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 103 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
2175.1.b.a	$2175$	$1$	2175.b	435.b	$2$	$2$	$2$	$1.085$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-87}) $	None					87.1.d.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-i q^{2}-i q^{3}-q^{6}-i q^{7}-i q^{8}+\cdots$
2175.1.b.b	$2175$	$1$	2175.b	435.b	$2$	$2$	$2$	$1.085$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-87}) $	None					87.1.d.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-i q^{2}-i q^{3}-q^{6}+i q^{7}-i q^{8}+\cdots$
2175.1.b.c	$2175$	$1$	2175.b	435.b	$2$	$6$	$6$	$1.085$	6.0.419904.1	$D_{9}$	$\Q(\sqrt{-87}) $	None		✓			2175.1.h.c	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\beta _{5}q^{2}-\beta _{3}q^{3}+(-1-\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots$
2175.1.b.d	$2175$	$1$	2175.b	435.b	$2$	$6$	$6$	$1.085$	6.0.419904.1	$D_{9}$	$\Q(\sqrt{-87}) $	None		✓			2175.1.h.c	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\beta _{1}q^{2}-\beta _{3}q^{3}+(-1+\beta _{2})q^{4}+(\beta _{2}+\cdots)q^{6}+\cdots$
2175.1.h.a	$2175$	$1$	2175.h	87.d	$2$	$1$	$1$	$1.085$	$\Q$	$D_{3}$	$\Q(\sqrt{-87}) $	None	✓				87.1.d.a	$2$	$0$	$-1$	$1$	$0$	$1$		$1$		$q-q^{2}+q^{3}-q^{6}+q^{7}+q^{8}+q^{9}+\cdots$
2175.1.h.b	$2175$	$1$	2175.h	87.d	$2$	$1$	$1$	$1.085$	$\Q$	$D_{3}$	$\Q(\sqrt{-87}) $	None	✓				87.1.d.a	$2$	$0$	$1$	$-1$	$0$	$1$		$1$		$q+q^{2}-q^{3}-q^{6}+q^{7}-q^{8}+q^{9}+\cdots$
2175.1.h.c	$2175$	$1$	2175.h	87.d	$2$	$3$	$3$	$1.085$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-87}) $	None	✓	✓			2175.1.h.c	$2$	$0$	$0$	$-3$	$0$	$0$		$1$		$q+(-\beta _{1}+\beta _{2})q^{2}-q^{3}+(1-\beta _{1})q^{4}+\cdots$
2175.1.h.d	$2175$	$1$	2175.h	87.d	$2$	$3$	$3$	$1.085$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-87}) $	None	✓	✓			2175.1.h.c	$2$	$0$	$0$	$-3$	$0$	$0$		$1$		$q+(-\beta _{1}+\beta _{2})q^{2}-q^{3}+(1-\beta _{1})q^{4}+\cdots$
2175.1.h.e	$2175$	$1$	2175.h	87.d	$2$	$3$	$3$	$1.085$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-87}) $	None	✓	✓			2175.1.h.c	$2$	$0$	$0$	$3$	$0$	$0$		$1$		$q+(\beta _{1}-\beta _{2})q^{2}+q^{3}+(1-\beta _{1})q^{4}+(\beta _{1}+\cdots)q^{6}+\cdots$
2175.1.h.f	$2175$	$1$	2175.h	87.d	$2$	$3$	$3$	$1.085$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-87}) $	None	✓	✓			2175.1.h.c	$2$	$0$	$0$	$3$	$0$	$0$		$1$		$q+(\beta _{1}-\beta _{2})q^{2}+q^{3}+(1-\beta _{1})q^{4}+(\beta _{1}+\cdots)q^{6}+\cdots$
2175.1.h.g	$2175$	$1$	2175.h	87.d	$2$	$4$	$4$	$1.085$	$\Q(\zeta_{8})$	$D_{4}$	None	$\Q(\sqrt{145}) $			✓		435.1.b.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-\zeta_{8}+\zeta_{8}^{3})q^{2}-\zeta_{8}q^{3}+q^{4}+(1+\cdots)q^{6}+\cdots$
