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 (47 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
1125.1.g.a	$1125$	$1$	1125.g	5.c	$4$	$8$	$4$	$0.561$	8.0.1024000000.2	$D_{10}$	$\Q(\sqrt{-15}) $	None		✓	✓	✓	1125.1.g.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta _{5}q^{2}+(\beta _{2}-\beta _{6})q^{4}+(-\beta _{3}+\beta _{7})q^{8}+\cdots$
1125.2.a.a	$1125$	$2$	1125.a	1.a	$1$	$2$	$2$	$8.983$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				375.2.a.a	$1$	$0$	$-3$	$0$	$0$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{2}+3\beta q^{4}+(3-\beta )q^{7}+\cdots$
1125.2.a.b	$1125$	$2$	1125.a	1.a	$1$	$2$	$2$	$8.983$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				375.2.a.b	$1$	$1$	$-1$	$0$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(-1+\beta )q^{4}+\beta q^{7}+(-1+\cdots)q^{8}+\cdots$
1125.2.a.c	$1125$	$2$	1125.a	1.a	$1$	$2$	$2$	$8.983$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				125.2.a.a	$1$	$0$	$-1$	$0$	$0$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(-1+\beta )q^{4}+3q^{7}+(-1+\cdots)q^{8}+\cdots$
1125.2.a.d	$1125$	$2$	1125.a	1.a	$1$	$2$	$2$	$8.983$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				125.2.a.a	$1$	$1$	$1$	$0$	$0$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(-1+\beta )q^{4}-3q^{7}+(1-2\beta )q^{8}+\cdots$
1125.2.a.e	$1125$	$2$	1125.a	1.a	$1$	$2$	$2$	$8.983$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				375.2.a.b	$1$	$1$	$1$	$0$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(-1+\beta )q^{4}-\beta q^{7}+(1-2\beta )q^{8}+\cdots$
1125.2.a.f	$1125$	$2$	1125.a	1.a	$1$	$2$	$2$	$8.983$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				375.2.a.a	$1$	$0$	$3$	$0$	$0$	$-5$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+3\beta q^{4}+(-3+\beta )q^{7}+\cdots$
1125.2.a.g	$1125$	$2$	1125.a	1.a	$1$	$4$	$4$	$8.983$	$\Q(\zeta_{15})^+$	$_{}$	$\Q(\sqrt{-15}) $	None	✓	✓			1125.2.a.g	$2$	$1$	$-5$	$0$	$0$	$0$	$+$	$1$	$N(\mathrm{U}(1))$	$q+(-1+\beta _{2}+\beta _{3})q^{2}+(1+\beta _{1}-2\beta _{2}+\cdots)q^{4}+\cdots$
1125.2.a.h	$1125$	$2$	1125.a	1.a	$1$	$4$	$4$	$8.983$	$\Q(\sqrt{11 +2 \sqrt{5}})$	$_{}$	None	None	✓		✓		375.2.a.e	$1$	$1$	$-3$	$0$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{3})q^{2}+(1+\beta _{1}-\beta _{2}+\beta _{3})q^{4}+\cdots$
1125.2.a.i	$1125$	$2$	1125.a	1.a	$1$	$4$	$4$	$8.983$	$\Q(\zeta_{20})^+$	$_{}$	None	None	✓	✓			1125.2.a.i	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-\beta _{1}-2\beta _{3})q^{7}+\cdots$
1125.2.a.j	$1125$	$2$	1125.a	1.a	$1$	$4$	$4$	$8.983$	$\Q(\zeta_{20})^+$	$_{}$	None	None	✓	✓			1125.2.a.i	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(\beta _{1}+2\beta _{3})q^{7}+\cdots$
