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 212 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
640.1.e.a	$640$	$1$	640.e	40.e	$2$	$1$	$1$	$0.319$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-10}) $	$\Q(\sqrt{10}) $	✓	✓			640.1.e.a	$4$	$0$	$0$	$0$	$-1$	$0$		$1$		$q-q^{5}+q^{9}+2q^{13}+q^{25}-2q^{37}+\cdots$
640.1.e.b	$640$	$1$	640.e	40.e	$2$	$1$	$1$	$0.319$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-10}) $	$\Q(\sqrt{10}) $	✓	✓			640.1.e.a	$4$	$0$	$0$	$0$	$1$	$0$		$1$		$q+q^{5}+q^{9}-2q^{13}+q^{25}+2q^{37}+\cdots$
640.1.e.c	$640$	$1$	640.e	40.e	$2$	$4$	$4$	$0.319$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-5}) $	None		✓	✓		640.1.e.c	$8$	$0$	$0$	$0$	$0$	$0$		$2$		$q+(-\zeta_{8}-\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{5}+(\zeta_{8}-\zeta_{8}^{3}+\cdots)q^{7}+\cdots$
640.1.m.a	$640$	$1$	640.m	40.i	$4$	$2$	$1$	$0.319$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		✓			640.1.m.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-i q^{5}-i q^{9}+(-i-1)q^{13}+(i+1)q^{17}+\cdots$
640.1.m.b	$640$	$1$	640.m	40.i	$4$	$2$	$1$	$0.319$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		✓			640.1.m.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+i q^{5}-i q^{9}+(i+1)q^{13}+(i+1)q^{17}+\cdots$
640.2.a.a	$640$	$2$	640.a	1.a	$1$	$1$	$1$	$5.110$	$\Q$	$_{}$	None	None	✓	✓			640.2.a.a	$1$	$0$	$0$	$-2$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-q^{5}+q^{9}-2q^{11}+2q^{13}+\cdots$
640.2.a.b	$640$	$2$	640.a	1.a	$1$	$1$	$1$	$5.110$	$\Q$	$_{}$	None	None	✓	✓			640.2.a.a	$1$	$1$	$0$	$-2$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{5}+q^{9}-2q^{11}-2q^{13}+\cdots$
640.2.a.c	$640$	$2$	640.a	1.a	$1$	$1$	$1$	$5.110$	$\Q$	$_{}$	None	None	✓	✓			640.2.a.c	$1$	$1$	$0$	$0$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-2q^{7}-3q^{9}+6q^{11}-2q^{13}+\cdots$
640.2.a.d	$640$	$2$	640.a	1.a	$1$	$1$	$1$	$5.110$	$\Q$	$_{}$	None	None	✓	✓			640.2.a.c	$1$	$1$	$0$	$0$	$-1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+2q^{7}-3q^{9}-6q^{11}-2q^{13}+\cdots$
640.2.a.e	$640$	$2$	640.a	1.a	$1$	$1$	$1$	$5.110$	$\Q$	$_{}$	None	None	✓	✓			640.2.a.c	$1$	$1$	$0$	$0$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-2q^{7}-3q^{9}-6q^{11}+2q^{13}+\cdots$
640.2.a.f	$640$	$2$	640.a	1.a	$1$	$1$	$1$	$5.110$	$\Q$	$_{}$	None	None	✓	✓			640.2.a.c	$1$	$0$	$0$	$0$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+2q^{7}-3q^{9}+6q^{11}+2q^{13}+\cdots$
640.2.a.g	$640$	$2$	640.a	1.a	$1$	$1$	$1$	$5.110$	$\Q$	$_{}$	None	None	✓	✓			640.2.a.a	$1$	$0$	$0$	$2$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-q^{5}+q^{9}+2q^{11}+2q^{13}+\cdots$
640.2.a.h	$640$	$2$	640.a	1.a	$1$	$1$	$1$	$5.110$	$\Q$	$_{}$	None	None	✓	✓			640.2.a.a	$1$	$0$	$0$	$2$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{5}+q^{9}+2q^{11}-2q^{13}+\cdots$
640.2.a.i	$640$	$2$	640.a	1.a	$1$	$2$	$2$	$5.110$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	✓	✓		640.2.a.i	$1$	$1$	$0$	$-2$	$-2$	$-2$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{3}-q^{5}+(-1+\beta )q^{7}+\cdots$
