LMFDB - Newform search results

Refine search

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

					Sort order	Select

Results (1-50 of 111 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	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
1100.1.e.a	$1100$	$1$	1100.e	55.d	$2$	$2$	$2$	$0.549$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-11}) $	None			✓	✓	44.1.d.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-i q^{3}+q^{11}-i q^{23}-i q^{27}-q^{31}+\cdots$
1100.1.f.a	$1100$	$1$	1100.f	11.b	$2$	$1$	$1$	$0.549$	$\Q$	$D_{3}$	$\Q(\sqrt{-11}) $	None	✓				44.1.d.a	$2$	$0$	$0$	$1$	$0$	$0$		$1$		$q+q^{3}+q^{11}+q^{23}-q^{27}-q^{31}+\cdots$
1100.1.f.b	$1100$	$1$	1100.f	11.b	$2$	$2$	$2$	$0.549$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-11}) $	None	✓		✓		220.1.e.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta q^{3}+2q^{9}-q^{11}+\beta q^{23}-\beta q^{27}+\cdots$
1100.1.i.a	$1100$	$1$	1100.i	220.i	$4$	$2$	$1$	$0.549$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-55}) $	None		✓			1100.1.i.a	$4$	$0$	$-2$	$0$	$0$	$2$		$1$		$q-q^{2}+q^{4}+(-i+1)q^{7}-q^{8}+\cdots$
1100.1.i.b	$1100$	$1$	1100.i	220.i	$4$	$2$	$1$	$0.549$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-55}) $	None		✓			1100.1.i.a	$4$	$0$	$0$	$0$	$0$	$-2$		$1$		$q-i q^{2}-q^{4}+(i-1)q^{7}+i q^{8}+\cdots$
1100.1.i.c	$1100$	$1$	1100.i	220.i	$4$	$2$	$1$	$0.549$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-55}) $	None		✓			1100.1.i.a	$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q+i q^{2}-q^{4}+(-i+1)q^{7}-i q^{8}+\cdots$
1100.1.i.d	$1100$	$1$	1100.i	220.i	$4$	$2$	$1$	$0.549$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-55}) $	None		✓			1100.1.i.a	$4$	$0$	$2$	$0$	$0$	$-2$		$1$		$q+q^{2}+q^{4}+(i-1)q^{7}+q^{8}+i q^{9}+\cdots$
1100.1.x.a	$1100$	$1$	1100.x	275.v	$10$	$8$	$2$	$0.549$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-11}) $	None		✓	✓	✓	1100.1.x.a	$4$	$0$	$0$	$2$	$-4$	$0$		$1$		$q+(\zeta_{30}^{2}+\zeta_{30}^{4})q^{3}-\zeta_{30}^{5}q^{5}+(\zeta_{30}^{4}+\cdots)q^{9}+\cdots$
1100.1.cd.a	$1100$	$1$	1100.cd	275.s	$10$	$8$	$2$	$0.549$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-11}) $	None		✓	✓	✓	1100.1.cd.a	$4$	$0$	$0$	$0$	$4$	$0$		$1$		$q+(-\zeta_{30}-\zeta_{30}^{2})q^{3}-\zeta_{30}^{10}q^{5}+\cdots$
1100.2.a.a	$1100$	$2$	1100.a	1.a	$1$	$1$	$1$	$8.784$	$\Q$	$_{}$	None	None	✓				220.2.a.b	$1$	$1$	$0$	$-2$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{9}+q^{11}+4q^{17}-4q^{19}+\cdots$
1100.2.a.b	$1100$	$2$	1100.a	1.a	$1$	$1$	$1$	$8.784$	$\Q$	$_{}$	None	None	✓				44.2.a.a	$1$	$0$	$0$	$-1$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{7}-2q^{9}-q^{11}+4q^{13}+\cdots$
1100.2.a.c	$1100$	$2$	1100.a	1.a	$1$	$1$	$1$	$8.784$	$\Q$	$_{}$	None	None	✓				220.2.b.a	$1$	$1$	$0$	$0$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{7}-3q^{9}-q^{11}+6q^{13}+2q^{17}+\cdots$
1100.2.a.d	$1100$	$2$	1100.a	1.a	$1$	$1$	$1$	$8.784$	$\Q$	$_{}$	None	None	✓				220.2.b.a	$1$	$1$	$0$	$0$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{7}-3q^{9}-q^{11}-6q^{13}-2q^{17}+\cdots$
