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 76 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
2420.1.h.a	$2420$	$1$	2420.h	20.d	$2$	$1$	$1$	$1.208$	$\Q$	$D_{3}$	$\Q(\sqrt{-5}) $	None	✓	✓			2420.1.h.a	$2$	$0$	$-1$	$-1$	$1$	$1$		$1$		$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+q^{7}+\cdots$
2420.1.h.b	$2420$	$1$	2420.h	20.d	$2$	$1$	$1$	$1.208$	$\Q$	$D_{2}$	$\Q(\sqrt{-5}) $, $\Q(\sqrt{-55}) $	$\Q(\sqrt{11}) $	✓	✓			2420.1.h.b	$4$	$0$	$-1$	$0$	$-1$	$-2$		$1$		$q-q^{2}+q^{4}-q^{5}-2q^{7}-q^{8}-q^{9}+\cdots$
2420.1.h.c	$2420$	$1$	2420.h	20.d	$2$	$1$	$1$	$1.208$	$\Q$	$D_{3}$	$\Q(\sqrt{-5}) $	None	✓	✓			2420.1.h.a	$2$	$0$	$-1$	$1$	$1$	$1$		$1$		$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+q^{7}+\cdots$
2420.1.h.d	$2420$	$1$	2420.h	20.d	$2$	$1$	$1$	$1.208$	$\Q$	$D_{3}$	$\Q(\sqrt{-5}) $	None	✓	✓			2420.1.h.a	$2$	$0$	$1$	$-1$	$1$	$-1$		$1$		$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots$
2420.1.h.e	$2420$	$1$	2420.h	20.d	$2$	$1$	$1$	$1.208$	$\Q$	$D_{2}$	$\Q(\sqrt{-5}) $, $\Q(\sqrt{-55}) $	$\Q(\sqrt{11}) $	✓	✓			2420.1.h.b	$4$	$0$	$1$	$0$	$-1$	$2$		$1$		$q+q^{2}+q^{4}-q^{5}+2q^{7}+q^{8}-q^{9}+\cdots$
2420.1.h.f	$2420$	$1$	2420.h	20.d	$2$	$1$	$1$	$1.208$	$\Q$	$D_{3}$	$\Q(\sqrt{-5}) $	None	✓	✓			2420.1.h.a	$2$	$0$	$1$	$1$	$1$	$-1$		$1$		$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-q^{7}+\cdots$
2420.1.h.g	$2420$	$1$	2420.h	20.d	$2$	$2$	$2$	$1.208$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-5}) $	None	✓	✓			2420.1.h.g	$4$	$0$	$-2$	$0$	$-2$	$2$		$1$		$q-q^{2}-\beta q^{3}+q^{4}-q^{5}+\beta q^{6}+q^{7}+\cdots$
2420.1.h.h	$2420$	$1$	2420.h	20.d	$2$	$2$	$2$	$1.208$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-55}) $	$\Q(\sqrt{55}) $		✓			2420.1.h.h	$8$	$0$	$0$	$0$	$2$	$0$		$1$		$q-i q^{2}-q^{4}+q^{5}+i q^{8}-q^{9}+\cdots$
2420.1.h.i	$2420$	$1$	2420.h	20.d	$2$	$2$	$2$	$1.208$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-5}) $	None	✓	✓			2420.1.h.g	$4$	$0$	$2$	$0$	$-2$	$-2$		$1$		$q+q^{2}-\beta q^{3}+q^{4}-q^{5}-\beta q^{6}-q^{7}+\cdots$
2420.1.h.j	$2420$	$1$	2420.h	20.d	$2$	$4$	$4$	$1.208$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-1}) $	None		✓	✓		2420.1.h.j	$8$	$0$	$0$	$0$	$-2$	$0$		$1$		$q-\zeta_{12}^{3}q^{2}-q^{4}+\zeta_{12}^{4}q^{5}+\zeta_{12}^{3}q^{8}+\cdots$
