LMFDB - Newform search results

Refine search

Level	Weight	Analytic conductor	$Nk^2$	Dim.

Bad $p$	Char.	Primitive character	Character order	Coefficient field

Self-twists	CM/RM discriminant	Inner twist count	Is self-dual	Analytic rank

Coefficient ring index	Coefficient ring gens.		Projective image	Projective image type
		Only for weight 1:

				Sort order	Select

Results (1-50 of 59 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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Coefficient ring index	Sato-Tate	$q$-expansion
417.1.l.a	$417$	$1$	417.l	417.l	$46$	$22$	$1$	$0.208$	$\Q(\zeta_{46})$	$D_{23}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-2$	$1$		$q-\zeta_{46}^{21}q^{3}+\zeta_{46}^{10}q^{4}+(-\zeta_{46}+\cdots)q^{7}+\cdots$
517.1.k.a	$517$	$1$	517.k	517.k	$46$	$22$	$1$	$0.258$	$\Q(\zeta_{46})$	$D_{23}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$-2$	$-2$	$0$	$1$		$q+(\zeta_{46}^{16}+\zeta_{46}^{20})q^{3}+\zeta_{46}^{14}q^{4}+\cdots$
647.1.b.a	$647$	$1$	647.b	647.b	$2$	$11$	$11$	$0.323$	$\Q(\zeta_{46})^+$	$D_{23}$	$\Q(\sqrt{-647}) $	None	✓	$2$	$0$	$-1$	$-1$	$0$	$-1$	$1$		$q-\beta _{3}q^{2}-\beta _{5}q^{3}+(1+\beta _{6})q^{4}+(\beta _{2}+\cdots)q^{6}+\cdots$
705.1.p.a	$705$	$1$	705.p	705.p	$46$	$22$	$1$	$0.352$	$\Q(\zeta_{46})$	$D_{23}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$-2$	$-1$	$-1$	$0$	$1$		$q+(\zeta_{46}^{4}+\zeta_{46}^{6})q^{2}-\zeta_{46}^{3}q^{3}+(\zeta_{46}^{8}+\cdots)q^{4}+\cdots$
705.1.p.b	$705$	$1$	705.p	705.p	$46$	$22$	$1$	$0.352$	$\Q(\zeta_{46})$	$D_{23}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$2$	$1$	$1$	$0$	$1$		$q+(-\zeta_{46}^{4}-\zeta_{46}^{6})q^{2}+\zeta_{46}^{3}q^{3}+\cdots$
831.1.p.a	$831$	$1$	831.p	831.p	$46$	$22$	$1$	$0.415$	$\Q(\zeta_{46})$	$D_{23}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-2$	$1$		$q+\zeta_{46}^{2}q^{3}-\zeta_{46}^{9}q^{4}+(\zeta_{46}^{10}+\zeta_{46}^{12}+\cdots)q^{7}+\cdots$
893.1.o.a	$893$	$1$	893.o	893.o	$46$	$22$	$1$	$0.446$	$\Q(\zeta_{46})$	$D_{23}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$-2$	$-2$	$1$		$q-\zeta_{46}^{19}q^{4}+(\zeta_{46}^{12}-\zeta_{46}^{21})q^{5}+\cdots$
940.1.p.a	$940$	$1$	940.p	940.p	$46$	$22$	$1$	$0.469$	$\Q(\zeta_{46})$	$D_{23}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$-1$	$-2$	$-1$	$-2$	$1$		$q-\zeta_{46}^{13}q^{2}+(-\zeta_{46}^{5}+\zeta_{46}^{6})q^{3}+\cdots$
