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 217 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
480.1.c.a	$480$	$1$	480.c	15.d	$2$	$4$	$4$	$0.240$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-5}) $	None		✓	✓	✓	480.1.c.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}q^{3}+\zeta_{8}^{2}q^{5}+(\zeta_{8}+\zeta_{8}^{3})q^{7}+\cdots$
480.1.i.a	$480$	$1$	480.i	120.i	$2$	$2$	$2$	$0.240$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-6}) $	$\Q(\sqrt{10}) $			✓	✓	120.1.i.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-iq^{3}-iq^{5}-q^{9}-q^{15}-q^{25}+\cdots$
480.1.bu.a	$480$	$1$	480.bu	480.au	$8$	$8$	$2$	$0.240$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-15}) $	None		✓	✓	✓	480.1.bu.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{16}^{3}q^{2}-\zeta_{16}^{7}q^{3}+\zeta_{16}^{6}q^{4}+\cdots$
480.2.a.a	$480$	$2$	480.a	1.a	$1$	$1$	$1$	$3.833$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	480.2.a.a	$1$	$0$	$0$	$-1$	$-1$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-4q^{7}+q^{9}+4q^{11}+6q^{13}+\cdots$
480.2.a.b	$480$	$2$	480.a	1.a	$1$	$1$	$1$	$3.833$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	480.2.a.b	$1$	$1$	$0$	$-1$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+q^{9}-4q^{11}+2q^{13}+\cdots$
480.2.a.c	$480$	$2$	480.a	1.a	$1$	$1$	$1$	$3.833$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	480.2.a.c	$1$	$1$	$0$	$-1$	$1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}-4q^{7}+q^{9}-2q^{13}-q^{15}+\cdots$
480.2.a.d	$480$	$2$	480.a	1.a	$1$	$1$	$1$	$3.833$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	480.2.a.d	$1$	$0$	$0$	$-1$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+q^{9}+2q^{13}-q^{15}+6q^{17}+\cdots$
480.2.a.e	$480$	$2$	480.a	1.a	$1$	$1$	$1$	$3.833$	$\Q$	$_{}$	None	None	✓	✓			480.2.a.b	$1$	$0$	$0$	$1$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+q^{9}+4q^{11}+2q^{13}+\cdots$
480.2.a.f	$480$	$2$	480.a	1.a	$1$	$1$	$1$	$3.833$	$\Q$	$_{}$	None	None	✓	✓			480.2.a.a	$1$	$0$	$0$	$1$	$-1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+4q^{7}+q^{9}-4q^{11}+6q^{13}+\cdots$
480.2.a.g	$480$	$2$	480.a	1.a	$1$	$1$	$1$	$3.833$	$\Q$	$_{}$	None	None	✓	✓			480.2.a.d	$1$	$0$	$0$	$1$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+q^{9}+2q^{13}+q^{15}+6q^{17}+\cdots$
480.2.a.h	$480$	$2$	480.a	1.a	$1$	$1$	$1$	$3.833$	$\Q$	$_{}$	None	None	✓	✓			480.2.a.c	$1$	$0$	$0$	$1$	$1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+4q^{7}+q^{9}-2q^{13}+q^{15}+\cdots$
480.2.b.a	$480$	$2$	480.b	24.f	$2$	$8$	$8$	$3.833$	8.0.1649659456.5	$_{}$	None	None					120.2.b.a	$2$	$0$	$0$	$0$	$-8$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{3}-q^{5}-\beta _{2}q^{7}+(-\beta _{3}-\beta _{5}+\cdots)q^{9}+\cdots$
480.2.b.b	$480$	$2$	480.b	24.f	$2$	$8$	$8$	$3.833$	8.0.1649659456.5	$_{}$	None	None					120.2.b.a	$2$	$0$	$0$	$0$	$8$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{3}+q^{5}+\beta _{2}q^{7}+(-\beta _{3}-\beta _{5}+\cdots)q^{9}+\cdots$
480.2.d.a	$480$	$2$	480.d	40.f	$2$	$6$	$6$	$3.833$	6.0.839056.1	$_{}$	None	None					120.2.d.a	$2$	$0$	$0$	$-6$	$0$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}-\beta _{2}q^{5}-\beta _{1}q^{7}+q^{9}+(\beta _{1}+\beta _{5})q^{11}+\cdots$
480.2.d.b	$480$	$2$	480.d	40.f	$2$	$6$	$6$	$3.833$	6.0.839056.1	$_{}$	None	None					120.2.d.a	$2$	$0$	$0$	$6$	$0$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{3}+\beta _{4}q^{5}+\beta _{1}q^{7}+q^{9}+(\beta _{1}+\beta _{5})q^{11}+\cdots$
480.2.f.a	$480$	$2$	480.f	5.b	$2$	$2$	$2$	$3.833$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			480.2.f.a	$2$	$1$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}+(-2+i)q^{5}-2iq^{7}-q^{9}+\cdots$
