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 226 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
700.1.d.a	$700$	$1$	700.d	7.b	$2$	$2$	$2$	$0.349$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-35}) $	None			✓	✓	140.1.h.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-iq^{3}-iq^{7}-q^{11}-iq^{13}+iq^{17}+\cdots$
700.1.j.a	$700$	$1$	700.j	140.j	$4$	$4$	$2$	$0.349$	$\Q(\zeta_{8})$	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-5}) $	$\Q(\sqrt{35}) $		✓			700.1.j.a	$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{7}-\zeta_{8}q^{8}+\cdots$
700.1.j.b	$700$	$1$	700.j	140.j	$4$	$8$	$4$	$0.349$	$\Q(\zeta_{24})$	$D_{6}$	$\Q(\sqrt{-7}) $	None		✓	✓		700.1.j.b	$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+\zeta_{24}^{3}q^{7}+\cdots$
700.1.u.a	$700$	$1$	700.u	28.g	$6$	$4$	$2$	$0.349$	$\Q(\zeta_{12})$	$D_{3}$	$\Q(\sqrt{-5}) $	None			✓	✓	140.1.p.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{12}q^{2}-\zeta_{12}^{5}q^{3}+\zeta_{12}^{2}q^{4}-q^{6}+\cdots$
700.1.bf.a	$700$	$1$	700.bf	140.x	$12$	$8$	$2$	$0.349$	$\Q(\zeta_{24})$	$D_{6}$	$\Q(\sqrt{-5}) $	None		✓	✓	✓	700.1.bf.a	$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}^{11}q^{2}+(\zeta_{24}^{5}+\zeta_{24}^{9})q^{3}-\zeta_{24}^{10}q^{4}+\cdots$
700.2.a.a	$700$	$2$	700.a	1.a	$1$	$1$	$1$	$5.590$	$\Q$	$_{}$	None	None	✓				140.2.e.a	$1$	$1$	$0$	$-3$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-q^{7}+6q^{9}+3q^{11}-q^{13}+\cdots$
700.2.a.b	$700$	$2$	700.a	1.a	$1$	$1$	$1$	$5.590$	$\Q$	$_{}$	None	None	✓				140.2.a.b	$1$	$1$	$0$	$-3$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}+q^{7}+6q^{9}-5q^{11}+3q^{13}+\cdots$
700.2.a.c	$700$	$2$	700.a	1.a	$1$	$1$	$1$	$5.590$	$\Q$	$_{}$	None	None	✓	✓			700.2.a.c	$1$	$0$	$0$	$-2$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{7}+q^{9}+3q^{11}-4q^{13}+\cdots$
700.2.a.d	$700$	$2$	700.a	1.a	$1$	$1$	$1$	$5.590$	$\Q$	$_{}$	None	None	✓				140.2.a.a	$1$	$0$	$0$	$-1$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{7}-2q^{9}+3q^{11}+q^{13}+\cdots$
700.2.a.e	$700$	$2$	700.a	1.a	$1$	$1$	$1$	$5.590$	$\Q$	$_{}$	None	None	✓	✓			700.2.a.e	$1$	$1$	$0$	$0$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{7}-3q^{9}-5q^{11}+6q^{13}-4q^{17}+\cdots$
700.2.a.f	$700$	$2$	700.a	1.a	$1$	$1$	$1$	$5.590$	$\Q$	$_{}$	None	None	✓				140.2.e.b	$1$	$1$	$0$	$0$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{7}-3q^{9}-4q^{13}-4q^{17}+4q^{19}+\cdots$
700.2.a.g	$700$	$2$	700.a	1.a	$1$	$1$	$1$	$5.590$	$\Q$	$_{}$	None	None	✓	✓			700.2.a.e	$1$	$1$	$0$	$0$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{7}-3q^{9}-5q^{11}-6q^{13}+4q^{17}+\cdots$
700.2.a.h	$700$	$2$	700.a	1.a	$1$	$1$	$1$	$5.590$	$\Q$	$_{}$	None	None	✓				140.2.e.b	$1$	$0$	$0$	$0$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{7}-3q^{9}+4q^{13}+4q^{17}+4q^{19}+\cdots$