940.1.p.b	$940$	$1$	940.p	940.p	$46$	$22$	$1$	$0.469$	$\Q(\zeta_{46})$	$D_{23}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$1$	$2$	$-1$	$2$	$1$		$q+\zeta_{46}^{13}q^{2}+(\zeta_{46}^{5}-\zeta_{46}^{6})q^{3}-\zeta_{46}^{3}q^{4}+\cdots$
1039.1.b.a	$1039$	$1$	1039.b	1039.b	$2$	$11$	$11$	$0.519$	$\Q(\zeta_{46})^+$	$D_{23}$	$\Q(\sqrt{-1039}) $	None	✓	$2$	$0$	$-1$	$0$	$-1$	$-1$	$1$		$q-\beta _{3}q^{2}+(1+\beta _{6})q^{4}+\beta _{2}q^{5}-\beta _{7}q^{7}+\cdots$
1081.1.l.a	$1081$	$1$	1081.l	1081.l	$46$	$22$	$1$	$0.539$	$\Q(\zeta_{46})$	$D_{23}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$-2$	$-2$	$0$	$0$	$1$		$q+(-\zeta_{46}^{15}+\zeta_{46}^{20})q^{2}+(-\zeta_{46}^{3}+\cdots)q^{3}+\cdots$
1103.1.b.a	$1103$	$1$	1103.b	1103.b	$2$	$11$	$11$	$0.550$	$\Q(\zeta_{46})^+$	$D_{23}$	$\Q(\sqrt{-1103}) $	None	✓	$2$	$0$	$-1$	$-1$	$0$	$0$	$1$		$q-\beta _{3}q^{2}+\beta _{4}q^{3}+(1+\beta _{6})q^{4}+(-\beta _{1}+\cdots)q^{6}+\cdots$
1108.1.o.a	$1108$	$1$	1108.o	1108.o	$46$	$22$	$1$	$0.553$	$\Q(\zeta_{46})$	$D_{23}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$-2$	$0$	$1$		$q+\zeta_{46}^{2}q^{2}+\zeta_{46}^{4}q^{4}+(-\zeta_{46}^{7}-\zeta_{46}^{19}+\cdots)q^{5}+\cdots$
1112.1.t.a	$1112$	$1$	1112.t	1112.t	$46$	$22$	$1$	$0.555$	$\Q(\zeta_{46})$	$D_{23}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$-1$	$-2$	$0$	$0$	$1$		$q-\zeta_{46}^{5}q^{2}+(\zeta_{46}^{8}-\zeta_{46}^{11})q^{3}+\zeta_{46}^{10}q^{4}+\cdots$
1279.1.b.a	$1279$	$1$	1279.b	1279.b	$2$	$11$	$11$	$0.638$	$\Q(\zeta_{46})^+$	$D_{23}$	$\Q(\sqrt{-1279}) $	None	✓	$2$	$0$	$-1$	$0$	$-1$	$-1$	$1$		$q-\beta _{3}q^{2}+(1+\beta _{6})q^{4}-\beta _{5}q^{5}-\beta _{7}q^{7}+\cdots$
1447.1.b.a	$1447$	$1$	1447.b	1447.b	$2$	$11$	$11$	$0.722$	$\Q(\zeta_{46})^+$	$D_{23}$	$\Q(\sqrt{-1447}) $	None	✓	$2$	$0$	$-1$	$0$	$0$	$-1$	$1$		$q-\beta _{3}q^{2}+(1+\beta _{6})q^{4}-\beta _{7}q^{7}+(-\beta _{3}+\cdots)q^{8}+\cdots$
1457.1.s.a	$1457$	$1$	1457.s	1457.s	$46$	$22$	$1$	$0.727$	$\Q(\zeta_{46})$	$D_{23}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$-2$	$0$	$-2$	$-2$	$1$		$q+(\zeta_{46}^{6}+\zeta_{46}^{18})q^{2}+(-\zeta_{46}+\zeta_{46}^{12}+\cdots)q^{4}+\cdots$
1471.1.b.a	$1471$	$1$	1471.b	1471.b	$2$	$11$	$11$	$0.734$	$\Q(\zeta_{46})^+$	$D_{23}$	$\Q(\sqrt{-1471}) $	None	✓	$2$	$0$	$-1$	$0$	$-1$	$0$	$1$		$q-\beta _{3}q^{2}+(1+\beta _{6})q^{4}+\beta _{2}q^{5}+(-\beta _{3}+\cdots)q^{8}+\cdots$
1645.1.bc.a	$1645$	$1$	1645.bc	1645.ac	$46$	$22$	$1$	$0.821$	$\Q(\zeta_{46})$	$D_{23}$	$\Q(\sqrt{-35}) $	None		$4$	$0$	$0$	$-2$	$-1$	$-1$	$1$		$q+(\zeta_{46}^{4}-\zeta_{46}^{9})q^{3}+\zeta_{46}^{14}q^{4}-\zeta_{46}^{17}q^{5}+\cdots$
