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 92 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
992.1.g.a	$992$	$1$	992.g	248.g	$2$	$1$	$1$	$0.495$	$\Q$	$D_{2}$	$\Q(\sqrt{-31}) $, $\Q(\sqrt{-62}) $	$\Q(\sqrt{2}) $	✓				248.1.g.a	$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q+2q^{7}-q^{9}+q^{25}-q^{31}-2q^{41}+\cdots$
992.1.g.b	$992$	$1$	992.g	248.g	$2$	$2$	$2$	$0.495$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-31}) $	None					248.1.g.c	$4$	$0$	$0$	$0$	$0$	$-2$		$2$		$q+(\zeta_{6}+\zeta_{6}^{2})q^{5}-q^{7}-q^{9}+(\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{19}+\cdots$
992.1.g.c	$992$	$1$	992.g	248.g	$2$	$2$	$2$	$0.495$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-62}) $	None	✓				248.1.g.b	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta q^{3}+q^{9}+\beta q^{11}-\beta q^{13}+q^{25}+\cdots$
992.1.y.a	$992$	$1$	992.y	992.y	$8$	$4$	$1$	$0.495$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-31}) $	None		✓			992.1.y.a	$4$	$0$	$0$	$0$	$4$	$0$		$1$		$q-\zeta_{8}^{2}q^{2}-q^{4}+(1-\zeta_{8})q^{5}+\zeta_{8}^{2}q^{8}+\cdots$
992.1.y.b	$992$	$1$	992.y	992.y	$8$	$8$	$2$	$0.495$	$\Q(\zeta_{24})$	$D_{24}$	$\Q(\sqrt{-31}) $	None		✓	✓		992.1.y.b	$4$	$0$	$0$	$0$	$-4$	$0$		$1$		$q-\zeta_{24}^{10}q^{2}-\zeta_{24}^{8}q^{4}+(-\zeta_{24}+\zeta_{24}^{8}+\cdots)q^{5}+\cdots$
992.1.bf.a	$992$	$1$	992.bf	124.l	$10$	$8$	$2$	$0.495$	$\Q(\zeta_{20})$	$A_{5}$	None	None		✓	✓	✓	992.1.bf.a	$4$	$0$	$0$	$0$	$4$	$0$		$1$		$q-\zeta_{20}^{7}q^{3}+(\zeta_{20}^{2}-\zeta_{20}^{8})q^{5}-\zeta_{20}q^{7}+\cdots$
992.2.a.a	$992$	$2$	992.a	1.a	$1$	$2$	$2$	$7.921$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓			992.2.a.a	$1$	$1$	$0$	$0$	$-2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-q^{5}+(-1-\beta )q^{7}-q^{9}+(2+\cdots)q^{11}+\cdots$
992.2.a.b	$992$	$2$	992.a	1.a	$1$	$2$	$2$	$7.921$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓			992.2.a.a	$1$	$1$	$0$	$0$	$-2$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-q^{5}+(1-\beta )q^{7}-q^{9}+(-2+\cdots)q^{11}+\cdots$
992.2.a.c	$992$	$2$	992.a	1.a	$1$	$3$	$3$	$7.921$	3.3.316.1	$_{}$	None	None	✓	✓	✓		992.2.a.c	$1$	$1$	$0$	$-2$	$0$	$-8$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1}-\beta _{2})q^{3}+\beta _{2}q^{5}+(-3+\cdots)q^{7}+\cdots$
992.2.a.d	$992$	$2$	992.a	1.a	$1$	$3$	$3$	$7.921$	3.3.316.1	$_{}$	None	None	✓	✓			992.2.a.c	$1$	$0$	$0$	$2$	$0$	$8$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1}+\beta _{2})q^{3}+\beta _{2}q^{5}+(3-\beta _{1}+\cdots)q^{7}+\cdots$
992.2.a.e	$992$	$2$	992.a	1.a	$1$	$4$	$4$	$7.921$	4.4.13968.1	$_{}$	None	None	✓	✓	✓		992.2.a.e	$1$	$1$	$0$	$-4$	$2$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{3}+(1-\beta _{1})q^{5}+(-1+\cdots)q^{7}+\cdots$