2420.1.i.a	$2420$	$1$	2420.i	220.i	$4$	$4$	$2$	$1.208$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-1}) $	None		✓			2420.1.i.a	$8$	$0$	$0$	$0$	$4$	$0$		$1$		$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+q^{5}-\zeta_{8}^{3}q^{8}+\cdots$
2420.1.i.b	$2420$	$1$	2420.i	220.i	$4$	$8$	$4$	$1.208$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-1}) $	None		✓	✓		2420.1.i.b	$8$	$0$	$0$	$0$	$-4$	$0$		$1$		$q+\zeta_{24}^{9}q^{2}-\zeta_{24}^{6}q^{4}+\zeta_{24}^{8}q^{5}+\cdots$
2420.1.j.a	$2420$	$1$	2420.j	5.c	$4$	$4$	$2$	$1.208$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-11}) $	None		✓	✓	✓	2420.1.j.a	$4$	$0$	$0$	$-2$	$0$	$0$		$1$		$q+(-\zeta_{12}-\zeta_{12}^{2})q^{3}+\zeta_{12}^{5}q^{5}+(\zeta_{12}^{2}+\cdots)q^{9}+\cdots$
2420.1.n.a	$2420$	$1$	2420.n	220.n	$10$	$4$	$1$	$1.208$	$\Q(\zeta_{10})$	$D_{3}$	$\Q(\sqrt{-5}) $	None		✓			2420.1.h.a	$8$	$0$	$-1$	$-1$	$-1$	$1$		$1$		$q+\zeta_{10}^{4}q^{2}+\zeta_{10}^{2}q^{3}-\zeta_{10}^{3}q^{4}+\cdots$
2420.1.n.b	$2420$	$1$	2420.n	220.n	$10$	$4$	$1$	$1.208$	$\Q(\zeta_{10})$	$D_{2}$	$\Q(\sqrt{-5}) $, $\Q(\sqrt{-55}) $	$\Q(\sqrt{11}) $		✓			2420.1.h.b	$16$	$0$	$-1$	$0$	$1$	$-2$		$1$		$q+\zeta_{10}^{4}q^{2}-\zeta_{10}^{3}q^{4}+\zeta_{10}q^{5}-\zeta_{10}^{3}q^{7}+\cdots$
2420.1.n.c	$2420$	$1$	2420.n	220.n	$10$	$4$	$1$	$1.208$	$\Q(\zeta_{10})$	$D_{3}$	$\Q(\sqrt{-5}) $	None		✓			2420.1.h.a	$8$	$0$	$-1$	$1$	$-1$	$1$		$1$		$q+\zeta_{10}^{4}q^{2}-\zeta_{10}^{2}q^{3}-\zeta_{10}^{3}q^{4}+\cdots$
2420.1.n.d	$2420$	$1$	2420.n	220.n	$10$	$4$	$1$	$1.208$	$\Q(\zeta_{10})$	$D_{3}$	$\Q(\sqrt{-5}) $	None		✓			2420.1.h.a	$8$	$0$	$1$	$-1$	$-1$	$-1$		$1$		$q-\zeta_{10}^{4}q^{2}+\zeta_{10}^{2}q^{3}-\zeta_{10}^{3}q^{4}+\cdots$
2420.1.n.e	$2420$	$1$	2420.n	220.n	$10$	$4$	$1$	$1.208$	$\Q(\zeta_{10})$	$D_{2}$	$\Q(\sqrt{-5}) $, $\Q(\sqrt{-55}) $	$\Q(\sqrt{11}) $		✓			2420.1.h.b	$16$	$0$	$1$	$0$	$1$	$2$		$1$		$q-\zeta_{10}^{4}q^{2}-\zeta_{10}^{3}q^{4}+\zeta_{10}q^{5}+\zeta_{10}^{3}q^{7}+\cdots$
2420.1.n.f	$2420$	$1$	2420.n	220.n	$10$	$4$	$1$	$1.208$	$\Q(\zeta_{10})$	$D_{3}$	$\Q(\sqrt{-5}) $	None		✓			2420.1.h.a	$8$	$0$	$1$	$1$	$-1$	$-1$		$1$		$q-\zeta_{10}^{4}q^{2}-\zeta_{10}^{2}q^{3}-\zeta_{10}^{3}q^{4}+\cdots$
2420.1.n.g	$2420$	$1$	2420.n	220.n	$10$	$8$	$2$	$1.208$	8.0.324000000.3	$D_{6}$	$\Q(\sqrt{-5}) $	None		✓			2420.1.h.g	$16$	$0$	$-2$	$0$	$2$	$2$		$1$		$q+\beta _{6}q^{2}+\beta _{3}q^{3}+\beta _{2}q^{4}-\beta _{4}q^{5}+\cdots$