700.2.a.i	$700$	$2$	700.a	1.a	$1$	$1$	$1$	$5.590$	$\Q$	$_{}$	None	None	✓	✓			700.2.a.c	$1$	$0$	$0$	$2$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-q^{7}+q^{9}+3q^{11}+4q^{13}+\cdots$
700.2.a.j	$700$	$2$	700.a	1.a	$1$	$1$	$1$	$5.590$	$\Q$	$_{}$	None	None	✓				140.2.e.a	$1$	$0$	$0$	$3$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}+q^{7}+6q^{9}+3q^{11}+q^{13}+\cdots$
700.2.c.a	$700$	$2$	700.c	140.c	$2$	$4$	$4$	$5.590$	$\Q(i, \sqrt{6})$	$_{}$	None	None		✓			700.2.g.b	$4$	$0$	$-4$	$0$	$0$	$-4$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1+\beta _{1})q^{2}+\beta _{2}q^{3}-2\beta _{1}q^{4}+\cdots$
700.2.c.b	$700$	$2$	700.c	140.c	$2$	$4$	$4$	$5.590$	$\Q(\zeta_{12})$	$_{}$	None	None					140.2.g.a	$2$	$1$	$-2$	$0$	$0$	$-8$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1-\zeta_{12}^{3})q^{2}+(\zeta_{12}^{2}-\zeta_{12}^{3})q^{3}+\cdots$
700.2.c.c	$700$	$2$	700.c	140.c	$2$	$4$	$4$	$5.590$	$\Q(\zeta_{12})$	$_{}$	None	None					140.2.g.a	$2$	$0$	$-2$	$0$	$0$	$-8$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1-\zeta_{12}^{3})q^{2}+(-\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+\cdots$
700.2.c.d	$700$	$2$	700.c	140.c	$2$	$4$	$4$	$5.590$	$\Q(i, \sqrt{7})$	$_{}$	$\Q(\sqrt{-7}) $	None					28.2.d.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-2\beta _{1}+\beta _{3})q^{7}+\cdots$
700.2.c.e	$700$	$2$	700.c	140.c	$2$	$4$	$4$	$5.590$	$\Q(\zeta_{12})$	$_{}$	None	None					140.2.g.a	$2$	$0$	$2$	$0$	$0$	$8$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+\zeta_{12}^{3})q^{2}+(-\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+\cdots$
700.2.c.f	$700$	$2$	700.c	140.c	$2$	$4$	$4$	$5.590$	$\Q(\zeta_{12})$	$_{}$	None	None					140.2.g.a	$2$	$0$	$2$	$0$	$0$	$8$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+\zeta_{12}^{3})q^{2}+(\zeta_{12}^{2}-\zeta_{12}^{3})q^{3}+\cdots$
700.2.c.g	$700$	$2$	700.c	140.c	$2$	$4$	$4$	$5.590$	$\Q(i, \sqrt{6})$	$_{}$	None	None		✓			700.2.g.b	$4$	$0$	$4$	$0$	$0$	$4$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(1-\beta _{1})q^{2}+\beta _{2}q^{3}-2\beta _{1}q^{4}+(\beta _{2}+\cdots)q^{6}+\cdots$
700.2.c.h	$700$	$2$	700.c	140.c	$2$	$8$	$8$	$5.590$	8.0.49787136.1	$_{}$	$\Q(\sqrt{-7}) $	None		✓			700.2.g.c	$8$	$0$	$0$	$0$	$0$	$0$		$2^{2}\cdot 5^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}+(\beta _{1}-\beta _{7})q^{7}+\cdots$
700.2.c.i	$700$	$2$	700.c	140.c	$2$	$8$	$8$	$5.590$	8.0.342102016.5	$_{}$	None	None					140.2.g.c	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{5}q^{2}+(\beta _{3}+\beta _{4})q^{3}+(\beta _{3}+\beta _{4}+\beta _{7})q^{4}+\cdots$
700.2.c.j	$700$	$2$	700.c	140.c	$2$	$8$	$8$	$5.590$	8.0.342102016.5	$_{}$	None	None					140.2.g.c	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{5}q^{2}+(-\beta _{3}-\beta _{4})q^{3}+(\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots$
