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 66 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
2300.1.f.a	$2300$	$1$	2300.f	23.b	$2$	$2$	$2$	$1.148$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-115}) $	None			✓	✓	460.1.d.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-i q^{7}-q^{9}-i q^{17}-i q^{23}+q^{29}+\cdots$
2300.1.k.a	$2300$	$1$	2300.k	460.k	$4$	$4$	$2$	$1.148$	$\Q(\zeta_{8})$	$D_{2}$	$\Q(\sqrt{-5}) $, $\Q(\sqrt{-23}) $	$\Q(\sqrt{115}) $		✓			2300.1.k.a	$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}q^{2}+\zeta_{8}^{3}q^{3}+\zeta_{8}^{2}q^{4}+2q^{6}+\cdots$
2300.1.k.b	$2300$	$1$	2300.k	460.k	$4$	$8$	$4$	$1.148$	$\Q(\zeta_{24})$	$D_{6}$	$\Q(\sqrt{-23}) $	None		✓			2300.1.k.b	$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}q^{2}-\zeta_{24}^{3}q^{3}+\zeta_{24}^{2}q^{4}+\zeta_{24}^{4}q^{6}+\cdots$
2300.1.k.c	$2300$	$1$	2300.k	460.k	$4$	$24$	$12$	$1.148$	$\Q(\zeta_{72})$	$D_{18}$	$\Q(\sqrt{-23}) $	None		✓	✓		2300.1.k.c	$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{72}^{19}q^{2}+(\zeta_{72}^{25}-\zeta_{72}^{29})q^{3}+\cdots$
2300.1.bf.a	$2300$	$1$	2300.bf	92.g	$22$	$20$	$2$	$1.148$	$\Q(\zeta_{44})$	$D_{11}$	$\Q(\sqrt{-5}) $	None			✓	✓	460.1.n.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{44}^{7}q^{2}+(-\zeta_{44}^{5}+\zeta_{44}^{19})q^{3}+\cdots$
2300.1.bh.a	$2300$	$1$	2300.bh	460.v	$44$	$40$	$2$	$1.148$	$\Q(\zeta_{88})$	$D_{22}$	$\Q(\sqrt{-5}) $	None		✓	✓	✓	2300.1.bh.a	$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{88}q^{2}+(-\zeta_{88}^{7}-\zeta_{88}^{31})q^{3}+\cdots$
2300.2.a.a	$2300$	$2$	2300.a	1.a	$1$	$1$	$1$	$18.366$	$\Q$	$_{}$	None	None	✓				460.2.a.d	$1$	$1$	$0$	$-3$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-2q^{7}+6q^{9}+3q^{13}-4q^{17}+\cdots$
2300.2.a.b	$2300$	$2$	2300.a	1.a	$1$	$1$	$1$	$18.366$	$\Q$	$_{}$	None	None	✓	✓			2300.2.a.b	$1$	$1$	$0$	$-2$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-q^{7}+q^{9}-3q^{11}+5q^{13}+\cdots$
2300.2.a.c	$2300$	$2$	2300.a	1.a	$1$	$1$	$1$	$18.366$	$\Q$	$_{}$	None	None	✓				92.2.a.b	$1$	$1$	$0$	$-1$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{7}-2q^{9}+q^{13}+6q^{17}+\cdots$
2300.2.a.d	$2300$	$2$	2300.a	1.a	$1$	$1$	$1$	$18.366$	$\Q$	$_{}$	None	None	✓				460.2.a.c	$1$	$0$	$0$	$-1$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+4q^{7}-2q^{9}-6q^{11}+q^{13}+\cdots$
2300.2.a.e	$2300$	$2$	2300.a	1.a	$1$	$1$	$1$	$18.366$	$\Q$	$_{}$	None	None	✓				460.2.a.b	$1$	$1$	$0$	$0$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{7}-3q^{9}+6q^{11}-6q^{13}-7q^{17}+\cdots$
2300.2.a.f	$2300$	$2$	2300.a	1.a	$1$	$1$	$1$	$18.366$	$\Q$	$_{}$	None	None	✓				460.2.a.a	$1$	$1$	$0$	$1$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{7}-2q^{9}-4q^{11}-q^{13}+\cdots$
2300.2.a.g	$2300$	$2$	2300.a	1.a	$1$	$1$	$1$	$18.366$	$\Q$	$_{}$	None	None	✓	✓			2300.2.a.b	$1$	$1$	$0$	$2$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{7}+q^{9}-3q^{11}-5q^{13}+\cdots$