640.2.a.j	$640$	$2$	640.a	1.a	$1$	$2$	$2$	$5.110$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	✓			640.2.a.i	$1$	$0$	$0$	$-2$	$2$	$2$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{3}+q^{5}+(1-\beta )q^{7}+(3+\cdots)q^{9}+\cdots$
640.2.a.k	$640$	$2$	640.a	1.a	$1$	$2$	$2$	$5.110$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	✓	✓		640.2.a.i	$1$	$0$	$0$	$2$	$-2$	$2$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}-q^{5}+(1-\beta )q^{7}+(3+2\beta )q^{9}+\cdots$
640.2.a.l	$640$	$2$	640.a	1.a	$1$	$2$	$2$	$5.110$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	✓			640.2.a.i	$1$	$0$	$0$	$2$	$2$	$-2$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+q^{5}+(-1+\beta )q^{7}+(3+\cdots)q^{9}+\cdots$
640.2.c.a	$640$	$2$	640.c	5.b	$2$	$6$	$6$	$5.110$	6.0.350464.1	$_{}$	None	None		✓			640.2.c.a	$2$	$0$	$0$	$0$	$-2$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{3}+(\beta _{2}+\beta _{5})q^{5}+(\beta _{2}-\beta _{3}-\beta _{4}+\cdots)q^{7}+\cdots$
640.2.c.b	$640$	$2$	640.c	5.b	$2$	$6$	$6$	$5.110$	6.0.350464.1	$_{}$	None	None		✓			640.2.c.a	$2$	$0$	$0$	$0$	$-2$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{3}+(-\beta _{2}+\beta _{3})q^{5}+(\beta _{2}-\beta _{3}+\cdots)q^{7}+\cdots$
640.2.c.c	$640$	$2$	640.c	5.b	$2$	$6$	$6$	$5.110$	6.0.350464.1	$_{}$	None	None		✓			640.2.c.a	$2$	$0$	$0$	$0$	$2$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{3}+(-\beta _{2}-\beta _{5})q^{5}+(-\beta _{2}+\beta _{3}+\cdots)q^{7}+\cdots$
640.2.c.d	$640$	$2$	640.c	5.b	$2$	$6$	$6$	$5.110$	6.0.350464.1	$_{}$	None	None		✓			640.2.c.a	$2$	$0$	$0$	$0$	$2$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{3}+(\beta _{2}-\beta _{3})q^{5}+(-\beta _{2}+\beta _{3}+\cdots)q^{7}+\cdots$
640.2.d.a	$640$	$2$	640.d	8.b	$2$	$4$	$4$	$5.110$	$\Q(i, \sqrt{10})$	$_{}$	None	None		✓			640.2.d.a	$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{3}+\beta _{1}q^{5}+\beta _{3}q^{7}-7q^{9}-6\beta _{1}q^{13}+\cdots$
640.2.d.b	$640$	$2$	640.d	8.b	$2$	$4$	$4$	$5.110$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			640.2.d.b	$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta_{2} q^{3}+\beta_1 q^{5}+3\beta_{3} q^{7}+q^{9}+\cdots$
640.2.d.c	$640$	$2$	640.d	8.b	$2$	$4$	$4$	$5.110$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			640.2.d.c	$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta_{2} q^{3}+\beta_1 q^{5}-\beta_{3} q^{7}+q^{9}+\cdots$
640.2.d.d	$640$	$2$	640.d	8.b	$2$	$4$	$4$	$5.110$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			640.2.d.d	$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta_{2} q^{3}+\beta_1 q^{5}-3\beta_{3} q^{7}+q^{9}+\cdots$
640.2.f.a	$640$	$2$	640.f	40.f	$2$	$2$	$2$	$5.110$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None		✓			640.2.f.a	$4$	$1$	$0$	$0$	$-2$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+(\beta-1)q^{5}-3 q^{9}-6 q^{13}-4\beta q^{17}+\cdots$