1100.2.a.e	$1100$	$2$	1100.a	1.a	$1$	$1$	$1$	$8.784$	$\Q$	$_{}$	None	None	✓				220.2.a.a	$1$	$0$	$0$	$2$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+4q^{7}+q^{9}-q^{11}+4q^{13}+\cdots$
1100.2.a.f	$1100$	$2$	1100.a	1.a	$1$	$2$	$2$	$8.784$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓	✓	✓		1100.2.a.f	$1$	$1$	$0$	$-3$	$0$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{3}+(-2-\beta )q^{7}+(1+3\beta )q^{9}+\cdots$
1100.2.a.g	$1100$	$2$	1100.a	1.a	$1$	$2$	$2$	$8.784$	$\Q(\sqrt{21}) $	$_{}$	None	None	✓	✓	✓		1100.2.a.g	$1$	$1$	$0$	$-1$	$0$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+(-3+\beta )q^{7}+(2+\beta )q^{9}-q^{11}+\cdots$
1100.2.a.h	$1100$	$2$	1100.a	1.a	$1$	$2$	$2$	$8.784$	$\Q(\sqrt{21}) $	$_{}$	None	None	✓	✓	✓		1100.2.a.g	$1$	$0$	$0$	$1$	$0$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(3-\beta )q^{7}+(2+\beta )q^{9}-q^{11}+\cdots$
1100.2.a.i	$1100$	$2$	1100.a	1.a	$1$	$2$	$2$	$8.784$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓	✓			1100.2.a.f	$1$	$0$	$0$	$3$	$0$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+(2+\beta )q^{7}+(1+3\beta )q^{9}+\cdots$
1100.2.a.j	$1100$	$2$	1100.a	1.a	$1$	$4$	$4$	$8.784$	$\Q(\sqrt{3}, \sqrt{19})$	$_{}$	None	None	✓		✓		220.2.b.b	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{2})q^{7}+(3+\beta _{3})q^{9}+\cdots$
1100.2.b.a	$1100$	$2$	1100.b	5.b	$2$	$2$	$2$	$8.784$	$\Q(\sqrt{-1}) $	$_{}$	None	None					220.2.a.a	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{3}-2\beta q^{7}-q^{9}-q^{11}+2\beta q^{13}+\cdots$
1100.2.b.b	$1100$	$2$	1100.b	5.b	$2$	$2$	$2$	$8.784$	$\Q(\sqrt{-1}) $	$_{}$	None	None					220.2.a.b	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{3}-q^{9}+q^{11}+2\beta q^{17}+4 q^{19}+\cdots$
1100.2.b.c	$1100$	$2$	1100.b	5.b	$2$	$2$	$2$	$8.784$	$\Q(\sqrt{-1}) $	$_{}$	None	None					44.2.a.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{3}-2 i q^{7}+2 q^{9}-q^{11}-4 i q^{13}+\cdots$
1100.2.b.d	$1100$	$2$	1100.b	5.b	$2$	$4$	$4$	$8.784$	$\Q(i, \sqrt{21})$	$_{}$	None	None		✓			1100.2.a.g	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+(\beta _{1}+3\beta _{2})q^{7}+(-3+\beta _{3})q^{9}+\cdots$
1100.2.b.e	$1100$	$2$	1100.b	5.b	$2$	$4$	$4$	$8.784$	$\Q(i, \sqrt{13})$	$_{}$	None	None		✓			1100.2.a.f	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}-\beta _{2})q^{3}+(-\beta _{1}+2\beta _{2})q^{7}+(-4+\cdots)q^{9}+\cdots$
1100.2.k.a	$1100$	$2$	1100.k	55.e	$4$	$4$	$2$	$8.784$	$\Q(i, \sqrt{11})$	$_{}$	None	None					220.2.k.a	$4$	$0$	$0$	$4$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+(1+\beta _{1})q^{3}+(\beta _{2}+\beta _{3})q^{7}-\beta _{1}q^{9}+\cdots$
1100.2.k.b	$1100$	$2$	1100.k	55.e	$4$	$8$	$4$	$8.784$	$\Q(i, \sqrt{3}, \sqrt{11})$	$_{}$	$\Q(\sqrt{-11}) $	None					220.2.k.b	$4$	$0$	$0$	$-2$	$0$	$0$		$2^{3}\cdot 5^{2}$	$\mathrm{U}(1)[D_{4}]$	$q-\beta _{1}q^{3}+(-\beta _{1}-4\beta _{2}+\beta _{4}-\beta _{5}+\cdots)q^{9}+\cdots$