1125.2.a.k	$1125$	$2$	1125.a	1.a	$1$	$4$	$4$	$8.983$	$\Q(\sqrt{14 +2 \sqrt{5}})$	$_{}$	None	None	✓				125.2.a.c	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{3}q^{2}+(1-2\beta _{2})q^{4}+(-\beta _{1}-\beta _{3})q^{7}+\cdots$
1125.2.a.l	$1125$	$2$	1125.a	1.a	$1$	$4$	$4$	$8.983$	$\Q(\sqrt{11 +2 \sqrt{5}})$	$_{}$	None	None	✓				375.2.a.e	$1$	$0$	$3$	$0$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{2}-\beta _{3})q^{2}+(2-\beta _{1}-\beta _{3})q^{4}+\cdots$
1125.2.a.m	$1125$	$2$	1125.a	1.a	$1$	$4$	$4$	$8.983$	$\Q(\zeta_{15})^+$	$_{}$	$\Q(\sqrt{-15}) $	None	✓	✓			1125.2.a.g	$2$	$0$	$5$	$0$	$0$	$0$	$-$	$1$	$N(\mathrm{U}(1))$	$q+(1-\beta _{2}-\beta _{3})q^{2}+(1+\beta _{1}-2\beta _{2}+\cdots)q^{4}+\cdots$
1125.2.b.a	$1125$	$2$	1125.b	5.b	$2$	$4$	$4$	$8.983$	$\Q(\sqrt{-14 +2 \sqrt{5}})$	$_{}$	None	None					125.2.a.c	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{2}+(-1-2\beta _{2})q^{4}+(\beta _{1}-\beta _{3})q^{7}+\cdots$
1125.2.b.b	$1125$	$2$	1125.b	5.b	$2$	$4$	$4$	$8.983$	$\Q(i, \sqrt{5})$	$_{}$	None	None					375.2.a.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}-\beta _{3})q^{2}+3\beta _{2}q^{4}+(\beta _{1}+3\beta _{3})q^{7}+\cdots$
1125.2.b.c	$1125$	$2$	1125.b	5.b	$2$	$4$	$4$	$8.983$	$\Q(\zeta_{10})$	$_{}$	None	None		✓			1125.2.a.i	$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta_{3} q^{2}+\beta_{2} q^{4}+(-\beta_{3}+2\beta_1)q^{7}+\cdots$
1125.2.b.d	$1125$	$2$	1125.b	5.b	$2$	$4$	$4$	$8.983$	$\Q(\zeta_{10})$	$_{}$	None	None		✓			1125.2.a.i	$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta_{3} q^{2}+\beta_{2} q^{4}+(\beta_{3}-2\beta_1)q^{7}+\cdots$
1125.2.b.e	$1125$	$2$	1125.b	5.b	$2$	$4$	$4$	$8.983$	$\Q(i, \sqrt{5})$	$_{}$	None	None					375.2.a.b	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{1}q^{7}+(2\beta _{1}+\cdots)q^{8}+\cdots$
1125.2.b.f	$1125$	$2$	1125.b	5.b	$2$	$4$	$4$	$8.983$	$\Q(i, \sqrt{5})$	$_{}$	None	None					125.2.a.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+3\beta _{3}q^{7}+(2\beta _{1}+\cdots)q^{8}+\cdots$
1125.2.b.g	$1125$	$2$	1125.b	5.b	$2$	$8$	$8$	$8.983$	8.0.1632160000.5	$_{}$	None	None					375.2.a.e	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{4}+\beta _{7})q^{2}+(-1+\beta _{2}+\beta _{5}+\beta _{6}+\cdots)q^{4}+\cdots$
1125.2.b.h	$1125$	$2$	1125.b	5.b	$2$	$8$	$8$	$8.983$	8.0.324000000.1	$_{}$	$\Q(\sqrt{-15}) $	None		✓			1125.2.a.g	$4$	$0$	$0$	$0$	$0$	$0$		$5^{5}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{1}q^{2}+(-2+\beta _{2})q^{4}+(2\beta _{1}+\beta _{7})q^{8}+\cdots$
1125.2.f.a	$1125$	$2$	1125.f	15.e	$4$	$32$	$16$	$8.983$		$_{}$	None	None		✓			1125.2.f.a	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
1125.2.f.b	$1125$	$2$	1125.f	15.e	$4$	$32$	$16$	$8.983$		$_{}$	None	None		✓			1125.2.f.b	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