700.2.c.k	$700$	$2$	700.c	140.c	$2$	$16$	$16$	$5.590$	16.0.$\cdots$.7	$_{}$	None	None		✓	✓		700.2.g.i	$8$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{7}q^{2}+(-\beta _{5}+\beta _{6}-\beta _{7}+\beta _{8}-\beta _{9}+\cdots)q^{3}+\cdots$
700.2.e.a	$700$	$2$	700.e	5.b	$2$	$2$	$2$	$5.590$	$\Q(\sqrt{-1}) $	$_{}$	None	None					140.2.a.b	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+3iq^{3}+iq^{7}-6q^{9}-5q^{11}-3iq^{13}+\cdots$
700.2.e.b	$700$	$2$	700.e	5.b	$2$	$2$	$2$	$5.590$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			700.2.a.c	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2iq^{3}+iq^{7}-q^{9}+3q^{11}+4iq^{13}+\cdots$
700.2.e.c	$700$	$2$	700.e	5.b	$2$	$2$	$2$	$5.590$	$\Q(\sqrt{-1}) $	$_{}$	None	None					140.2.a.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}-iq^{7}+2q^{9}+3q^{11}-iq^{13}+\cdots$
700.2.e.d	$700$	$2$	700.e	5.b	$2$	$2$	$2$	$5.590$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			700.2.a.e	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-iq^{7}+3q^{9}-5q^{11}-6iq^{13}-4iq^{17}+\cdots$
700.2.g.a	$700$	$2$	700.g	28.d	$2$	$2$	$2$	$5.590$	$\Q(\sqrt{-7}) $	$_{}$	$\Q(\sqrt{-7}) $	None					28.2.d.a	$4$	$0$	$1$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+\beta q^{2}+(-2+\beta )q^{4}+(1-2\beta )q^{7}+\cdots$
700.2.g.b	$700$	$2$	700.g	28.d	$2$	$4$	$4$	$5.590$	$\Q(i, \sqrt{6})$	$_{}$	None	None		✓			700.2.g.b	$4$	$0$	$-4$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1+\beta _{1})q^{2}-\beta _{3}q^{3}-2\beta _{1}q^{4}+\cdots$
700.2.g.c	$700$	$2$	700.g	28.d	$2$	$4$	$4$	$5.590$	$\Q(\sqrt{-3}, \sqrt{-7})$	$_{}$	$\Q(\sqrt{-7}) $	None		✓			700.2.g.c	$4$	$0$	$-1$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+(-\beta _{1}-\beta _{3})q^{2}+(1+\beta _{2})q^{4}+(1-2\beta _{3})q^{7}+\cdots$
700.2.g.d	$700$	$2$	700.g	28.d	$2$	$4$	$4$	$5.590$	$\Q(\sqrt{-2}, \sqrt{-5})$	$_{}$	$\Q(\sqrt{-5}) $	None					140.2.c.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{2}q^{2}+(2\beta _{1}-\beta _{2})q^{3}-2q^{4}+2\beta _{3}q^{6}+\cdots$
700.2.g.e	$700$	$2$	700.g	28.d	$2$	$4$	$4$	$5.590$	$\Q(\sqrt{-3}, \sqrt{-7})$	$_{}$	$\Q(\sqrt{-7}) $	None		✓			700.2.g.c	$4$	$0$	$1$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+(\beta _{1}+\beta _{3})q^{2}+(1+\beta _{2})q^{4}+(-1+2\beta _{3})q^{7}+\cdots$
700.2.g.f	$700$	$2$	700.g	28.d	$2$	$4$	$4$	$5.590$	$\Q(\zeta_{12})$	$_{}$	None	None					140.2.g.a	$2$	$0$	$2$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(\zeta_{12}-\zeta_{12}^{2})q^{2}+(-\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{3}+\cdots$
700.2.g.g	$700$	$2$	700.g	28.d	$2$	$4$	$4$	$5.590$	$\Q(\zeta_{12})$	$_{}$	None	None					140.2.g.a	$2$	$0$	$2$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(\zeta_{12}-\zeta_{12}^{2})q^{2}+(\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+\cdots$
700.2.g.h	$700$	$2$	700.g	28.d	$2$	$4$	$4$	$5.590$	$\Q(i, \sqrt{6})$	$_{}$	None	None		✓			700.2.g.b	$4$	$0$	$4$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(1-\beta _{1})q^{2}-\beta _{3}q^{3}-2\beta _{1}q^{4}+(\beta _{2}+\cdots)q^{6}+\cdots$