2420.1.n.h	$2420$	$1$	2420.n	220.n	$10$	$8$	$2$	$1.208$	$\Q(\zeta_{20})$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-55}) $	$\Q(\sqrt{55}) $		✓			2420.1.h.h	$32$	$0$	$0$	$0$	$-2$	$0$		$1$		$q-\zeta_{20}^{3}q^{2}+\zeta_{20}^{6}q^{4}-\zeta_{20}^{2}q^{5}+\cdots$
2420.1.n.i	$2420$	$1$	2420.n	220.n	$10$	$8$	$2$	$1.208$	8.0.324000000.3	$D_{6}$	$\Q(\sqrt{-5}) $	None		✓			2420.1.h.g	$16$	$0$	$2$	$0$	$2$	$-2$		$1$		$q-\beta _{6}q^{2}+\beta _{3}q^{3}+\beta _{2}q^{4}-\beta _{4}q^{5}+\cdots$
2420.1.n.j	$2420$	$1$	2420.n	220.n	$10$	$16$	$4$	$1.208$	$\Q(\zeta_{60})$	$D_{6}$	$\Q(\sqrt{-1}) $	None		✓	✓		2420.1.h.j	$32$	$0$	$0$	$0$	$2$	$0$		$1$		$q+\zeta_{60}^{9}q^{2}+\zeta_{60}^{18}q^{4}-\zeta_{60}^{26}q^{5}+\cdots$
2420.1.q.a	$2420$	$1$	2420.q	55.h	$10$	$8$	$2$	$1.208$	$\Q(\zeta_{15})$	$D_{6}$	$\Q(\sqrt{-11}) $	None			✓	✓	220.1.e.a	$16$	$0$	$0$	$0$	$-1$	$0$		$1$		$q+(\zeta_{30}^{2}+\zeta_{30}^{7})q^{3}+\zeta_{30}^{11}q^{5}+(\zeta_{30}^{4}+\cdots)q^{9}+\cdots$
2420.1.x.a	$2420$	$1$	2420.x	220.w	$20$	$16$	$2$	$1.208$	$\Q(\zeta_{40})$	$D_{4}$	$\Q(\sqrt{-1}) $	None		✓			2420.1.i.a	$32$	$0$	$0$	$0$	$-4$	$0$		$1$		$q+\zeta_{40}^{13}q^{2}-\zeta_{40}^{6}q^{4}-\zeta_{40}^{12}q^{5}+\cdots$
2420.1.x.b	$2420$	$1$	2420.x	220.w	$20$	$32$	$4$	$1.208$	$\Q(\zeta_{120})$	$D_{12}$	$\Q(\sqrt{-1}) $	None		✓	✓		2420.1.i.b	$32$	$0$	$0$	$0$	$4$	$0$		$1$		$q+\zeta_{120}^{27}q^{2}+\zeta_{120}^{54}q^{4}-\zeta_{120}^{28}q^{5}+\cdots$
2420.1.y.a	$2420$	$1$	2420.y	55.k	$20$	$16$	$2$	$1.208$	$\Q(\zeta_{60})$	$D_{12}$	$\Q(\sqrt{-11}) $	None		✓	✓	✓	2420.1.j.a	$16$	$0$	$0$	$2$	$0$	$0$		$1$		$q+(\zeta_{60}^{23}+\zeta_{60}^{28})q^{3}-\zeta_{60}^{19}q^{5}+\cdots$
2420.2.a.a	$2420$	$2$	2420.a	1.a	$1$	$1$	$1$	$19.324$	$\Q$	$_{}$	None	None	✓				20.2.a.a	$1$	$1$	$0$	$-2$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-q^{5}-2q^{7}+q^{9}-2q^{13}+\cdots$
2420.2.a.b	$2420$	$2$	2420.a	1.a	$1$	$1$	$1$	$19.324$	$\Q$	$_{}$	None	None	✓				220.2.a.a	$1$	$0$	$0$	$-2$	$1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{5}+4q^{7}+q^{9}+4q^{13}+\cdots$
2420.2.a.c	$2420$	$2$	2420.a	1.a	$1$	$1$	$1$	$19.324$	$\Q$	$_{}$	None	None	✓	✓			2420.2.a.c	$1$	$0$	$0$	$0$	$-1$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-4q^{7}-3q^{9}-4q^{13}+4q^{17}+\cdots$
2420.2.a.d	$2420$	$2$	2420.a	1.a	$1$	$1$	$1$	$19.324$	$\Q$	$_{}$	None	None	✓	✓			2420.2.a.c	$1$	$0$	$0$	$0$	$-1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+4q^{7}-3q^{9}+4q^{13}-4q^{17}+\cdots$
