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 121 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
297.1.h.a	$297$	$1$	297.h	99.h	$6$	$2$	$1$	$0.148$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-11}) $	None			✓	✓	99.1.h.a	$4$	$0$	$0$	$0$	$-1$	$0$		$1$		$q+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{5}+\zeta_{6}q^{11}-\zeta_{6}q^{16}+\cdots$
297.1.q.a	$297$	$1$	297.q	297.q	$18$	$6$	$1$	$0.148$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-11}) $	None		✓	✓	✓	297.1.q.a	$4$	$0$	$0$	$0$	$-3$	$0$		$1$		$q+\zeta_{18}^{8}q^{3}+\zeta_{18}^{2}q^{4}+(-\zeta_{18}^{3}-\zeta_{18}^{7}+\cdots)q^{5}+\cdots$
297.2.a.a	$297$	$2$	297.a	1.a	$1$	$1$	$1$	$2.372$	$\Q$	$_{}$	None	None	✓	✓			297.2.a.a	$1$	$1$	$-2$	$0$	$-2$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}-2q^{5}+q^{7}+4q^{10}+\cdots$
297.2.a.b	$297$	$2$	297.a	1.a	$1$	$1$	$1$	$2.372$	$\Q$	$_{}$	None	None	✓	✓			297.2.a.b	$1$	$1$	$-1$	$0$	$2$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+2q^{5}-5q^{7}+3q^{8}-2q^{10}+\cdots$
297.2.a.c	$297$	$2$	297.a	1.a	$1$	$1$	$1$	$2.372$	$\Q$	$_{}$	None	None	✓	✓			297.2.a.b	$1$	$1$	$1$	$0$	$-2$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-2q^{5}-5q^{7}-3q^{8}-2q^{10}+\cdots$
297.2.a.d	$297$	$2$	297.a	1.a	$1$	$1$	$1$	$2.372$	$\Q$	$_{}$	None	None	✓	✓			297.2.a.a	$1$	$0$	$2$	$0$	$2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}+2q^{5}+q^{7}+4q^{10}+\cdots$
297.2.a.e	$297$	$2$	297.a	1.a	$1$	$2$	$2$	$2.372$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	✓	✓		297.2.a.e	$1$	$1$	$-2$	$0$	$-2$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+(2-2\beta )q^{4}+(-1-\beta )q^{5}+\cdots$
297.2.a.f	$297$	$2$	297.a	1.a	$1$	$2$	$2$	$2.372$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	✓			297.2.a.e	$1$	$0$	$2$	$0$	$2$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+(2+2\beta )q^{4}+(1-\beta )q^{5}+\cdots$
297.2.a.g	$297$	$2$	297.a	1.a	$1$	$3$	$3$	$2.372$	3.3.564.1	$_{}$	None	None	✓	✓	✓		297.2.a.g	$1$	$0$	$-1$	$0$	$2$	$7$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(1+\beta _{2})q^{5}+\cdots$
297.2.a.h	$297$	$2$	297.a	1.a	$1$	$3$	$3$	$2.372$	3.3.564.1	$_{}$	None	None	✓	✓	✓		297.2.a.g	$1$	$0$	$1$	$0$	$-2$	$7$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-1-\beta _{2})q^{5}+\cdots$
297.2.d.a	$297$	$2$	297.d	33.d	$2$	$8$	$8$	$2.372$	8.0.$\cdots$.14	$_{}$	None	None		✓			297.2.d.a	$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{7}q^{2}+(1+\beta _{2})q^{4}-\beta _{5}q^{5}-\beta _{3}q^{7}+\cdots$
297.2.d.b	$297$	$2$	297.d	33.d	$2$	$8$	$8$	$2.372$	8.0.764411904.5	$_{}$	None	None		✓			297.2.d.b	$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{6}q^{2}+(1+\beta _{5})q^{4}+\beta _{2}q^{5}+(\beta _{4}+\cdots)q^{7}+\cdots$