2300.2.a.h	$2300$	$2$	2300.a	1.a	$1$	$1$	$1$	$18.366$	$\Q$	$_{}$	None	None	✓				92.2.a.a	$1$	$0$	$0$	$3$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}+4q^{7}+6q^{9}+2q^{11}+5q^{13}+\cdots$
2300.2.a.i	$2300$	$2$	2300.a	1.a	$1$	$2$	$2$	$18.366$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓				460.2.a.e	$1$	$0$	$0$	$-1$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+(-1+\beta )q^{7}+(1+\beta )q^{9}+2q^{11}+\cdots$
2300.2.a.j	$2300$	$2$	2300.a	1.a	$1$	$3$	$3$	$18.366$	3.3.321.1	$_{}$	None	None	✓	✓	✓		2300.2.a.j	$1$	$1$	$0$	$-2$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}-2\beta _{1}q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots$
2300.2.a.k	$2300$	$2$	2300.a	1.a	$1$	$3$	$3$	$18.366$	3.3.321.1	$_{}$	None	None	✓	✓			2300.2.a.j	$1$	$1$	$0$	$2$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+2\beta _{1}q^{7}+(1-\beta _{1}+\beta _{2})q^{9}+\cdots$
2300.2.a.l	$2300$	$2$	2300.a	1.a	$1$	$4$	$4$	$18.366$	4.4.53121.1	$_{}$	None	None	✓	✓			2300.2.a.l	$1$	$0$	$0$	$0$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(-\beta _{1}+\beta _{3})q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots$
2300.2.a.m	$2300$	$2$	2300.a	1.a	$1$	$4$	$4$	$18.366$	4.4.53121.1	$_{}$	None	None	✓	✓	✓		2300.2.a.l	$1$	$0$	$0$	$0$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(\beta _{1}-\beta _{3})q^{7}+(1+\beta _{2})q^{9}+\cdots$
2300.2.a.n	$2300$	$2$	2300.a	1.a	$1$	$6$	$6$	$18.366$	6.6.143376304.1	$_{}$	None	None	✓		✓		460.2.c.a	$1$	$1$	$0$	$-4$	$0$	$-9$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{3}+(-2+\beta _{3})q^{7}+(2+\cdots)q^{9}+\cdots$
2300.2.a.o	$2300$	$2$	2300.a	1.a	$1$	$6$	$6$	$18.366$	6.6.143376304.1	$_{}$	None	None	✓		✓		460.2.c.a	$1$	$0$	$0$	$4$	$0$	$9$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{3}+(2-\beta _{3})q^{7}+(2+\beta _{1}+\cdots)q^{9}+\cdots$
2300.2.c.a	$2300$	$2$	2300.c	5.b	$2$	$2$	$2$	$18.366$	$\Q(\sqrt{-1}) $	$_{}$	None	None					460.2.a.d	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+3 i q^{3}-2 i q^{7}-6 q^{9}-3 i q^{13}+\cdots$
2300.2.c.b	$2300$	$2$	2300.c	5.b	$2$	$2$	$2$	$18.366$	$\Q(\sqrt{-1}) $	$_{}$	None	None					92.2.a.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+3 i q^{3}-4 i q^{7}-6 q^{9}+2 q^{11}+\cdots$
2300.2.c.c	$2300$	$2$	2300.c	5.b	$2$	$2$	$2$	$18.366$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			2300.2.a.b	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2 i q^{3}-i q^{7}-q^{9}-3 q^{11}-5 i q^{13}+\cdots$
2300.2.c.d	$2300$	$2$	2300.c	5.b	$2$	$2$	$2$	$18.366$	$\Q(\sqrt{-1}) $	$_{}$	None	None					460.2.a.c	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{3}+4 i q^{7}+2 q^{9}-6 q^{11}+\cdots$
2300.2.c.e	$2300$	$2$	2300.c	5.b	$2$	$2$	$2$	$18.366$	$\Q(\sqrt{-1}) $	$_{}$	None	None					460.2.a.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{3}-2 i q^{7}+2 q^{9}-4 q^{11}+\cdots$