2420.2.a.e	$2420$	$2$	2420.a	1.a	$1$	$1$	$1$	$19.324$	$\Q$	$_{}$	None	None	✓	✓			2420.2.a.e	$1$	$1$	$0$	$1$	$-1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-q^{7}-2q^{9}+2q^{13}-q^{15}+\cdots$
2420.2.a.f	$2420$	$2$	2420.a	1.a	$1$	$1$	$1$	$19.324$	$\Q$	$_{}$	None	None	✓	✓			2420.2.a.e	$1$	$1$	$0$	$1$	$-1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+q^{7}-2q^{9}-2q^{13}-q^{15}+\cdots$
2420.2.a.g	$2420$	$2$	2420.a	1.a	$1$	$1$	$1$	$19.324$	$\Q$	$_{}$	None	None	✓				220.2.a.b	$1$	$0$	$0$	$2$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{5}+q^{9}+2q^{15}+4q^{17}+\cdots$
2420.2.a.h	$2420$	$2$	2420.a	1.a	$1$	$2$	$2$	$19.324$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	✓			2420.2.a.h	$2$	$1$	$0$	$-2$	$2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+\beta q^{7}-2q^{9}-q^{15}-4\beta q^{19}+\cdots$
2420.2.a.i	$2420$	$2$	2420.a	1.a	$1$	$3$	$3$	$19.324$	3.3.1524.1	$_{}$	None	None	✓	✓			2420.2.a.i	$1$	$0$	$0$	$1$	$3$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+q^{5}+\beta _{2}q^{7}+(2+\beta _{1}+\beta _{2})q^{9}+\cdots$
2420.2.a.j	$2420$	$2$	2420.a	1.a	$1$	$3$	$3$	$19.324$	3.3.1524.1	$_{}$	None	None	✓	✓			2420.2.a.i	$1$	$0$	$0$	$1$	$3$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+q^{5}-\beta _{2}q^{7}+(2+\beta _{1}+\beta _{2})q^{9}+\cdots$
2420.2.a.k	$2420$	$2$	2420.a	1.a	$1$	$4$	$4$	$19.324$	4.4.2525.1	$_{}$	None	None	✓		✓		220.2.m.b	$1$	$1$	$0$	$0$	$4$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-\beta _{1}-\beta _{2})q^{3}+q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots$
2420.2.a.l	$2420$	$2$	2420.a	1.a	$1$	$4$	$4$	$19.324$	4.4.2525.1	$_{}$	None	None	✓		✓		220.2.m.b	$1$	$0$	$0$	$0$	$4$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-\beta _{1}-\beta _{2})q^{3}+q^{5}+(1-\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots$
2420.2.a.m	$2420$	$2$	2420.a	1.a	$1$	$4$	$4$	$19.324$	4.4.5125.1	$_{}$	None	None	✓		✓		220.2.m.a	$1$	$1$	$0$	$2$	$-4$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}-q^{5}+(-\beta _{1}+\beta _{2}-\beta _{3})q^{7}+\cdots$
2420.2.a.n	$2420$	$2$	2420.a	1.a	$1$	$4$	$4$	$19.324$	4.4.5125.1	$_{}$	None	None	✓				220.2.m.a	$1$	$0$	$0$	$2$	$-4$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}-q^{5}+(\beta _{1}-\beta _{2}+\beta _{3})q^{7}+\cdots$