1100.2.k.c	$1100$	$2$	1100.k	55.e	$4$	$8$	$4$	$8.784$	$\Q(i, \sqrt{2}, \sqrt{5})$	$_{}$	None	None		✓			1100.2.k.c	$8$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{2}q^{3}-\beta _{7}q^{7}+\beta _{1}q^{9}+(-1-\beta _{5}+\cdots)q^{11}+\cdots$
1100.2.k.d	$1100$	$2$	1100.k	55.e	$4$	$8$	$4$	$8.784$	$\Q(i, \sqrt{6}, \sqrt{14})$	$_{}$	None	None		✓			1100.2.k.d	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{3}+(-2\beta _{1}+\beta _{3})q^{7}+\beta _{6}q^{9}+\cdots$
1100.2.k.e	$1100$	$2$	1100.k	55.e	$4$	$8$	$4$	$8.784$	$\Q(i, \sqrt{6}, \sqrt{14})$	$_{}$	None	None		✓			1100.2.k.d	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{3}+(2\beta _{1}-\beta _{3})q^{7}+\beta _{6}q^{9}+(-\beta _{2}+\cdots)q^{11}+\cdots$
1100.2.n.a	$1100$	$2$	1100.n	11.c	$5$	$4$	$1$	$8.784$	$\Q(\zeta_{10})$	$_{}$	None	None					44.2.e.a	$2$	$0$	$0$	$1$	$0$	$7$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(\zeta_{10}+\zeta_{10}^{2}+\zeta_{10}^{3})q^{3}+(3-3\zeta_{10}+\cdots)q^{7}+\cdots$
1100.2.n.b	$1100$	$2$	1100.n	11.c	$5$	$8$	$2$	$8.784$	8.0.159390625.1	$_{}$	None	None					220.2.m.b	$2$	$0$	$0$	$-5$	$0$	$1$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\beta _{1}-\beta _{2}-\beta _{3}+\beta _{5}-\beta _{6}+\beta _{7})q^{3}+\cdots$
1100.2.n.c	$1100$	$2$	1100.n	11.c	$5$	$8$	$2$	$8.784$	8.0.26265625.1	$_{}$	None	None					220.2.m.a	$2$	$0$	$0$	$1$	$0$	$-1$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(\beta _{1}+\beta _{7})q^{3}+(1-\beta _{1}-2\beta _{2}+2\beta _{3}+\cdots)q^{7}+\cdots$
1100.2.n.d	$1100$	$2$	1100.n	11.c	$5$	$16$	$4$	$8.784$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓			1100.2.n.d	$2$	$0$	$0$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\beta _{1}+\beta _{4}-\beta _{7}-\beta _{12})q^{3}+(\beta _{1}+\cdots)q^{7}+\cdots$
1100.2.n.e	$1100$	$2$	1100.n	11.c	$5$	$16$	$4$	$8.784$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓			1100.2.n.d	$2$	$0$	$0$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(\beta _{1}-\beta _{4}+\beta _{7}+\beta _{12})q^{3}+(-\beta _{1}+\cdots)q^{7}+\cdots$
1100.2.n.f	$1100$	$2$	1100.n	11.c	$5$	$24$	$6$	$8.784$		$_{}$	None	None			✓		220.2.t.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{5}]$
1100.2.q.a	$1100$	$2$	1100.q	25.d	$5$	$44$	$11$	$8.784$		$_{}$	None	None		✓			1100.2.q.a	$2$	$0$	$0$	$-2$	$9$	$0$			$\mathrm{SU}(2)[C_{5}]$
1100.2.q.b	$1100$	$2$	1100.q	25.d	$5$	$52$	$13$	$8.784$		$_{}$	None	None		✓	✓		1100.2.q.b	$2$	$0$	$0$	$0$	$-3$	$0$			$\mathrm{SU}(2)[C_{5}]$
1100.2.cb.a	$1100$	$2$	1100.cb	55.j	$10$	$8$	$2$	$8.784$	$\Q(\zeta_{20})$	$_{}$	None	None					44.2.e.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(2\zeta_{20}+\zeta_{20}^{5}-\zeta_{20}^{7})q^{3}+(2\zeta_{20}+\cdots)q^{7}+\cdots$
1100.2.cb.b	$1100$	$2$	1100.cb	55.j	$10$	$16$	$4$	$8.784$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None					220.2.m.b	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(\beta _{2}-\beta _{6}-\beta _{10}-\beta _{12}-\beta _{13}+\beta _{14}+\cdots)q^{3}+\cdots$