2300.2.c.f	$2300$	$2$	2300.c	5.b	$2$	$2$	$2$	$18.366$	$\Q(\sqrt{-1}) $	$_{}$	None	None					92.2.a.b	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{3}-2 i q^{7}+2 q^{9}-i q^{13}+\cdots$
2300.2.c.g	$2300$	$2$	2300.c	5.b	$2$	$2$	$2$	$18.366$	$\Q(\sqrt{-1}) $	$_{}$	None	None					460.2.a.b	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{7}+3 q^{9}+6 q^{11}+6 i q^{13}+\cdots$
2300.2.c.h	$2300$	$2$	2300.c	5.b	$2$	$4$	$4$	$18.366$	$\Q(i, \sqrt{17})$	$_{}$	None	None					460.2.a.e	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+(\beta _{1}+\beta _{2})q^{7}+(-2+\beta _{3})q^{9}+\cdots$
2300.2.c.i	$2300$	$2$	2300.c	5.b	$2$	$6$	$6$	$18.366$	6.0.6594624.1	$_{}$	None	None		✓			2300.2.a.j	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}-\beta _{4})q^{3}+2\beta _{1}q^{7}+(-1+\beta _{2}+\cdots)q^{9}+\cdots$
2300.2.c.j	$2300$	$2$	2300.c	5.b	$2$	$8$	$8$	$18.366$	8.0.$\cdots$.1	$_{}$	None	None		✓	✓		2300.2.a.l	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{5})q^{7}+(-1+\beta _{2}+\cdots)q^{9}+\cdots$
2300.2.i.a	$2300$	$2$	2300.i	115.e	$4$	$8$	$4$	$18.366$	8.0.$\cdots$.122	$_{}$	$\Q(\sqrt{-115}) $	None		✓			2300.2.i.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q-\beta _{1}q^{7}-3\beta _{2}q^{9}+(\beta _{1}-2\beta _{5})q^{17}+\cdots$
2300.2.i.b	$2300$	$2$	2300.i	115.e	$4$	$8$	$4$	$18.366$	8.0.157351936.1	$_{}$	None	None		✓			2300.2.i.b	$8$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{2}q^{3}-\beta _{5}q^{7}+4\beta _{3}q^{9}-\beta _{1}q^{11}+\cdots$
2300.2.i.c	$2300$	$2$	2300.i	115.e	$4$	$8$	$4$	$18.366$	8.0.$\cdots$.3	$_{}$	None	None					460.2.i.a	$4$	$0$	$0$	$8$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+(1+\beta _{3})q^{3}+\beta _{2}q^{7}-\beta _{3}q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots$
2300.2.i.d	$2300$	$2$	2300.i	115.e	$4$	$16$	$8$	$18.366$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None					460.2.i.b	$4$	$0$	$0$	$-4$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{5}q^{3}+(\beta _{10}-\beta _{12}-\beta _{15})q^{7}+(\beta _{3}+\cdots)q^{9}+\cdots$
2300.2.i.e	$2300$	$2$	2300.i	115.e	$4$	$16$	$8$	$18.366$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		✓			2300.2.i.e	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{3}+(\beta _{1}+\beta _{5}-\beta _{9})q^{7}+(\beta _{6}-\beta _{7}+\cdots)q^{9}+\cdots$
2300.2.i.f	$2300$	$2$	2300.i	115.e	$4$	$16$	$8$	$18.366$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		✓			2300.2.i.e	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{5}+\beta _{9})q^{7}+(\beta _{6}+\cdots)q^{9}+\cdots$
2300.3.d.a	$2300$	$3$	2300.d	115.c	$2$	$8$	$8$	$62.670$	8.0.$\cdots$.3	$_{}$	None	None					92.3.d.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{9}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{3}+(-\beta _{1}-\beta _{5})q^{7}+(-2+\beta _{2}+\cdots)q^{9}+\cdots$
2300.3.d.b	$2300$	$3$	2300.d	115.c	$2$	$32$	$32$	$62.670$		$_{}$	None	None					460.3.f.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