1125.3.c.a	$1125$	$3$	1125.c	3.b	$2$	$32$	$32$	$30.654$		$_{}$	None	None		✓			1125.3.c.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1125.3.c.b	$1125$	$3$	1125.c	3.b	$2$	$32$	$32$	$30.654$		$_{}$	None	None		✓			1125.3.c.b	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1125.3.d.a	$1125$	$3$	1125.d	15.d	$2$	$16$	$16$	$30.654$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓			1125.3.c.a	$2$	$0$	$-10$	$0$	$0$	$0$		$3^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1+\beta _{2})q^{2}+(3-\beta _{2}-\beta _{3})q^{4}+\cdots$
1125.3.d.b	$1125$	$3$	1125.d	15.d	$2$	$16$	$16$	$30.654$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓			1125.3.c.a	$2$	$0$	$10$	$0$	$0$	$0$		$3^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q+(1-\beta _{2})q^{2}+(3-\beta _{2}-\beta _{3})q^{4}+(-\beta _{6}+\cdots)q^{7}+\cdots$
1125.3.d.c	$1125$	$3$	1125.d	15.d	$2$	$32$	$32$	$30.654$		$_{}$	None	None		✓	✓		1125.3.c.b	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1125.4.a.a	$1125$	$4$	1125.a	1.a	$1$	$4$	$4$	$66.377$	$\Q(\zeta_{15})^+$	$_{}$	$\Q(\sqrt{-15}) $	None	✓	✓			1125.4.a.a	$2$	$1$	$-5$	$0$	$0$	$0$	$-$	$3^{2}$	$N(\mathrm{U}(1))$	$q+(-1-\beta _{2})q^{2}+(13-6\beta _{1}+2\beta _{2}+\cdots)q^{4}+\cdots$
1125.4.a.b	$1125$	$4$	1125.a	1.a	$1$	$4$	$4$	$66.377$	$\Q(\sqrt{5}, \sqrt{21})$	$_{}$	None	None	✓				375.4.a.a	$1$	$1$	$-4$	$0$	$0$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1}+\beta _{3})q^{2}+(-1-3\beta _{1}+\cdots)q^{4}+\cdots$
1125.4.a.c	$1125$	$4$	1125.a	1.a	$1$	$4$	$4$	$66.377$	$\Q(\sqrt{6 + \sqrt{5}})$	$_{}$	None	None	✓				125.4.a.a	$2$	$1$	$0$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(-1+2\beta _{2})q^{4}+(2\beta _{1}-9\beta _{3})q^{7}+\cdots$
1125.4.a.d	$1125$	$4$	1125.a	1.a	$1$	$4$	$4$	$66.377$	$\Q(\sqrt{5}, \sqrt{21})$	$_{}$	None	None	✓				375.4.a.a	$1$	$0$	$4$	$0$	$0$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+(2-\beta _{1}+\beta _{3})q^{2}+(2-\beta _{1}-2\beta _{2}+\cdots)q^{4}+\cdots$
1125.4.a.e	$1125$	$4$	1125.a	1.a	$1$	$4$	$4$	$66.377$	$\Q(\zeta_{15})^+$	$_{}$	$\Q(\sqrt{-15}) $	None	✓	✓			1125.4.a.a	$2$	$0$	$5$	$0$	$0$	$0$	$+$	$3^{2}$	$N(\mathrm{U}(1))$	$q+(1+\beta _{3})q^{2}+(7+7\beta _{1}-\beta _{2}+2\beta _{3})q^{4}+\cdots$
1125.4.a.f	$1125$	$4$	1125.a	1.a	$1$	$6$	$6$	$66.377$	6.6.497918125.1	$_{}$	None	None	✓				125.4.a.b	$1$	$0$	$-7$	$0$	$0$	$67$	$+$	$5^{2}$	$\mathrm{SU}(2)$	$q+(-1+\beta _{2})q^{2}+(5-\beta _{2}+\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots$
1125.4.a.g	$1125$	$4$	1125.a	1.a	$1$	$6$	$6$	$66.377$	6.6.920588125.1	$_{}$	None	None	✓				375.4.a.c	$1$	$0$	$-5$	$0$	$0$	$28$	$+$	$5^{2}$	$\mathrm{SU}(2)$	$q+(-1+\beta _{2})q^{2}+(4-\beta _{1}-2\beta _{2}+\beta _{5})q^{4}+\cdots$
1125.4.a.h	$1125$	$4$	1125.a	1.a	$1$	$6$	$6$	$66.377$	6.6.3126413125.1	$_{}$	None	None	✓				375.4.a.d	$1$	$1$	$-3$	$0$	$0$	$44$	$-$	$5^{2}$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(5-\beta _{1}+\beta _{3})q^{4}+\cdots$