1645.1.bc.b	$1645$	$1$	1645.bc	1645.ac	$46$	$22$	$1$	$0.821$	$\Q(\zeta_{46})$	$D_{23}$	$\Q(\sqrt{-35}) $	None		$4$	$0$	$0$	$2$	$1$	$1$	$1$		$q+(-\zeta_{46}^{4}+\zeta_{46}^{9})q^{3}+\zeta_{46}^{14}q^{4}+\cdots$
1811.1.b.a	$1811$	$1$	1811.b	1811.b	$2$	$11$	$11$	$0.904$	$\Q(\zeta_{46})^+$	$D_{23}$	$\Q(\sqrt{-1811}) $	None	✓	$2$	$0$	$0$	$-1$	$-1$	$-1$	$1$		$q-\beta _{3}q^{3}+q^{4}-\beta _{5}q^{5}-\beta _{7}q^{7}+(1+\cdots)q^{9}+\cdots$
1833.1.z.a	$1833$	$1$	1833.z	1833.z	$46$	$22$	$1$	$0.915$	$\Q(\zeta_{46})$	$D_{23}$	$\Q(\sqrt{-39}) $	None		$4$	$0$	$-2$	$-1$	$-2$	$0$	$1$		$q+(\zeta_{46}^{16}-\zeta_{46}^{19})q^{2}+\zeta_{46}^{22}q^{3}+\cdots$
1833.1.z.b	$1833$	$1$	1833.z	1833.z	$46$	$22$	$1$	$0.915$	$\Q(\zeta_{46})$	$D_{23}$	$\Q(\sqrt{-39}) $	None		$4$	$0$	$2$	$-1$	$2$	$0$	$1$		$q+(-\zeta_{46}^{16}+\zeta_{46}^{19})q^{2}+\zeta_{46}^{22}q^{3}+\cdots$
1844.1.o.a	$1844$	$1$	1844.o	1844.o	$46$	$22$	$1$	$0.920$	$\Q(\zeta_{46})$	$D_{23}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$-2$	$0$	$1$		$q-\zeta_{46}^{19}q^{2}-\zeta_{46}^{15}q^{4}+(-\zeta_{46}+\cdots)q^{5}+\cdots$
1880.1.bh.a	$1880$	$1$	1880.bh	1880.ah	$46$	$22$	$1$	$0.938$	$\Q(\zeta_{46})$	$D_{23}$	$\Q(\sqrt{-10}) $	None		$4$	$0$	$-1$	$0$	$-1$	$-2$	$1$		$q-\zeta_{46}^{13}q^{2}-\zeta_{46}^{3}q^{4}+\zeta_{46}^{2}q^{5}+\cdots$
1880.1.bh.b	$1880$	$1$	1880.bh	1880.ah	$46$	$22$	$1$	$0.938$	$\Q(\zeta_{46})$	$D_{23}$	$\Q(\sqrt{-10}) $	None		$4$	$0$	$1$	$0$	$1$	$2$	$1$		$q+\zeta_{46}^{13}q^{2}-\zeta_{46}^{3}q^{4}-\zeta_{46}^{2}q^{5}+\cdots$
1939.1.bf.a	$1939$	$1$	1939.bf	1939.af	$46$	$22$	$1$	$0.968$	$\Q(\zeta_{46})$	$D_{23}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-2$	$0$	$0$	$-1$	$1$		$q+(\zeta_{46}^{6}+\zeta_{46}^{18})q^{2}+(-\zeta_{46}+\zeta_{46}^{12}+\cdots)q^{4}+\cdots$
1979.1.b.a	$1979$	$1$	1979.b	1979.b	$2$	$11$	$11$	$0.988$	$\Q(\zeta_{46})^+$	$D_{23}$	$\Q(\sqrt{-1979}) $	None	✓	$2$	$0$	$0$	$-1$	$-1$	$-1$	$1$		$q-\beta _{3}q^{3}+q^{4}+\beta _{4}q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots$
2021.1.t.a	$2021$	$1$	2021.t	2021.t	$46$	$22$	$1$	$1.009$	$\Q(\zeta_{46})$	$D_{23}$	$\Q(\sqrt{-43}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{46}^{2}q^{4}-\zeta_{46}^{15}q^{9}+(-\zeta_{46}^{13}+\cdots)q^{11}+\cdots$
2073.1.t.a	$2073$	$1$	2073.t	2073.t	$46$	$22$	$1$	$1.035$	$\Q(\zeta_{46})$	$D_{23}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-2$	$1$		$q+\zeta_{46}^{12}q^{3}+\zeta_{46}^{16}q^{4}+(-\zeta_{46}^{11}+\cdots)q^{7}+\cdots$