2300.3.d.c	$2300$	$3$	2300.d	115.c	$2$	$32$	$32$	$62.670$		$_{}$	None	None		✓			2300.3.f.c	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
2300.3.f.a	$2300$	$3$	2300.f	23.b	$2$	$4$	$4$	$62.670$	4.0.53792.1	$_{}$	None	None					92.3.d.a	$2$	$0$	$0$	$-2$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{3}+(-\beta _{1}-\beta _{2})q^{7}+(1+\beta _{3})q^{9}+\cdots$
2300.3.f.b	$2300$	$3$	2300.f	23.b	$2$	$4$	$4$	$62.670$	$\Q(i, \sqrt{345})$	$_{}$	$\Q(\sqrt{-115}) $	None					460.3.d.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+(\beta _{1}-4\beta _{2})q^{7}-9q^{9}+(-3\beta _{1}+4\beta _{2}+\cdots)q^{17}+\cdots$
2300.3.f.c	$2300$	$3$	2300.f	23.b	$2$	$16$	$16$	$62.670$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		✓			2300.3.f.c	$2$	$0$	$0$	$0$	$0$	$0$		$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{3}+\beta _{1}q^{7}+(4+\beta _{3})q^{9}-\beta _{8}q^{11}+\cdots$
2300.3.f.d	$2300$	$3$	2300.f	23.b	$2$	$16$	$16$	$62.670$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		✓			2300.3.f.c	$2$	$0$	$0$	$0$	$0$	$0$		$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{3}+\beta _{1}q^{7}+(4+\beta _{3})q^{9}+\beta _{8}q^{11}+\cdots$
2300.3.f.e	$2300$	$3$	2300.f	23.b	$2$	$16$	$16$	$62.670$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None					460.3.f.a	$2$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{3}+\beta _{7}q^{7}+(4-\beta _{1})q^{9}+(\beta _{4}+\cdots)q^{11}+\cdots$
2300.3.f.f	$2300$	$3$	2300.f	23.b	$2$	$20$	$20$	$62.670$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None			✓		460.3.d.c	$4$	$0$	$0$	$0$	$0$	$0$		$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{3}-\beta _{16}q^{7}+(4+\beta _{2})q^{9}-\beta _{12}q^{11}+\cdots$
2300.4.a.a	$2300$	$4$	2300.a	1.a	$1$	$3$	$3$	$135.704$	3.3.28669.1	$_{}$	None	None	✓				92.4.a.b	$1$	$1$	$0$	$-8$	$0$	$-42$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-3-\beta _{2})q^{3}+(-14+\beta _{1})q^{7}+(28+\cdots)q^{9}+\cdots$
2300.4.a.b	$2300$	$4$	2300.a	1.a	$1$	$3$	$3$	$135.704$	3.3.1229.1	$_{}$	None	None	✓				92.4.a.a	$1$	$0$	$0$	$4$	$0$	$46$	$+$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{3}+(18-5\beta _{1}-3\beta _{2})q^{7}+\cdots$
2300.4.a.c	$2300$	$4$	2300.a	1.a	$1$	$5$	$5$	$135.704$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	$_{}$	None	None	✓				460.4.a.b	$1$	$0$	$0$	$3$	$0$	$-8$	$+$	$2$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+(-2+\beta _{2}+\beta _{3})q^{7}+\cdots$
2300.4.a.d	$2300$	$4$	2300.a	1.a	$1$	$5$	$5$	$135.704$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	$_{}$	None	None	✓				460.4.a.a	$1$	$1$	$0$	$7$	$0$	$20$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta _{3})q^{3}+(5+\beta _{1}+2\beta _{2}-\beta _{3}+\cdots)q^{7}+\cdots$

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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.