297.2.e.a	$297$	$2$	297.e	9.c	$3$	$2$	$1$	$2.372$	$\Q(\sqrt{-3}) $	$_{}$	None	None					99.2.e.c	$2$	$1$	$-2$	$0$	$-2$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2+2\zeta_{6})q^{2}-2\zeta_{6}q^{4}-2\zeta_{6}q^{5}+\cdots$
297.2.e.b	$297$	$2$	297.e	9.c	$3$	$2$	$1$	$2.372$	$\Q(\sqrt{-3}) $	$_{}$	None	None					99.2.e.b	$2$	$0$	$0$	$0$	$-3$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+2\zeta_{6}q^{4}-3\zeta_{6}q^{5}+(4-4\zeta_{6})q^{7}+\cdots$
297.2.e.c	$297$	$2$	297.e	9.c	$3$	$2$	$1$	$2.372$	$\Q(\sqrt{-3}) $	$_{}$	None	None					99.2.e.a	$2$	$0$	$1$	$0$	$1$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}+\zeta_{6}q^{5}+(-4+\cdots)q^{7}+\cdots$
297.2.e.d	$297$	$2$	297.e	9.c	$3$	$6$	$3$	$2.372$	$\Q(\zeta_{18})$	$_{}$	None	None					99.2.e.d	$2$	$0$	$0$	$0$	$3$	$3$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta_{5}+\beta_{4}+\cdots-\beta_{2})q^{2}+\cdots+\beta_{5} q^{4}+\cdots$
297.2.e.e	$297$	$2$	297.e	9.c	$3$	$8$	$4$	$2.372$	8.0.508277025.1	$_{}$	None	None			✓		99.2.e.e	$2$	$0$	$1$	$0$	$4$	$-1$		$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{2}+\beta _{6})q^{2}+(\beta _{3}+3\beta _{5})q^{4}+(\beta _{3}+\cdots)q^{5}+\cdots$
297.2.f.a	$297$	$2$	297.f	11.c	$5$	$16$	$4$	$2.372$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓			297.2.f.a	$2$	$0$	$-2$	$0$	$-1$	$-2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\beta _{6}+\beta _{12})q^{2}+(-1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
297.2.f.b	$297$	$2$	297.f	11.c	$5$	$16$	$4$	$2.372$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓			297.2.f.b	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{12}q^{2}+(-\beta _{2}-\beta _{5}+\beta _{6}-\beta _{7}+\cdots)q^{4}+\cdots$
297.2.f.c	$297$	$2$	297.f	11.c	$5$	$16$	$4$	$2.372$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		✓			297.2.f.c	$4$	$0$	$0$	$0$	$0$	$8$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{4}q^{2}+(1+\beta _{2}-2\beta _{3}-\beta _{5}-\beta _{6}+\cdots)q^{4}+\cdots$
297.2.f.d	$297$	$2$	297.f	11.c	$5$	$16$	$4$	$2.372$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓			297.2.f.a	$2$	$0$	$2$	$0$	$1$	$-2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(\beta _{6}-\beta _{12})q^{2}+(-1-\beta _{1}+\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots$
297.2.g.a	$297$	$2$	297.g	99.g	$6$	$4$	$2$	$2.372$	$\Q(\sqrt{-3}, \sqrt{-11})$	$_{}$	$\Q(\sqrt{-11}) $	None					99.2.g.a	$4$	$0$	$0$	$0$	$9$	$0$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+(2-2\beta _{2})q^{4}+(2-\beta _{1}+\beta _{2})q^{5}+(\beta _{2}+\cdots)q^{11}+\cdots$