992.2.a.f	$992$	$2$	992.a	1.a	$1$	$4$	$4$	$7.921$	4.4.13968.1	$_{}$	None	None	✓	✓			992.2.a.e	$1$	$0$	$0$	$4$	$2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{3}+\beta _{1}q^{5}+(1+\beta _{1}-\beta _{3})q^{7}+\cdots$
992.2.a.g	$992$	$2$	992.a	1.a	$1$	$6$	$6$	$7.921$	6.6.66862976.1	$_{}$	None	None	✓	✓	✓		992.2.a.g	$1$	$0$	$0$	$-2$	$2$	$2$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{3}-\beta _{3}q^{5}+\beta _{4}q^{7}+(2-\beta _{1}+\cdots)q^{9}+\cdots$
992.2.a.h	$992$	$2$	992.a	1.a	$1$	$6$	$6$	$7.921$	6.6.66862976.1	$_{}$	None	None	✓	✓	✓		992.2.a.g	$1$	$0$	$0$	$2$	$2$	$-2$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{3}-\beta _{3}q^{5}-\beta _{4}q^{7}+(2-\beta _{1}+\cdots)q^{9}+\cdots$
992.2.b.a	$992$	$2$	992.b	248.b	$2$	$6$	$6$	$7.921$	6.0.21717639.1	$_{}$	$\Q(\sqrt{-31}) $	None					248.2.b.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{5}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{5}-\beta _{5}q^{7}+3q^{9}+(\beta _{3}+2\beta _{4}+\cdots)q^{19}+\cdots$
992.2.b.b	$992$	$2$	992.b	248.b	$2$	$24$	$24$	$7.921$		$_{}$	None	None			✓		248.2.b.b	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
992.2.c.a	$992$	$2$	992.c	8.b	$2$	$12$	$12$	$7.921$	12.0.$\cdots$.1	$_{}$	None	None					248.2.c.a	$2$	$0$	$0$	$0$	$0$	$2$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}-\beta _{2}q^{5}+\beta _{4}q^{7}+\beta _{9}q^{9}+\cdots$
992.2.c.b	$992$	$2$	992.c	8.b	$2$	$18$	$18$	$7.921$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	$_{}$	None	None			✓		248.2.c.b	$2$	$0$	$0$	$0$	$0$	$2$		$2^{17}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{3}+\beta _{2}q^{5}+\beta _{3}q^{7}+(-2-\beta _{16}+\cdots)q^{9}+\cdots$
992.2.h.a	$992$	$2$	992.h	124.d	$2$	$32$	$32$	$7.921$		$_{}$	None	None		✓	✓	✓	992.2.h.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
992.2.i.a	$992$	$2$	992.i	31.c	$3$	$2$	$1$	$7.921$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			992.2.i.a	$2$	$0$	$0$	$-1$	$-1$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+\cdots$
992.2.i.b	$992$	$2$	992.i	31.c	$3$	$2$	$1$	$7.921$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			992.2.i.a	$2$	$0$	$0$	$1$	$-1$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}+\cdots$
992.2.i.c	$992$	$2$	992.i	31.c	$3$	$4$	$2$	$7.921$	$\Q(\sqrt{-3}, \sqrt{5})$	$_{}$	None	None		✓			992.2.i.c	$2$	$0$	$0$	$-2$	$-4$	$4$		$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{3}+(-2-2\beta _{1}-\beta _{2})q^{5}+(-2\beta _{1}+\cdots)q^{7}+\cdots$
992.2.i.d	$992$	$2$	992.i	31.c	$3$	$4$	$2$	$7.921$	$\Q(\sqrt{-3}, \sqrt{5})$	$_{}$	None	None		✓			992.2.i.d	$2$	$0$	$0$	$0$	$2$	$-4$		$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{2}q^{3}-\beta _{1}q^{5}+(-2-2\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots$