2420.2.a.o	$2420$	$2$	2420.a	1.a	$1$	$6$	$6$	$19.324$	6.6.507624192.1	$_{}$	None	None	✓	✓	✓		2420.2.a.o	$2$	$0$	$0$	$-2$	$-6$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{4}q^{3}-q^{5}+(\beta _{1}-\beta _{2})q^{7}+(3-\beta _{3}+\cdots)q^{9}+\cdots$
2420.2.b.a	$2420$	$2$	2420.b	5.b	$2$	$2$	$2$	$19.324$	$\Q(\sqrt{-1}) $	$_{}$	None	None					220.2.b.a	$2$	$0$	$0$	$0$	$-2$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta-1)q^{5}-\beta q^{7}+3 q^{9}-3\beta q^{13}+\cdots$
2420.2.b.b	$2420$	$2$	2420.b	5.b	$2$	$4$	$4$	$19.324$	$\Q(\sqrt{-3}, \sqrt{-11})$	$_{}$	$\Q(\sqrt{-11}) $	None		✓			2420.2.b.b	$4$	$0$	$0$	$0$	$-3$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{2}q^{3}+(-1+\beta _{3})q^{5}+(-1+\beta _{1}+\cdots)q^{9}+\cdots$
2420.2.b.c	$2420$	$2$	2420.b	5.b	$2$	$4$	$4$	$19.324$	$\Q(\sqrt{-2}, \sqrt{3})$	$_{}$	None	None		✓			2420.2.b.c	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+(\beta _{1}-\beta _{2}-\beta _{3})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$
2420.2.b.d	$2420$	$2$	2420.b	5.b	$2$	$4$	$4$	$19.324$	$\Q(\sqrt{-2}, \sqrt{3})$	$_{}$	None	None		✓			2420.2.b.c	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+(\beta _{1}-\beta _{2}-\beta _{3})q^{5}+(\beta _{1}-2\beta _{3})q^{7}+\cdots$
2420.2.b.e	$2420$	$2$	2420.b	5.b	$2$	$4$	$4$	$19.324$	$\Q(\sqrt{-3}, \sqrt{-19})$	$_{}$	None	None					220.2.b.b	$2$	$0$	$0$	$0$	$1$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}-\beta _{2})q^{3}+\beta _{2}q^{5}+(-\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots$
2420.2.b.f	$2420$	$2$	2420.b	5.b	$2$	$6$	$6$	$19.324$	6.0.301925376.2	$_{}$	None	None		✓			2420.2.b.f	$2$	$0$	$0$	$0$	$-1$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+\beta _{4}q^{5}+(-\beta _{3}+\beta _{4}-\beta _{5})q^{7}+\cdots$
2420.2.b.g	$2420$	$2$	2420.b	5.b	$2$	$6$	$6$	$19.324$	6.0.301925376.2	$_{}$	None	None		✓			2420.2.b.f	$2$	$0$	$0$	$0$	$-1$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+\beta _{4}q^{5}+(\beta _{3}-\beta _{4}+\beta _{5})q^{7}+\cdots$
2420.2.b.h	$2420$	$2$	2420.b	5.b	$2$	$12$	$12$	$19.324$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None					220.2.t.a	$2$	$0$	$0$	$0$	$3$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+\beta _{6}q^{5}-\beta _{8}q^{7}+(-2+\beta _{9}+\cdots)q^{9}+\cdots$

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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.