2175.2.a.a	$2175$	$2$	2175.a	1.a	$1$	$1$	$1$	$17.367$	$\Q$	$_{}$	None	None	✓				435.2.c.a	$1$	$0$	$-2$	$1$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+q^{3}+2q^{4}-2q^{6}-2q^{7}+\cdots$
2175.2.a.b	$2175$	$2$	2175.a	1.a	$1$	$1$	$1$	$17.367$	$\Q$	$_{}$	None	None	✓				435.2.a.d	$1$	$2$	$-1$	$-1$	$0$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}-q^{4}+q^{6}-4q^{7}+3q^{8}+\cdots$
2175.2.a.c	$2175$	$2$	2175.a	1.a	$1$	$1$	$1$	$17.367$	$\Q$	$_{}$	None	None	✓				435.2.c.b	$1$	$1$	$-1$	$-1$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}-q^{4}+q^{6}+2q^{7}+3q^{8}+\cdots$
2175.2.a.d	$2175$	$2$	2175.a	1.a	$1$	$1$	$1$	$17.367$	$\Q$	$_{}$	None	None	✓				435.2.a.c	$1$	$1$	$0$	$-1$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{4}-2q^{7}+q^{9}+3q^{11}+\cdots$
2175.2.a.e	$2175$	$2$	2175.a	1.a	$1$	$1$	$1$	$17.367$	$\Q$	$_{}$	None	None	✓	✓			2175.2.a.e	$1$	$1$	$0$	$-1$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{4}+q^{7}+q^{9}-2q^{11}+2q^{12}+\cdots$
2175.2.a.f	$2175$	$2$	2175.a	1.a	$1$	$1$	$1$	$17.367$	$\Q$	$_{}$	None	None	✓	✓			2175.2.a.e	$1$	$1$	$0$	$1$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}-q^{7}+q^{9}-2q^{11}-2q^{12}+\cdots$
2175.2.a.g	$2175$	$2$	2175.a	1.a	$1$	$1$	$1$	$17.367$	$\Q$	$_{}$	None	None	✓				435.2.a.b	$1$	$1$	$0$	$1$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}+2q^{7}+q^{9}+q^{11}-2q^{12}+\cdots$
2175.2.a.h	$2175$	$2$	2175.a	1.a	$1$	$1$	$1$	$17.367$	$\Q$	$_{}$	None	None	✓				435.2.a.a	$1$	$0$	$1$	$-1$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}-q^{4}-q^{6}+4q^{7}-3q^{8}+\cdots$
2175.2.a.i	$2175$	$2$	2175.a	1.a	$1$	$1$	$1$	$17.367$	$\Q$	$_{}$	None	None	✓				435.2.c.b	$1$	$0$	$1$	$1$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}-q^{4}+q^{6}-2q^{7}-3q^{8}+\cdots$
2175.2.a.j	$2175$	$2$	2175.a	1.a	$1$	$1$	$1$	$17.367$	$\Q$	$_{}$	None	None	✓				435.2.c.a	$1$	$1$	$2$	$-1$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-q^{3}+2q^{4}-2q^{6}+2q^{7}+\cdots$
2175.2.a.k	$2175$	$2$	2175.a	1.a	$1$	$2$	$2$	$17.367$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				435.2.c.c	$1$	$1$	$-2$	$2$	$0$	$0$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}-q^{4}-q^{6}-\beta q^{7}+3q^{8}+\cdots$
2175.2.a.l	$2175$	$2$	2175.a	1.a	$1$	$2$	$2$	$17.367$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				87.2.a.a	$1$	$1$	$-1$	$-2$	$0$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}-q^{3}+(-1+\beta )q^{4}+\beta q^{6}+\cdots$
2175.2.a.m	$2175$	$2$	2175.a	1.a	$1$	$2$	$2$	$17.367$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓				435.2.a.h	$1$	$0$	$-1$	$-2$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}-q^{3}+(2+\beta )q^{4}+\beta q^{6}+(-2+\cdots)q^{7}+\cdots$
2175.2.a.n	$2175$	$2$	2175.a	1.a	$1$	$2$	$2$	$17.367$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓			2175.2.a.n	$1$	$1$	$0$	$-2$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-q^{3}-\beta q^{6}+q^{7}-2\beta q^{8}+\cdots$