297.2.g.b	$297$	$2$	297.g	99.g	$6$	$16$	$8$	$2.372$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None			✓		99.2.g.b	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{2}+(-1-\beta _{2}+\beta _{7}+\beta _{9}-\beta _{12}+\cdots)q^{4}+\cdots$
297.2.j.a	$297$	$2$	297.j	27.e	$9$	$6$	$1$	$2.372$	$\Q(\zeta_{18})$	$_{}$	None	None		✓			297.2.j.a	$2$	$1$	$-3$	$-9$	$-9$	$-3$		$1$	$\mathrm{SU}(2)[C_{9}]$	$q+(\zeta_{18}^{2}-\zeta_{18}^{3})q^{2}+(-2+\zeta_{18}^{3}+\cdots)q^{3}+\cdots$
297.2.j.b	$297$	$2$	297.j	27.e	$9$	$72$	$12$	$2.372$		$_{}$	None	None		✓			297.2.j.b	$2$	$0$	$3$	$9$	$12$	$3$			$\mathrm{SU}(2)[C_{9}]$
297.2.j.c	$297$	$2$	297.j	27.e	$9$	$102$	$17$	$2.372$		$_{}$	None	None		✓	✓		297.2.j.c	$2$	$0$	$0$	$0$	$-6$	$0$			$\mathrm{SU}(2)[C_{9}]$
297.2.k.a	$297$	$2$	297.k	33.f	$10$	$32$	$8$	$2.372$		$_{}$	None	None		✓			297.2.k.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
297.2.k.b	$297$	$2$	297.k	33.f	$10$	$32$	$8$	$2.372$		$_{}$	None	None		✓			297.2.k.b	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
297.2.n.a	$297$	$2$	297.n	99.m	$15$	$8$	$1$	$2.372$	$\Q(\zeta_{15})$	$_{}$	None	None					99.2.m.a	$4$	$0$	$4$	$0$	$-6$	$-1$		$1$	$\mathrm{SU}(2)[C_{15}]$	$q+(-\zeta_{15}-\zeta_{15}^{2}-\zeta_{15}^{5}-\zeta_{15}^{6}+\cdots)q^{2}+\cdots$
297.2.n.b	$297$	$2$	297.n	99.m	$15$	$72$	$9$	$2.372$		$_{}$	None	None			✓		99.2.m.b	$4$	$0$	$1$	$0$	$8$	$-2$			$\mathrm{SU}(2)[C_{15}]$
297.2.o.a	$297$	$2$	297.o	297.o	$18$	$12$	$2$	$2.372$	12.0.$\cdots$.1	$_{}$	$\Q(\sqrt{-11}) $	None		✓			297.2.o.a	$4$	$0$	$0$	$0$	$9$	$0$		$1$	$\mathrm{U}(1)[D_{18}]$	$q+(\beta _{3}-\beta _{7}-\beta _{9}-\beta _{10})q^{3}+(2\beta _{3}-2\beta _{7}+\cdots)q^{4}+\cdots$
297.2.o.b	$297$	$2$	297.o	297.o	$18$	$192$	$32$	$2.372$		$_{}$	None	None		✓	✓		297.2.o.b	$4$	$0$	$0$	$-12$	$-18$	$0$			$\mathrm{SU}(2)[C_{18}]$
297.2.t.a	$297$	$2$	297.t	99.p	$30$	$80$	$10$	$2.372$		$_{}$	None	None			✓	✓	99.2.p.a	$4$	$0$	$15$	$0$	$6$	$-5$			$\mathrm{SU}(2)[C_{30}]$
297.2.u.a	$297$	$2$	297.u	297.u	$45$	$816$	$34$	$2.372$		$_{}$	None	None		✓	✓	✓	297.2.u.a	$4$	$0$	$-18$	$-18$	$-21$	$-18$			$\mathrm{SU}(2)[C_{45}]$
297.2.x.a	$297$	$2$	297.x	297.x	$90$	$816$	$34$	$2.372$		$_{}$	None	None		✓	✓	✓	297.2.x.a	$4$	$0$	$-30$	$-18$	$-21$	$-30$			$\mathrm{SU}(2)[C_{90}]$
297.3.b.a	$297$	$3$	297.b	3.b	$2$	$2$	$2$	$8.093$	$\Q(\sqrt{-11}) $	$_{}$	None	None		✓			297.3.b.a	$2$	$0$	$0$	$0$	$0$	$-4$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta q^{2}-7q^{4}-\beta q^{5}-2q^{7}+3\beta q^{8}+\cdots$
297.3.b.b	$297$	$3$	297.b	3.b	$2$	$4$	$4$	$8.093$	$\Q(\sqrt{-3}, \sqrt{-11})$	$_{}$	None	None		✓			297.3.b.b	$2$	$0$	$0$	$0$	$0$	$22$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{3}q^{4}+(\beta _{1}-4\beta _{2})q^{5}+(5+\cdots)q^{7}+\cdots$