1100.2.cb.c	$1100$	$2$	1100.cb	55.j	$10$	$16$	$4$	$8.784$	16.0.$\cdots$.9	$_{}$	None	None					220.2.m.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(2\beta _{1}-\beta _{2}+\beta _{7}-\beta _{9}-\beta _{11}+\beta _{13}+\cdots)q^{3}+\cdots$
1100.2.cb.d	$1100$	$2$	1100.cb	55.j	$10$	$32$	$8$	$8.784$		$_{}$	None	None		✓	✓		1100.2.n.d	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
1100.3.e.a	$1100$	$3$	1100.e	55.d	$2$	$4$	$4$	$29.973$	$\Q(i, \sqrt{33})$	$_{}$	$\Q(\sqrt{-11}) $	None					44.3.d.a	$4$	$0$	$0$	$0$	$0$	$0$		$2\cdot 5^{2}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{1}q^{3}+(-6+\beta _{3})q^{9}-11q^{11}+\cdots$
1100.3.e.b	$1100$	$3$	1100.e	55.d	$2$	$16$	$16$	$29.973$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None					220.3.f.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{25}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{9}+\beta _{10})q^{3}-\beta _{4}q^{7}+(-3+\beta _{1}+\cdots)q^{9}+\cdots$
1100.3.e.c	$1100$	$3$	1100.e	55.d	$2$	$16$	$16$	$29.973$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		✓			1100.3.f.c	$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}\cdot 5^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{8}q^{3}+\beta _{3}q^{7}+(-2+\beta _{5})q^{9}-\beta _{14}q^{11}+\cdots$
1100.3.f.a	$1100$	$3$	1100.f	11.b	$2$	$2$	$2$	$29.973$	$\Q(\sqrt{33}) $	$_{}$	$\Q(\sqrt{-11}) $	None	✓				44.3.d.a	$2$	$0$	$0$	$-5$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+(-2-\beta )q^{3}+(3+5\beta )q^{9}-11q^{11}+\cdots$
1100.3.f.b	$1100$	$3$	1100.f	11.b	$2$	$4$	$4$	$29.973$	$\Q(\sqrt{3}, \sqrt{11})$	$_{}$	$\Q(\sqrt{-11}) $	None	✓				220.3.e.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{3}\cdot 5^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{3}+(13+\beta _{3})q^{9}+11q^{11}+(5\beta _{1}+\cdots)q^{23}+\cdots$
1100.3.f.c	$1100$	$3$	1100.f	11.b	$2$	$8$	$8$	$29.973$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	$_{}$	None	None		✓			1100.3.f.c	$2$	$0$	$0$	$-4$	$0$	$0$		$5$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1+\beta _{2})q^{3}-\beta _{1}q^{7}+(2+\beta _{3})q^{9}+\cdots$
1100.3.f.d	$1100$	$3$	1100.f	11.b	$2$	$8$	$8$	$29.973$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None					220.3.e.b	$4$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{5}q^{3}+\beta _{4}q^{7}+(-3-\beta _{1})q^{9}+(-5+\cdots)q^{11}+\cdots$
1100.3.f.e	$1100$	$3$	1100.f	11.b	$2$	$8$	$8$	$29.973$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	$_{}$	None	None		✓			1100.3.f.c	$2$	$0$	$0$	$4$	$0$	$0$		$5$	$\mathrm{SU}(2)[C_{2}]$	$q+(1-\beta _{2})q^{3}+\beta _{1}q^{7}+(2+\beta _{3})q^{9}+\cdots$
1100.3.f.f	$1100$	$3$	1100.f	11.b	$2$	$8$	$8$	$29.973$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	$_{}$	None	None					220.3.f.a	$2$	$0$	$0$	$8$	$0$	$0$		$2^{6}\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+\beta _{1})q^{3}-\beta _{4}q^{7}+(4+\beta _{1}-\beta _{7})q^{9}+\cdots$

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 $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Learn more

Refine search

Results (1-50 of 111 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.