2085.1.bb.a	$2085$	$1$	2085.bb	2085.ab	$46$	$22$	$1$	$1.041$	$\Q(\zeta_{46})$	$D_{23}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$-2$	$-1$	$-1$	$0$	$1$		$q+(\zeta_{46}^{6}-\zeta_{46}^{11})q^{2}-\zeta_{46}^{15}q^{3}+\cdots$
2085.1.bb.b	$2085$	$1$	2085.bb	2085.ab	$46$	$22$	$1$	$1.041$	$\Q(\zeta_{46})$	$D_{23}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$2$	$1$	$1$	$0$	$1$		$q+(-\zeta_{46}^{6}+\zeta_{46}^{11})q^{2}+\zeta_{46}^{15}q^{3}+\cdots$
2411.1.b.a	$2411$	$1$	2411.b	2411.b	$2$	$11$	$11$	$1.203$	$\Q(\zeta_{46})^+$	$D_{23}$	$\Q(\sqrt{-2411}) $	None	✓	$2$	$0$	$0$	$-1$	$-1$	$-1$	$1$		$q-\beta _{3}q^{3}+q^{4}-\beta _{7}q^{5}+\beta _{2}q^{7}+(1+\cdots)q^{9}+\cdots$
2444.1.be.a	$2444$	$1$	2444.be	2444.ae	$46$	$22$	$1$	$1.220$	$\Q(\zeta_{46})$	$D_{23}$	$\Q(\sqrt{-13}) $	None		$4$	$0$	$-1$	$0$	$0$	$-2$	$1$		$q-\zeta_{46}^{13}q^{2}-\zeta_{46}^{3}q^{4}+(-\zeta_{46}^{17}+\cdots)q^{7}+\cdots$
2444.1.be.b	$2444$	$1$	2444.be	2444.ae	$46$	$22$	$1$	$1.220$	$\Q(\zeta_{46})$	$D_{23}$	$\Q(\sqrt{-13}) $	None		$4$	$0$	$1$	$0$	$0$	$2$	$1$		$q+\zeta_{46}^{13}q^{2}-\zeta_{46}^{3}q^{4}+(\zeta_{46}^{17}+\zeta_{46}^{19}+\cdots)q^{7}+\cdots$
2487.1.u.a	$2487$	$1$	2487.u	2487.u	$46$	$22$	$1$	$1.241$	$\Q(\zeta_{46})$	$D_{23}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-2$	$1$		$q-\zeta_{46}^{5}q^{3}-\zeta_{46}^{7}q^{4}+(-\zeta_{46}^{3}+\zeta_{46}^{16}+\cdots)q^{7}+\cdots$
2615.1.d.a	$2615$	$1$	2615.d	2615.d	$2$	$11$	$11$	$1.305$	$\Q(\zeta_{46})^+$	$D_{23}$	$\Q(\sqrt{-2615}) $	None	✓	$2$	$0$	$-1$	$-1$	$11$	$0$	$1$		$q-\beta _{3}q^{2}-\beta _{5}q^{3}+(1+\beta _{6})q^{4}+q^{5}+\cdots$
2615.1.d.b	$2615$	$1$	2615.d	2615.d	$2$	$11$	$11$	$1.305$	$\Q(\zeta_{46})^+$	$D_{23}$	$\Q(\sqrt{-2615}) $	None	✓	$2$	$0$	$1$	$1$	$-11$	$0$	$1$		$q+\beta _{3}q^{2}+\beta _{5}q^{3}+(1+\beta _{6})q^{4}-q^{5}+\cdots$
2641.1.bj.a	$2641$	$1$	2641.bj	2641.aj	$46$	$22$	$1$	$1.318$	$\Q(\zeta_{46})$	$D_{23}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$-2$	$-2$	$1$		$q-\zeta_{46}^{13}q^{4}+(-\zeta_{46}^{15}+\zeta_{46}^{22}+\cdots)q^{5}+\cdots$
2671.1.b.a	$2671$	$1$	2671.b	2671.b	$2$	$11$	$11$	$1.333$	$\Q(\zeta_{46})^+$	$D_{23}$	$\Q(\sqrt{-2671}) $	None	✓	$2$	$0$	$-1$	$0$	$-1$	$0$	$1$		$q-\beta _{3}q^{2}+(1+\beta _{6})q^{4}+\beta _{4}q^{5}+(-\beta _{3}+\cdots)q^{8}+\cdots$