297.3.b.c	$297$	$3$	297.b	3.b	$2$	$8$	$8$	$8.093$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	$_{}$	None	None		✓			297.3.b.c	$2$	$0$	$0$	$0$	$0$	$-8$		$2^{4}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-4+\beta _{2})q^{4}+(-\beta _{1}-\beta _{4}+\cdots)q^{5}+\cdots$
297.3.b.d	$297$	$3$	297.b	3.b	$2$	$12$	$12$	$8.093$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		✓	✓		297.3.b.d	$2$	$0$	$0$	$0$	$0$	$-12$		$2^{6}\cdot 3^{10}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{5}q^{2}+(-1-\beta _{1})q^{4}+(\beta _{5}-\beta _{9}+\cdots)q^{5}+\cdots$
297.3.c.a	$297$	$3$	297.c	11.b	$2$	$16$	$16$	$8.093$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓			297.3.c.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{5}\cdot 3^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{11}q^{2}+(-2-\beta _{2})q^{4}+\beta _{10}q^{5}+\cdots$
297.3.c.b	$297$	$3$	297.c	11.b	$2$	$16$	$16$	$8.093$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		✓			297.3.c.b	$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}\cdot 3^{10}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{8}q^{2}+(-2+\beta _{2})q^{4}-\beta _{10}q^{5}+\cdots$
297.3.h.a	$297$	$3$	297.h	99.h	$6$	$4$	$2$	$8.093$	$\Q(\sqrt{-3}, \sqrt{-11})$	$_{}$	$\Q(\sqrt{-11}) $	None					99.3.h.a	$4$	$0$	$0$	$0$	$1$	$0$		$3^{3}$	$\mathrm{U}(1)[D_{6}]$	$q+(-4-4\beta _{1})q^{4}+(1+\beta _{1}-\beta _{3})q^{5}+\cdots$
297.3.h.b	$297$	$3$	297.h	99.h	$6$	$40$	$20$	$8.093$		$_{}$	None	None			✓		99.3.h.b	$4$	$0$	$0$	$0$	$-2$	$0$			$\mathrm{SU}(2)[C_{6}]$
297.3.i.a	$297$	$3$	297.i	9.d	$6$	$40$	$20$	$8.093$		$_{}$	None	None			✓	✓	99.3.i.a	$2$	$0$	$0$	$0$	$9$	$2$			$\mathrm{SU}(2)[C_{6}]$
297.3.l.a	$297$	$3$	297.l	11.d	$10$	$64$	$16$	$8.093$		$_{}$	None	None		✓			297.3.l.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
297.3.l.b	$297$	$3$	297.l	11.d	$10$	$64$	$16$	$8.093$		$_{}$	None	None		✓			297.3.l.b	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
297.3.m.a	$297$	$3$	297.m	33.h	$10$	$8$	$2$	$8.093$	8.0.484000000.6	$_{}$	None	None		✓			297.3.m.a	$4$	$0$	$0$	$0$	$0$	$6$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(\beta _{1}-\beta _{4})q^{2}+(-1-\beta _{2}-\beta _{3}+\beta _{5}+\cdots)q^{4}+\cdots$
297.3.m.b	$297$	$3$	297.m	33.h	$10$	$24$	$6$	$8.093$		$_{}$	None	None		✓			297.3.m.b	$4$	$0$	$0$	$0$	$0$	$2$			$\mathrm{SU}(2)[C_{10}]$
297.3.m.c	$297$	$3$	297.m	33.h	$10$	$32$	$8$	$8.093$		$_{}$	None	None		✓			297.3.m.c	$4$	$0$	$0$	$0$	$0$	$8$			$\mathrm{SU}(2)[C_{10}]$
297.3.m.d	$297$	$3$	297.m	33.h	$10$	$64$	$16$	$8.093$		$_{}$	None	None		✓	✓		297.3.m.d	$4$	$0$	$0$	$0$	$0$	$-8$			$\mathrm{SU}(2)[C_{10}]$

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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.