2175.2.a.o	$2175$	$2$	2175.a	1.a	$1$	$2$	$2$	$17.367$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				435.2.a.g	$1$	$1$	$0$	$-2$	$0$	$-4$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta q^{2}-q^{3}+3q^{4}+\beta q^{6}-2q^{7}+\cdots$
2175.2.a.p	$2175$	$2$	2175.a	1.a	$1$	$2$	$2$	$17.367$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓			2175.2.a.n	$1$	$1$	$0$	$2$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{3}+\beta q^{6}-q^{7}-2\beta q^{8}+\cdots$
2175.2.a.q	$2175$	$2$	2175.a	1.a	$1$	$2$	$2$	$17.367$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				435.2.a.e	$1$	$0$	$1$	$-2$	$0$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}-\beta q^{6}+\cdots$
2175.2.a.r	$2175$	$2$	2175.a	1.a	$1$	$2$	$2$	$17.367$	$\Q(\sqrt{21}) $	$_{}$	None	None	✓				435.2.a.f	$1$	$0$	$1$	$-2$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-q^{3}+(3+\beta )q^{4}-\beta q^{6}-q^{7}+\cdots$
2175.2.a.s	$2175$	$2$	2175.a	1.a	$1$	$2$	$2$	$17.367$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				435.2.c.c	$1$	$0$	$2$	$-2$	$0$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}-q^{4}-q^{6}+\beta q^{7}-3q^{8}+\cdots$
2175.2.a.t	$2175$	$2$	2175.a	1.a	$1$	$3$	$3$	$17.367$	3.3.229.1	$_{}$	None	None	✓		✓		87.2.a.b	$1$	$1$	$-2$	$3$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{2}+q^{3}+(2+\beta _{1})q^{4}+\cdots$
2175.2.a.u	$2175$	$2$	2175.a	1.a	$1$	$3$	$3$	$17.367$	3.3.469.1	$_{}$	None	None	✓				435.2.a.i	$1$	$0$	$-1$	$3$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots$
2175.2.a.v	$2175$	$2$	2175.a	1.a	$1$	$4$	$4$	$17.367$	4.4.2225.1	$_{}$	None	None	✓				435.2.a.j	$1$	$0$	$3$	$4$	$0$	$-2$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots$
2175.2.a.w	$2175$	$2$	2175.a	1.a	$1$	$5$	$5$	$17.367$	5.5.246832.1	$_{}$	None	None	✓		✓		435.2.c.e	$1$	$1$	$-3$	$-5$	$0$	$-8$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}-q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
2175.2.a.x	$2175$	$2$	2175.a	1.a	$1$	$5$	$5$	$17.367$	5.5.331312.1	$_{}$	None	None	✓		✓		435.2.c.d	$1$	$1$	$-2$	$5$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{2}+q^{3}+(1+\beta _{1}-\beta _{3}-\beta _{4})q^{4}+\cdots$
2175.2.a.y	$2175$	$2$	2175.a	1.a	$1$	$5$	$5$	$17.367$	5.5.331312.1	$_{}$	None	None	✓				435.2.c.d	$1$	$0$	$2$	$-5$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{3}q^{2}-q^{3}+(1+\beta _{1}-\beta _{3}-\beta _{4})q^{4}+\cdots$
2175.2.a.z	$2175$	$2$	2175.a	1.a	$1$	$5$	$5$	$17.367$	5.5.246832.1	$_{}$	None	None	✓				435.2.c.e	$1$	$0$	$3$	$5$	$0$	$8$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+q^{3}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots$