2901.1.t.a	$2901$	$1$	2901.t	2901.t	$46$	$22$	$1$	$1.448$	$\Q(\zeta_{46})$	$D_{23}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-2$	$1$		$q+\zeta_{46}^{4}q^{3}+\zeta_{46}^{20}q^{4}+(\zeta_{46}^{6}+\zeta_{46}^{18}+\cdots)q^{7}+\cdots$
3119.1.b.c	$3119$	$1$	3119.b	3119.b	$2$	$11$	$11$	$1.557$	$\Q(\zeta_{46})^+$	$D_{23}$	$\Q(\sqrt{-3119}) $	None	✓	$2$	$0$	$-1$	$-1$	$-1$	$0$	$1$		$q-\beta _{3}q^{2}+\beta _{4}q^{3}+(1+\beta _{6})q^{4}+\beta _{4}q^{5}+\cdots$
3149.1.q.a	$3149$	$1$	3149.q	3149.q	$46$	$22$	$1$	$1.572$	$\Q(\zeta_{46})$	$D_{23}$	$\Q(\sqrt{-67}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{46}^{6}q^{4}+\zeta_{46}^{22}q^{9}+\zeta_{46}^{12}q^{16}+\cdots$
3191.1.b.b	$3191$	$1$	3191.b	3191.b	$2$	$11$	$11$	$1.593$	$\Q(\zeta_{46})^+$	$D_{23}$	$\Q(\sqrt{-3191}) $	None	✓	$2$	$0$	$-1$	$-1$	$-1$	$-1$	$1$		$q-\beta _{3}q^{2}+\beta _{6}q^{3}+(1+\beta _{6})q^{4}+\beta _{4}q^{5}+\cdots$
3197.1.o.a	$3197$	$1$	3197.o	3197.o	$46$	$22$	$1$	$1.596$	$\Q(\zeta_{46})$	$D_{23}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$-2$	$-2$	$0$	$0$	$1$		$q+(-\zeta_{46}^{9}+\zeta_{46}^{22})q^{2}+(\zeta_{46}^{10}-\zeta_{46}^{19}+\cdots)q^{3}+\cdots$
3316.1.v.a	$3316$	$1$	3316.v	3316.v	$46$	$22$	$1$	$1.655$	$\Q(\zeta_{46})$	$D_{23}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$-2$	$0$	$1$		$q+\zeta_{46}^{6}q^{2}+\zeta_{46}^{12}q^{4}+(-\zeta_{46}^{9}+\cdots)q^{5}+\cdots$
3359.1.b.b	$3359$	$1$	3359.b	3359.b	$2$	$11$	$11$	$1.676$	$\Q(\zeta_{46})^+$	$D_{23}$	$\Q(\sqrt{-3359}) $	None	✓	$2$	$0$	$-1$	$-1$	$-1$	$-1$	$1$		$q-\beta _{3}q^{2}+\beta _{8}q^{3}+(1+\beta _{6})q^{4}+\beta _{8}q^{5}+\cdots$
3383.1.d.a	$3383$	$1$	3383.d	3383.d	$2$	$11$	$11$	$1.688$	$\Q(\zeta_{46})^+$	$D_{23}$	$\Q(\sqrt{-3383}) $	None	✓	$2$	$0$	$-1$	$-1$	$0$	$0$	$1$		$q-\beta _{9}q^{2}-\beta _{3}q^{3}+(1-\beta _{5})q^{4}+(-1+\cdots)q^{6}+\cdots$
3383.1.d.b	$3383$	$1$	3383.d	3383.d	$2$	$11$	$11$	$1.688$	$\Q(\zeta_{46})^+$	$D_{23}$	$\Q(\sqrt{-3383}) $	None	✓	$2$	$0$	$-1$	$1$	$0$	$0$	$1$		$q-\beta _{9}q^{2}+\beta _{3}q^{3}+(1-\beta _{5})q^{4}+(1-\beta _{1}+\cdots)q^{6}+\cdots$
3491.1.b.a	$3491$	$1$	3491.b	3491.b	$2$	$11$	$11$	$1.742$	$\Q(\zeta_{46})^+$	$D_{23}$	$\Q(\sqrt{-3491}) $	None	✓	$2$	$0$	$0$	$-1$	$-1$	$-1$	$1$		$q-\beta _{3}q^{3}+q^{4}+\beta _{8}q^{5}-\beta _{1}q^{7}+(1+\cdots)q^{9}+\cdots$

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 $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Learn more

Refine search

Results (1-50 of 59 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.