$4$	$4$	$2$	$1.797$	$\Q(\zeta_{8})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$8$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\zeta_{8}q^{2}-\zeta_{8}^{2}q^{4}+(2-2\zeta_{8}^{2})q^{7}+\cdots$
225.2.f.b	$225$	$2$	225.f	15.e	$4$	$8$	$4$	$1.797$	$\Q(\zeta_{24})$	$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{6}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q-\zeta_{24}^{6}q^{2}-4\zeta_{24}^{2}q^{4}+\zeta_{24}q^{7}+\cdots$
225.2.h.a	$225$	$2$	225.h	25.d	$5$	$4$	$1$	$1.797$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$1$	$0$	$-5$	$0$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+\zeta_{10}^{3}q^{4}+\cdots$
225.2.h.b	$225$	$2$	225.h	25.d	$5$	$4$	$1$	$1.797$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$2$	$0$	$5$	$-2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(\zeta_{10}-\zeta_{10}^{2})q^{2}+(-1+\zeta_{10}+\zeta_{10}^{3})q^{4}+\cdots$
225.2.h.c	$225$	$2$	225.h	25.d	$5$	$8$	$2$	$1.797$	8.0.26265625.1	$_{}$	None	None		$2$	$0$	$1$	$0$	$5$	$4$		$5$	$\mathrm{SU}(2)[C_{5}]$	$q+(\beta _{3}+\beta _{7})q^{2}+(-1+2\beta _{1}+2\beta _{3}+\cdots)q^{4}+\cdots$
225.2.h.d	$225$	$2$	225.h	25.d	$5$	$12$	$3$	$1.797$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$6$	$-12$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{2}q^{2}+(-1+\beta _{1}-\beta _{5}-2\beta _{8}+\beta _{9}+\cdots)q^{4}+\cdots$
225.2.h.e	$225$	$2$	225.h	25.d	$5$	$16$	$4$	$1.797$	16.0.$\cdots$.3	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$5^{2}$	$\mathrm{SU}(2)[C_{5}]$	$q+(\beta _{3}-\beta _{10}+\beta _{12}-\beta _{14})q^{2}+(-\beta _{8}+\cdots)q^{4}+\cdots$
225.2.k.a	$225$	$2$	225.k	45.j	$6$	$4$	$2$	$1.797$	$\Q(\zeta_{12})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\zeta_{12}q^{2}+(-\zeta_{12}-\zeta_{12}^{3})q^{3}-\zeta_{12}^{2}q^{4}+\cdots$
225.2.k.b	$225$	$2$	225.k	45.j	$6$	$12$	$6$	$1.797$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{6}]$	$q+(\beta _{1}+\beta _{6}-\beta _{7})q^{2}+\beta _{6}q^{3}+(2+2\beta _{8}+\cdots)q^{4}+\cdots$
225.2.k.c	$225$	$2$	225.k	45.j	$6$	$16$	$8$	$1.797$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{2}+(-\beta _{10}+\beta _{14})q^{3}+(1-\beta _{3}+\cdots)q^{4}+\cdots$
225.2.m.a	$225$	$2$	225.m	25.e	$10$	$8$	$2$	$1.797$	8.0.58140625.2	$_{}$	None	None		$2$	$0$	$5$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(1-\beta _{1})q^{2}+(1-2\beta _{1}-\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots$
225.2.m.b	$225$	$2$	225.m	25.e	$10$	$16$	$4$	$1.797$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(\beta _{1}-\beta _{3}+\beta _{4}-\beta _{10}+\beta _{15})q^{2}+\cdots$
225.2.m.c	$225$	$2$	225.m	25.e	$10$	$24$	$6$	$1.797$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
225.2.p.a	$225$	$2$	225.p	45.l	$12$	$16$	$4$	$1.797$	16.0.$\cdots$.9	$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{6}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{12}]$	$q+(-\beta _{6}-\beta _{13})q^{2}+\beta _{1}q^{3}+(-\beta _{9}+\cdots)q^{4}+\cdots$
225.2.p.b	$225$	$2$	225.p	45.l	$12$	$16$	$4$	$1.797$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$4$	$0$	$6$	$6$	$0$	$2$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+\beta _{5}q^{2}+(1-\beta _{9}+\beta _{11}+\beta _{12}+\beta _{13}+\cdots)q^{3}+\cdots$
225.2.p.c	$225$	$2$	225.p	45.l	$12$	$32$	$8$	$1.797$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{12}]$
225.2.q.a	$225$	$2$	225.q	225.q	$15$	$224$	$28$	$1.797$		$_{}$	None	None		$4$	$0$	$-3$	$-8$	$-8$	$-8$			$\mathrm{SU}(2)[C_{15}]$
225.2.s.a	$225$	$2$	225.s	75.l	$20$	$80$	$10$	$1.797$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$8$			$\mathrm{SU}(2)[C_{20}]$