480.2.f.b	$480$	$2$	480.f	5.b	$2$	$2$	$2$	$3.833$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			480.2.f.a	$2$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}+(-2-i)q^{5}-2iq^{7}-q^{9}+\cdots$
480.2.f.c	$480$	$2$	480.f	5.b	$2$	$2$	$2$	$3.833$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			480.2.f.c	$2$	$0$	$0$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}+(1+2i)q^{5}+4iq^{7}-q^{9}+\cdots$
480.2.f.d	$480$	$2$	480.f	5.b	$2$	$2$	$2$	$3.833$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			480.2.f.c	$2$	$0$	$0$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}+(1-2i)q^{5}+4iq^{7}-q^{9}+\cdots$
480.2.f.e	$480$	$2$	480.f	5.b	$2$	$4$	$4$	$3.833$	$\Q(i, \sqrt{5})$	$_{}$	None	None		✓	✓		480.2.f.e	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}-\beta _{2}q^{5}-2\beta _{1}q^{7}-q^{9}-2\beta _{3}q^{11}+\cdots$
480.2.h.a	$480$	$2$	480.h	12.b	$2$	$4$	$4$	$3.833$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			480.2.h.a	$2$	$0$	$0$	$-4$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1-\zeta_{8}^{2})q^{3}+\zeta_{8}q^{5}+(-2\zeta_{8}+\cdots)q^{7}+\cdots$
480.2.h.b	$480$	$2$	480.h	12.b	$2$	$4$	$4$	$3.833$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			480.2.h.b	$2$	$0$	$0$	$-4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1-\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{5}+\cdots$
480.2.h.c	$480$	$2$	480.h	12.b	$2$	$4$	$4$	$3.833$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			480.2.h.a	$2$	$0$	$0$	$4$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+\zeta_{8}^{2})q^{3}+\zeta_{8}q^{5}+(2\zeta_{8}-2\zeta_{8}^{2}+\cdots)q^{7}+\cdots$
480.2.h.d	$480$	$2$	480.h	12.b	$2$	$4$	$4$	$3.833$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			480.2.h.b	$2$	$0$	$0$	$4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{5}+(-\zeta_{8}+\cdots)q^{7}+\cdots$
480.2.k.a	$480$	$2$	480.k	8.b	$2$	$2$	$2$	$3.833$	$\Q(\sqrt{-1}) $	$_{}$	None	None					120.2.k.a	$2$	$0$	$0$	$0$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}+iq^{5}-2q^{7}-q^{9}+4iq^{11}+\cdots$
480.2.k.b	$480$	$2$	480.k	8.b	$2$	$6$	$6$	$3.833$	6.0.399424.1	$_{}$	None	None			✓		120.2.k.b	$2$	$0$	$0$	$0$	$0$	$-4$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{3}+\beta _{2}q^{5}+(-1+\beta _{3})q^{7}-q^{9}+\cdots$
480.2.m.a	$480$	$2$	480.m	120.m	$2$	$4$	$4$	$3.833$	$\Q(\sqrt{3}, \sqrt{-5})$	$_{}$	$\Q(\sqrt{-15}) $	None					120.2.m.a	$8$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{3}q^{3}-\beta _{1}q^{5}+3q^{9}+\beta _{2}q^{15}+\cdots$
480.2.m.b	$480$	$2$	480.m	120.m	$2$	$16$	$16$	$3.833$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None			✓		120.2.m.b	$8$	$0$	$0$	$0$	$0$	$0$		$2^{17}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{14}q^{3}+(\beta _{1}+\beta _{10})q^{5}-\beta _{4}q^{7}+\cdots$
480.2.o.a	$480$	$2$	480.o	60.h	$2$	$24$	$24$	$3.833$		$_{}$	None	None		✓	✓	✓	480.2.o.a	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
480.2.v.a	$480$	$2$	480.v	15.e	$4$	$4$	$2$	$3.833$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			480.2.v.a	$4$	$1$	$0$	$-4$	$0$	$-12$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1-\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+(-2\zeta_{8}-\zeta_{8}^{3})q^{5}+\cdots$
480.2.v.b	$480$	$2$	480.v	15.e	$4$	$4$	$2$	$3.833$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			480.2.v.a	$4$	$0$	$0$	$4$	$0$	$12$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+(2\zeta_{8}+\zeta_{8}^{3})q^{5}+\cdots$
480.2.v.c	$480$	$2$	480.v	15.e	$4$	$16$	$8$	$3.833$	16.0.$\cdots$.9	$_{}$	None	None		✓			480.2.v.c	$8$	$0$	$0$	$0$	$0$	$0$		$2^{18}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{4}q^{3}+\beta _{13}q^{5}+(\beta _{5}+\beta _{11})q^{7}+\cdots$