640.2.f.b	$640$	$2$	640.f	40.f	$2$	$2$	$2$	$5.110$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None		✓			640.2.f.a	$4$	$0$	$0$	$0$	$2$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+(\beta+1)q^{5}-3 q^{9}+6 q^{13}+4\beta q^{17}+\cdots$
640.2.f.c	$640$	$2$	640.f	40.f	$2$	$4$	$4$	$5.110$	$\Q(i, \sqrt{6})$	$_{}$	None	None		✓			640.2.f.c	$4$	$0$	$0$	$0$	$-8$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{3}+(-2-\beta _{1})q^{5}+\beta _{2}q^{7}+3q^{9}+\cdots$
640.2.f.d	$640$	$2$	640.f	40.f	$2$	$4$	$4$	$5.110$	$\Q(\sqrt{-2}, \sqrt{5})$	$_{}$	$\Q(\sqrt{-10}) $	None		✓			640.2.f.d	$8$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{3}q^{5}-\beta _{1}q^{7}-3q^{9}-\beta _{2}q^{11}+\cdots$
640.2.f.e	$640$	$2$	640.f	40.f	$2$	$4$	$4$	$5.110$	$\Q(\sqrt{2}, \sqrt{-5})$	$_{}$	$\Q(\sqrt{-5}) $	None		✓			640.2.f.e	$8$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{3}-\beta _{3}q^{5}+\beta _{2}q^{7}-q^{9}+\beta _{2}q^{15}+\cdots$
640.2.f.f	$640$	$2$	640.f	40.f	$2$	$4$	$4$	$5.110$	$\Q(\sqrt{-2}, \sqrt{-5})$	$_{}$	$\Q(\sqrt{-5}) $	None		✓			640.2.f.f	$8$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{3}q^{3}-\beta _{2}q^{5}-3\beta _{1}q^{7}+7q^{9}+\cdots$
640.2.f.g	$640$	$2$	640.f	40.f	$2$	$4$	$4$	$5.110$	$\Q(i, \sqrt{6})$	$_{}$	None	None		✓			640.2.f.c	$4$	$0$	$0$	$0$	$8$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{3}+(2+\beta _{1})q^{5}+\beta _{2}q^{7}+3q^{9}+\cdots$
640.2.j.a	$640$	$2$	640.j	80.j	$4$	$2$	$1$	$5.110$	$\Q(\sqrt{-1}) $	$_{}$	None	None					80.2.j.a	$2$	$0$	$0$	$0$	$-2$	$-6$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-2 i q^{3}+(-2 i-1)q^{5}+(-3 i-3)q^{7}+\cdots$
640.2.j.b	$640$	$2$	640.j	80.j	$4$	$2$	$1$	$5.110$	$\Q(\sqrt{-1}) $	$_{}$	None	None					80.2.j.a	$2$	$0$	$0$	$0$	$-2$	$6$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+2 i q^{3}+(-2 i-1)q^{5}+(3 i+3)q^{7}+\cdots$
640.2.j.c	$640$	$2$	640.j	80.j	$4$	$18$	$9$	$5.110$	$\mathbb{Q}[x]/(x^{18} + \cdots)$	$_{}$	None	None					80.2.j.b	$2$	$0$	$0$	$0$	$4$	$-2$		$2^{13}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{12}q^{3}-\beta _{6}q^{5}-\beta _{11}q^{7}+(-1+\cdots)q^{9}+\cdots$
640.2.j.d	$640$	$2$	640.j	80.j	$4$	$18$	$9$	$5.110$	$\mathbb{Q}[x]/(x^{18} + \cdots)$	$_{}$	None	None					80.2.j.b	$2$	$0$	$0$	$0$	$4$	$2$		$2^{13}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{12}q^{3}+\beta _{4}q^{5}-\beta _{10}q^{7}+(-1+\cdots)q^{9}+\cdots$
640.2.l.a	$640$	$2$	640.l	16.e	$4$	$16$	$8$	$5.110$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None					80.2.l.a	$2$	$0$	$0$	$0$	$0$	$0$		$2^{12}$	$\mathrm{SU}(2)[C_{4}]$	$q+(\beta _{5}-\beta _{7})q^{3}-\beta _{1}q^{5}+(\beta _{1}-\beta _{4}-\beta _{7}+\cdots)q^{7}+\cdots$
640.2.l.b	$640$	$2$	640.l	16.e	$4$	$16$	$8$	$5.110$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None					80.2.l.a	$2$	$0$	$0$	$0$	$0$	$0$		$2^{12}$	$\mathrm{SU}(2)[C_{4}]$	$q+(-\beta _{5}+\beta _{7})q^{3}-\beta _{1}q^{5}+(-\beta _{1}+\beta _{4}+\cdots)q^{7}+\cdots$