992.2.i.e	$992$	$2$	992.i	31.c	$3$	$4$	$2$	$7.921$	$\Q(\sqrt{-3}, \sqrt{5})$	$_{}$	None	None		✓			992.2.i.d	$2$	$0$	$0$	$0$	$2$	$4$		$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{2}q^{3}-\beta _{1}q^{5}+(2+2\beta _{1}+\beta _{2})q^{7}+\cdots$
992.2.i.f	$992$	$2$	992.i	31.c	$3$	$4$	$2$	$7.921$	$\Q(\sqrt{-3}, \sqrt{5})$	$_{}$	None	None		✓			992.2.i.c	$2$	$0$	$0$	$2$	$-4$	$-4$		$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{3}+(-2-2\beta _{1}-\beta _{2})q^{5}+(2\beta _{1}+\cdots)q^{7}+\cdots$
992.2.i.g	$992$	$2$	992.i	31.c	$3$	$8$	$4$	$7.921$	8.0.$\cdots$.6	$_{}$	None	None		✓			992.2.i.g	$4$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{3}+(-\beta _{2}+\beta _{4}+\beta _{6})q^{5}+\beta _{3}q^{7}+\cdots$
992.2.i.h	$992$	$2$	992.i	31.c	$3$	$10$	$5$	$7.921$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None		✓			992.2.i.h	$2$	$0$	$0$	$-3$	$-1$	$-3$		$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{5}-\beta _{8})q^{3}+(-\beta _{1}-\beta _{4}-\beta _{6}+\beta _{9})q^{5}+\cdots$
992.2.i.i	$992$	$2$	992.i	31.c	$3$	$10$	$5$	$7.921$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None		✓			992.2.i.h	$2$	$0$	$0$	$3$	$-1$	$3$		$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{5}+\beta _{8})q^{3}+(-\beta _{1}-\beta _{4}-\beta _{6}+\cdots)q^{5}+\cdots$
992.2.i.j	$992$	$2$	992.i	31.c	$3$	$16$	$8$	$7.921$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		✓	✓		992.2.i.j	$4$	$0$	$0$	$0$	$4$	$0$		$2^{12}$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{12}q^{3}+(1-\beta _{5}-\beta _{7})q^{5}+(\beta _{12}+\cdots)q^{7}+\cdots$
992.2.n.a	$992$	$2$	992.n	31.d	$5$	$32$	$8$	$7.921$		$_{}$	None	None		✓			992.2.n.a	$2$	$0$	$0$	$-2$	$0$	$0$			$\mathrm{SU}(2)[C_{5}]$
992.2.n.b	$992$	$2$	992.n	31.d	$5$	$32$	$8$	$7.921$		$_{}$	None	None		✓			992.2.n.b	$4$	$0$	$0$	$0$	$-4$	$0$			$\mathrm{SU}(2)[C_{5}]$
992.2.n.c	$992$	$2$	992.n	31.d	$5$	$32$	$8$	$7.921$		$_{}$	None	None		✓			992.2.n.c	$4$	$0$	$0$	$0$	$4$	$0$			$\mathrm{SU}(2)[C_{5}]$
992.2.n.d	$992$	$2$	992.n	31.d	$5$	$32$	$8$	$7.921$		$_{}$	None	None		✓			992.2.n.a	$2$	$0$	$0$	$2$	$0$	$0$			$\mathrm{SU}(2)[C_{5}]$
992.2.o.a	$992$	$2$	992.o	124.g	$6$	$64$	$32$	$7.921$		$_{}$	None	None		✓	✓	✓	992.2.o.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
992.2.t.a	$992$	$2$	992.t	248.p	$6$	$4$	$2$	$7.921$	$\Q(\sqrt{-3}, \sqrt{-7})$	$_{}$	None	None					248.2.p.a	$4$	$0$	$0$	$0$	$0$	$-2$		$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{3}-\beta _{3}q^{5}+(-1+\beta _{2})q^{7}+4\beta _{2}q^{9}+\cdots$
992.2.t.b	$992$	$2$	992.t	248.p	$6$	$56$	$28$	$7.921$		$_{}$	None	None			✓		248.2.p.b	$4$	$0$	$0$	$0$	$0$	$4$			$\mathrm{SU}(2)[C_{6}]$