480.2.v.d	$480$	$2$	480.v	15.e	$4$	$24$	$12$	$3.833$		$_{}$	None	None		✓	✓		480.2.v.d	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
480.2.w.a	$480$	$2$	480.w	20.e	$4$	$4$	$2$	$3.833$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			480.2.w.a	$2$	$0$	$0$	$0$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\zeta_{8}q^{3}+(2\zeta_{8}-\zeta_{8}^{3})q^{5}+(-1+\zeta_{8}^{2}+\cdots)q^{7}+\cdots$
480.2.w.b	$480$	$2$	480.w	20.e	$4$	$4$	$2$	$3.833$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			480.2.w.a	$2$	$0$	$0$	$0$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\zeta_{8}q^{3}+(-2\zeta_{8}+\zeta_{8}^{3})q^{5}+(1-\zeta_{8}^{2}+\cdots)q^{7}+\cdots$
480.2.w.c	$480$	$2$	480.w	20.e	$4$	$8$	$4$	$3.833$	8.0.1698758656.6	$_{}$	None	None		✓			480.2.w.c	$2$	$0$	$0$	$0$	$0$	$-4$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{1}q^{3}+(-\beta _{2}-\beta _{3}-\beta _{5})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$
480.2.w.d	$480$	$2$	480.w	20.e	$4$	$8$	$4$	$3.833$	8.0.1698758656.6	$_{}$	None	None		✓			480.2.w.c	$2$	$0$	$0$	$0$	$0$	$4$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{3}+(-\beta _{2}-\beta _{3}-\beta _{5})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots$
480.2.bh.a	$480$	$2$	480.bh	40.k	$4$	$24$	$12$	$3.833$		$_{}$	None	None			✓	✓	120.2.v.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
480.2.bi.a	$480$	$2$	480.bi	120.w	$4$	$4$	$2$	$3.833$	$\Q(i, \sqrt{6})$	$_{}$	$\Q(\sqrt{-6}) $	None					120.2.w.a	$4$	$0$	$0$	$0$	$-4$	$4$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+\beta _{1}q^{3}+(-1-\beta _{2}+\beta _{3})q^{5}+(1-\beta _{2}+\cdots)q^{7}+\cdots$
480.2.bi.b	$480$	$2$	480.bi	120.w	$4$	$4$	$2$	$3.833$	$\Q(i, \sqrt{6})$	$_{}$	$\Q(\sqrt{-6}) $	None					120.2.w.a	$4$	$0$	$0$	$0$	$4$	$4$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+\beta _{1}q^{3}+(1+\beta _{2}+\beta _{3})q^{5}+(1-\beta _{2}+\cdots)q^{7}+\cdots$
480.2.bi.c	$480$	$2$	480.bi	120.w	$4$	$32$	$16$	$3.833$		$_{}$	None	None			✓		120.2.w.c	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
480.2.bo.a	$480$	$2$	480.bo	160.u	$8$	$192$	$48$	$3.833$		$_{}$	None	None		✓	✓	✓	480.2.bo.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{8}]$
480.2.br.a	$480$	$2$	480.br	480.ar	$8$	$368$	$92$	$3.833$		$_{}$	None	None		✓	✓	✓	480.2.br.a	$4$	$0$	$0$	$-4$	$0$	$0$			$\mathrm{SU}(2)[C_{8}]$
480.2.bs.a	$480$	$2$	480.bs	480.as	$8$	$16$	$4$	$3.833$	16.0.$\cdots$.3	$_{}$	$\Q(\sqrt{-15}) $	None		✓			480.2.bs.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{8}]$	$q+\beta _{1}q^{2}+(-\beta _{9}-\beta _{12})q^{3}+\beta _{2}q^{4}+\cdots$
480.2.bs.b	$480$	$2$	480.bs	480.as	$8$	$352$	$88$	$3.833$		$_{}$	None	None		✓	✓		480.2.bs.b	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{8}]$
480.2.bv.a	$480$	$2$	480.bv	32.g	$8$	$56$	$14$	$3.833$		$_{}$	None	None		✓			480.2.bv.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{8}]$
480.2.bv.b	$480$	$2$	480.bv	32.g	$8$	$72$	$18$	$3.833$		$_{}$	None	None		✓	✓		480.2.bv.b	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{8}]$
480.2.bx.a	$480$	$2$	480.bx	96.o	$8$	$256$	$64$	$3.833$		$_{}$	None	None		✓	✓	✓	480.2.bx.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{8}]$
480.2.by.a	$480$	$2$	480.by	160.z	$8$	$192$	$48$	$3.833$		$_{}$	None	None		✓	✓	✓	480.2.by.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{8}]$
480.2.cb.a	$480$	$2$	480.cb	480.bb	$8$	$368$	$92$	$3.833$		$_{}$	None	None		✓	✓	✓	480.2.br.a	$4$	$0$	$0$	$-4$	$0$	$-16$			$\mathrm{SU}(2)[C_{8}]$

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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.