2175.2.a.ba	$2175$	$2$	2175.a	1.a	$1$	$7$	$7$	$17.367$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	✓	✓		2175.2.a.ba	$1$	$0$	$-2$	$-7$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots$
2175.2.a.bb	$2175$	$2$	2175.a	1.a	$1$	$7$	$7$	$17.367$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	✓	✓		2175.2.a.ba	$1$	$0$	$2$	$7$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots$
2175.2.a.bc	$2175$	$2$	2175.a	1.a	$1$	$8$	$8$	$17.367$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	✓	✓		2175.2.a.bc	$1$	$0$	$-2$	$-8$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots$
2175.2.a.bd	$2175$	$2$	2175.a	1.a	$1$	$8$	$8$	$17.367$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	✓	✓		2175.2.a.bc	$1$	$0$	$2$	$8$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots$
2175.2.c.a	$2175$	$2$	2175.c	5.b	$2$	$2$	$2$	$17.367$	$\Q(\sqrt{-1}) $	$_{}$	None	None					435.2.a.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}+i q^{3}+q^{4}-q^{6}+4 i q^{7}+\cdots$
2175.2.c.b	$2175$	$2$	2175.c	5.b	$2$	$2$	$2$	$17.367$	$\Q(\sqrt{-1}) $	$_{}$	None	None					435.2.a.d	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}-i q^{3}+q^{4}+q^{6}+4 i q^{7}+\cdots$
2175.2.c.c	$2175$	$2$	2175.c	5.b	$2$	$2$	$2$	$17.367$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			2175.2.a.e	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{3}+2 q^{4}-i q^{7}-q^{9}-2 q^{11}+\cdots$
2175.2.c.d	$2175$	$2$	2175.c	5.b	$2$	$2$	$2$	$17.367$	$\Q(\sqrt{-1}) $	$_{}$	None	None					435.2.a.b	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{3}+2 q^{4}+2 i q^{7}-q^{9}+q^{11}+\cdots$
2175.2.c.e	$2175$	$2$	2175.c	5.b	$2$	$2$	$2$	$17.367$	$\Q(\sqrt{-1}) $	$_{}$	None	None					435.2.a.c	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{3}+2 q^{4}-2 i q^{7}-q^{9}+3 q^{11}+\cdots$
2175.2.c.f	$2175$	$2$	2175.c	5.b	$2$	$4$	$4$	$17.367$	$\Q(i, \sqrt{21})$	$_{}$	None	None					435.2.a.f	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-\beta _{2}q^{3}+(-4+\beta _{3})q^{4}+(-1+\cdots)q^{6}+\cdots$
2175.2.c.g	$2175$	$2$	2175.c	5.b	$2$	$4$	$4$	$17.367$	$\Q(i, \sqrt{5})$	$_{}$	None	None					435.2.a.g	$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}+\beta _{1}q^{3}-3q^{4}-\beta _{3}q^{6}-2\beta _{1}q^{7}+\cdots$
2175.2.c.h	$2175$	$2$	2175.c	5.b	$2$	$4$	$4$	$17.367$	$\Q(i, \sqrt{17})$	$_{}$	None	None					435.2.a.h	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{2}q^{3}+(-3+\beta _{3})q^{4}+(1+\cdots)q^{6}+\cdots$
2175.2.c.i	$2175$	$2$	2175.c	5.b	$2$	$4$	$4$	$17.367$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			2175.2.a.n	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta_{2} q^{2}+\beta_1 q^{3}-\beta_{3} q^{6}+\beta_1 q^{7}+\cdots$

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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.