225.2.u.a	$225$	$2$	225.u	225.u	$30$	$224$	$28$	$1.797$		$_{}$	None	None		$4$	$0$	$-5$	$-10$	$0$	$0$			$\mathrm{SU}(2)[C_{30}]$
225.2.w.a	$225$	$2$	225.w	225.w	$60$	$448$	$28$	$1.797$		$_{}$	None	None		$4$	$0$	$-24$	$-14$	$-24$	$-8$			$\mathrm{SU}(2)[C_{60}]$
225.3.c.a	$225$	$3$	225.c	3.b	$2$	$2$	$2$	$6.131$	$\Q(\sqrt{-2}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-18$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{2}+2q^{4}-9q^{7}+6\beta q^{8}+13\beta q^{11}+\cdots$
225.3.c.b	$225$	$3$	225.c	3.b	$2$	$2$	$2$	$6.131$	$\Q(\sqrt{-2}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$18$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{2}+2q^{4}+9q^{7}+6\beta q^{8}-13\beta q^{11}+\cdots$
225.3.c.c	$225$	$3$	225.c	3.b	$2$	$4$	$4$	$6.131$	$\Q(\sqrt{-2}, \sqrt{-5})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-16$		$2\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}+(-3-2\beta _{1})q^{4}+(-4-\beta _{1}+\cdots)q^{7}+\cdots$
225.3.c.d	$225$	$3$	225.c	3.b	$2$	$4$	$4$	$6.131$	$\Q(\sqrt{-2}, \sqrt{-7})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}-3q^{4}-\beta _{1}q^{7}-\beta _{2}q^{8}-\beta _{3}q^{11}+\cdots$
225.3.d.a	$225$	$3$	225.d	15.d	$2$	$4$	$4$	$6.131$	$\Q(\zeta_{8})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\zeta_{8}^{3}q^{2}-2q^{4}+9\zeta_{8}q^{7}-6\zeta_{8}^{3}q^{8}+\cdots$
225.3.d.b	$225$	$3$	225.d	15.d	$2$	$8$	$8$	$6.131$	8.0.40960000.1	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{10}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{4}q^{2}+(3-\beta _{6})q^{4}+(2\beta _{1}-\beta _{3})q^{7}+\cdots$
225.3.g.a	$225$	$3$	225.g	5.c	$4$	$4$	$2$	$6.131$	$\Q(i, \sqrt{6})$	$_{}$	None	None		$2$	$0$	$-4$	$0$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1+\beta _{1}-\beta _{2})q^{2}+(-2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
225.3.g.b	$225$	$3$	225.g	5.c	$4$	$4$	$2$	$6.131$	$\Q(i, \sqrt{6})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+2\beta _{1}q^{2}+8\beta _{2}q^{4}+5\beta _{1}q^{7}+8\beta _{3}q^{8}+\cdots$
225.3.g.c	$225$	$3$	225.g	5.c	$4$	$4$	$2$	$6.131$	$\Q(i, \sqrt{30})$	$_{}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+\beta _{1}q^{2}+11\beta _{2}q^{4}+7\beta _{3}q^{8}-61q^{16}+\cdots$
225.3.g.d	$225$	$3$	225.g	5.c	$4$	$4$	$2$	$6.131$	$\Q(i, \sqrt{6})$	$_{}$	$\Q(\sqrt{-3}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$5^{2}$	$\mathrm{U}(1)[D_{4}]$	$q-4\beta _{2}q^{4}+\beta _{1}q^{7}-3\beta _{3}q^{13}-2^{4}q^{16}+\cdots$
225.3.g.e	$225$	$3$	225.g	5.c	$4$	$4$	$2$	$6.131$	$\Q(i, \sqrt{6})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{2}-\beta _{2}q^{4}+4\beta _{1}q^{7}-5\beta _{3}q^{8}+\cdots$
225.3.g.f	$225$	$3$	225.g	5.c	$4$	$4$	$2$	$6.131$	$\Q(i, \sqrt{6})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{2}-\beta _{2}q^{4}-6\beta _{1}q^{7}-5\beta _{3}q^{8}+\cdots$
225.3.g.g	$225$	$3$	225.g	5.c	$4$	$4$	$2$	$6.131$	$\Q(i, \sqrt{10})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$20$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(5+5\beta _{2})q^{7}-3\beta _{3}q^{8}+\cdots$
225.3.i.a	$225$	$3$	225.i	45.h	$6$	$4$	$2$	$6.131$	$\Q(\zeta_{12})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\zeta_{12}-\zeta_{12}^{3})q^{2}+(-3\zeta_{12}+3\zeta_{12}^{3})q^{3}+\cdots$
225.3.i.b	$225$	$3$	225.i	45.h	$6$	$32$	$16$	$6.131$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$

Next Download displayed columns for results to

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Learn more

Refine search

Results (1-50 of 356 matches)

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.