1125.4.a.i	$1125$	$4$	1125.a	1.a	$1$	$6$	$6$	$66.377$	6.6.3126413125.1	$_{}$	None	None	✓				375.4.a.d	$1$	$1$	$3$	$0$	$0$	$-44$	$-$	$5^{2}$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(5-\beta _{1}+\beta _{3})q^{4}+(-7+\cdots)q^{7}+\cdots$
1125.4.a.j	$1125$	$4$	1125.a	1.a	$1$	$6$	$6$	$66.377$	6.6.920588125.1	$_{}$	None	None	✓				375.4.a.c	$1$	$0$	$5$	$0$	$0$	$-28$	$+$	$5^{2}$	$\mathrm{SU}(2)$	$q+(1-\beta _{2})q^{2}+(4-\beta _{1}-2\beta _{2}+\beta _{5})q^{4}+\cdots$
1125.4.a.k	$1125$	$4$	1125.a	1.a	$1$	$6$	$6$	$66.377$	6.6.497918125.1	$_{}$	None	None	✓				125.4.a.b	$1$	$1$	$7$	$0$	$0$	$-67$	$-$	$5^{2}$	$\mathrm{SU}(2)$	$q+(1-\beta _{2})q^{2}+(5-\beta _{2}+\beta _{3}+\beta _{4})q^{4}+\cdots$
1125.4.a.l	$1125$	$4$	1125.a	1.a	$1$	$8$	$8$	$66.377$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓		✓		375.4.a.g	$1$	$1$	$-7$	$0$	$0$	$19$	$-$	$5^{4}$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(5-\beta _{1}+\beta _{2})q^{4}+\cdots$
1125.4.a.m	$1125$	$4$	1125.a	1.a	$1$	$8$	$8$	$66.377$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	✓			1125.4.a.m	$2$	$0$	$0$	$0$	$0$	$0$	$+$	$2^{2}\cdot 5^{4}$	$\mathrm{SU}(2)$	$q+(-\beta _{1}+\beta _{4})q^{2}+(\beta _{1}-\beta _{4}-2\beta _{5}+\cdots)q^{4}+\cdots$
1125.4.a.n	$1125$	$4$	1125.a	1.a	$1$	$8$	$8$	$66.377$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	✓			1125.4.a.m	$2$	$1$	$0$	$0$	$0$	$0$	$-$	$2^{2}\cdot 5^{4}$	$\mathrm{SU}(2)$	$q+(\beta _{1}-\beta _{4})q^{2}+(\beta _{1}-\beta _{4}-2\beta _{5})q^{4}+\cdots$
1125.4.a.o	$1125$	$4$	1125.a	1.a	$1$	$8$	$8$	$66.377$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓				125.4.a.d	$2$	$0$	$0$	$0$	$0$	$0$	$+$	$2^{2}\cdot 5^{4}$	$\mathrm{SU}(2)$	$q-\beta _{5}q^{2}+(5-\beta _{3})q^{4}+(-2\beta _{4}-\beta _{5}+\cdots)q^{7}+\cdots$
1125.4.a.p	$1125$	$4$	1125.a	1.a	$1$	$8$	$8$	$66.377$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓				375.4.a.g	$1$	$0$	$7$	$0$	$0$	$-19$	$+$	$5^{4}$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(5-\beta _{1}+\beta _{2})q^{4}+(-3+\cdots)q^{7}+\cdots$
1125.4.a.q	$1125$	$4$	1125.a	1.a	$1$	$12$	$12$	$66.377$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None	✓	✓	✓		1125.4.a.q	$2$	$1$	$0$	$0$	$0$	$0$	$-$	$2^{2}\cdot 5^{8}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(5+\beta _{2})q^{4}+(-2\beta _{1}-\beta _{10}+\cdots)q^{7}+\cdots$
1125.4.a.r	$1125$	$4$	1125.a	1.a	$1$	$12$	$12$	$66.377$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None	✓	✓	✓		1125.4.a.q	$2$	$0$	$0$	$0$	$0$	$0$	$+$	$2^{2}\cdot 5^{8}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(5+\beta _{2})q^{4}+(2\beta _{1}+\beta _{10}+\cdots)q^{7}+\cdots$

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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.