700.2.g.i	$700$	$2$	700.g	28.d	$2$	$8$	$8$	$5.590$	8.0.5473632256.3	$_{}$	None	None		✓			700.2.g.i	$4$	$0$	$-4$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1+\beta _{4})q^{2}+(-1+\beta _{1}-\beta _{2}+\beta _{5}+\cdots)q^{3}+\cdots$
700.2.g.j	$700$	$2$	700.g	28.d	$2$	$8$	$8$	$5.590$	8.0.342102016.5	$_{}$	None	None					140.2.g.c	$4$	$0$	$-2$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(\beta _{5}-\beta _{7})q^{3}+(-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
700.2.g.k	$700$	$2$	700.g	28.d	$2$	$8$	$8$	$5.590$	8.0.5473632256.3	$_{}$	None	None		✓			700.2.g.i	$4$	$0$	$4$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(1-\beta _{4})q^{2}+(1-\beta _{1}+\beta _{2}-\beta _{5})q^{3}+\cdots$
700.2.g.l	$700$	$2$	700.g	28.d	$2$	$16$	$16$	$5.590$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None			✓		140.2.c.b	$8$	$0$	$0$	$0$	$0$	$0$		$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}+\beta _{10}q^{3}+(1-\beta _{4})q^{4}+\beta _{14}q^{6}+\cdots$
700.2.i.a	$700$	$2$	700.i	7.c	$3$	$2$	$1$	$5.590$	$\Q(\sqrt{-3}) $	$_{}$	None	None					140.2.i.b	$2$	$0$	$0$	$-3$	$0$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-3+3\zeta_{6})q^{3}+(1-3\zeta_{6})q^{7}-6\zeta_{6}q^{9}+\cdots$
700.2.i.b	$700$	$2$	700.i	7.c	$3$	$2$	$1$	$5.590$	$\Q(\sqrt{-3}) $	$_{}$	None	None					140.2.i.a	$2$	$0$	$0$	$1$	$0$	$-5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{3}+(-3+\zeta_{6})q^{7}+2\zeta_{6}q^{9}+\cdots$
700.2.i.c	$700$	$2$	700.i	7.c	$3$	$2$	$1$	$5.590$	$\Q(\sqrt{-3}) $	$_{}$	None	None					28.2.e.a	$2$	$0$	$0$	$1$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{3}+(3-2\zeta_{6})q^{7}+2\zeta_{6}q^{9}+\cdots$
700.2.i.d	$700$	$2$	700.i	7.c	$3$	$6$	$3$	$5.590$	6.0.1783323.2	$_{}$	None	None		✓			700.2.i.d	$2$	$0$	$0$	$-1$	$0$	$4$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{3}+\beta _{5})q^{3}+(1-\beta _{2}-\beta _{3}+\beta _{5})q^{7}+\cdots$
700.2.i.e	$700$	$2$	700.i	7.c	$3$	$6$	$3$	$5.590$	6.0.1783323.2	$_{}$	None	None		✓			700.2.i.d	$2$	$0$	$0$	$1$	$0$	$-4$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{3}-\beta _{5})q^{3}+(-1+\beta _{2}+\beta _{3}-\beta _{5})q^{7}+\cdots$
700.2.i.f	$700$	$2$	700.i	7.c	$3$	$8$	$4$	$5.590$	8.0.2702336256.1	$_{}$	None	None			✓		140.2.q.a	$4$	$0$	$0$	$0$	$0$	$0$		$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{4}-\beta _{6})q^{3}+(\beta _{3}-\beta _{4})q^{7}+(1+\beta _{1}+\cdots)q^{11}+\cdots$
700.2.k.a	$700$	$2$	700.k	20.e	$4$	$24$	$12$	$5.590$		$_{}$	None	None		✓			700.2.k.a	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
700.2.k.b	$700$	$2$	700.k	20.e	$4$	$36$	$18$	$5.590$		$_{}$	None	None					140.2.k.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$

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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.