992.2.u.a	$992$	$2$	992.u	248.q	$6$	$4$	$2$	$7.921$	$\Q(\sqrt{-2}, \sqrt{-3})$	$_{}$	None	None					248.2.q.b	$2$	$0$	$0$	$6$	$-6$	$6$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(2+\beta _{1}-\beta _{2}-\beta _{3})q^{3}+(-1+\beta _{1}+\cdots)q^{5}+\cdots$
992.2.u.b	$992$	$2$	992.u	248.q	$6$	$4$	$2$	$7.921$	$\Q(\zeta_{12})$	$_{}$	None	None					248.2.q.a	$4$	$0$	$0$	$6$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(2-\zeta_{12}^{2})q^{3}-\zeta_{12}q^{5}+(-3\zeta_{12}+\cdots)q^{7}+\cdots$
992.2.u.c	$992$	$2$	992.u	248.q	$6$	$4$	$2$	$7.921$	$\Q(\sqrt{-2}, \sqrt{-3})$	$_{}$	None	None					248.2.q.b	$2$	$0$	$0$	$6$	$6$	$-6$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(2+\beta _{1}-\beta _{2}-\beta _{3})q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$
992.2.u.d	$992$	$2$	992.u	248.q	$6$	$48$	$24$	$7.921$		$_{}$	None	None			✓		248.2.q.d	$4$	$0$	$0$	$-12$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
992.2.v.a	$992$	$2$	992.v	32.g	$8$	$4$	$1$	$7.921$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			992.2.v.a	$2$	$0$	$0$	$4$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{8}]$	$q+(-\zeta_{8}+\zeta_{8}^{3})q^{2}+(1-\zeta_{8}-\zeta_{8}^{2}+\cdots)q^{3}+\cdots$
992.2.v.b	$992$	$2$	992.v	32.g	$8$	$224$	$56$	$7.921$		$_{}$	None	None		✓			992.2.v.b	$2$	$0$	$0$	$-4$	$4$	$0$			$\mathrm{SU}(2)[C_{8}]$
992.2.v.c	$992$	$2$	992.v	32.g	$8$	$252$	$63$	$7.921$		$_{}$	None	None		✓	✓		992.2.v.c	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{8}]$
992.2.w.a	$992$	$2$	992.w	992.w	$8$	$24$	$6$	$7.921$		$_{}$	$\Q(\sqrt{-31}) $	None		✓			992.2.w.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{U}(1)[D_{8}]$
992.2.w.b	$992$	$2$	992.w	992.w	$8$	$480$	$120$	$7.921$		$_{}$	None	None		✓	✓		992.2.w.b	$4$	$0$	$-8$	$0$	$-8$	$-8$			$\mathrm{SU}(2)[C_{8}]$
992.2.bb.a	$992$	$2$	992.bb	124.j	$10$	$128$	$32$	$7.921$		$_{}$	None	None		✓	✓	✓	992.2.bb.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
992.2.bc.a	$992$	$2$	992.bc	248.u	$10$	$120$	$30$	$7.921$		$_{}$	None	None			✓	✓	248.2.u.a	$4$	$0$	$0$	$0$	$0$	$6$			$\mathrm{SU}(2)[C_{10}]$
992.2.bd.a	$992$	$2$	992.bd	248.v	$10$	$120$	$30$	$7.921$		$_{}$	None	None			✓	✓	248.2.v.a	$4$	$0$	$0$	$10$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
992.2.bk.a	$992$	$2$	992.bk	31.g	$15$	$64$	$8$	$7.921$		$_{}$	None	None		✓			992.2.bk.a	$2$	$0$	$0$	$-2$	$0$	$0$			$\mathrm{SU}(2)[C_{15}]$
992.2.bk.b	$992$	$2$	992.bk	31.g	$15$	$64$	$8$	$7.921$		$_{}$	None	None		✓			992.2.bk.b	$4$	$0$	$0$	$0$	$-4$	$0$			$\mathrm{SU}(2)[C_{15}]$

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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.