640.2.n.a	$640$	$2$	640.n	20.e	$4$	$12$	$6$	$5.110$	12.0.$\cdots$.1	$_{}$	None	None		✓			640.2.n.a	$2$	$0$	$0$	$0$	$0$	$-8$		$2^{9}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{2}q^{3}+\beta _{9}q^{5}+(-1-\beta _{3}-\beta _{5}+\cdots)q^{7}+\cdots$
640.2.n.b	$640$	$2$	640.n	20.e	$4$	$12$	$6$	$5.110$	12.0.$\cdots$.1	$_{}$	None	None		✓			640.2.n.a	$2$	$0$	$0$	$0$	$0$	$-8$		$2^{9}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{3}q^{3}-\beta _{8}q^{5}+(-1-\beta _{2}+\beta _{4}+\cdots)q^{7}+\cdots$
640.2.n.c	$640$	$2$	640.n	20.e	$4$	$12$	$6$	$5.110$	12.0.$\cdots$.1	$_{}$	None	None		✓			640.2.n.a	$2$	$0$	$0$	$0$	$0$	$8$		$2^{9}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{3}q^{3}+\beta _{8}q^{5}+(1+\beta _{2}-\beta _{4}-\beta _{6}+\cdots)q^{7}+\cdots$
640.2.n.d	$640$	$2$	640.n	20.e	$4$	$12$	$6$	$5.110$	12.0.$\cdots$.1	$_{}$	None	None		✓			640.2.n.a	$2$	$0$	$0$	$0$	$0$	$8$		$2^{9}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{2}q^{3}-\beta _{9}q^{5}+(1+\beta _{3}+\beta _{5}-\beta _{7}+\cdots)q^{7}+\cdots$
640.2.o.a	$640$	$2$	640.o	40.k	$4$	$2$	$1$	$5.110$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			640.2.o.a	$2$	$1$	$0$	$-4$	$-4$	$-4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(2 i-2)q^{3}+(i-2)q^{5}+(2 i-2)q^{7}+\cdots$
640.2.o.b	$640$	$2$	640.o	40.k	$4$	$2$	$1$	$5.110$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			640.2.o.a	$2$	$0$	$0$	$-4$	$4$	$4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(2 i-2)q^{3}+(-i+2)q^{5}+(-2 i+2)q^{7}+\cdots$
640.2.o.c	$640$	$2$	640.o	40.k	$4$	$2$	$1$	$5.110$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None		✓			640.2.o.c	$4$	$1$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(i-2)q^{5}+3 i q^{9}+(-5 i-5)q^{13}+\cdots$
640.2.o.d	$640$	$2$	640.o	40.k	$4$	$2$	$1$	$5.110$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None		✓			640.2.o.d	$4$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(-i-2)q^{5}+3 i q^{9}+(i+1)q^{13}+\cdots$
640.2.o.e	$640$	$2$	640.o	40.k	$4$	$2$	$1$	$5.110$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None		✓			640.2.o.d	$4$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(i+2)q^{5}+3 i q^{9}+(-i-1)q^{13}+\cdots$
640.2.o.f	$640$	$2$	640.o	40.k	$4$	$2$	$1$	$5.110$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None		✓			640.2.o.c	$4$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(-i+2)q^{5}+3 i q^{9}+(5 i+5)q^{13}+\cdots$
640.2.o.g	$640$	$2$	640.o	40.k	$4$	$2$	$1$	$5.110$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			640.2.o.a	$2$	$0$	$0$	$4$	$-4$	$4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-2 i+2)q^{3}+(i-2)q^{5}+(-2 i+2)q^{7}+\cdots$
640.2.o.h	$640$	$2$	640.o	40.k	$4$	$2$	$1$	$5.110$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			640.2.o.a	$2$	$0$	$0$	$4$	$4$	$-4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-2 i+2)q^{3}+(-i+2)q^{5}+(2 i-2)q^{7}+\cdots$

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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.