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 52 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
4000.1.b.a	$4000$	$1$	4000.b	4.b	$2$	$4$	$4$	$1.996$	$\Q(i, \sqrt{5})$	$A_{5}$	None	None		✓			4000.1.b.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-\beta _{1}-\beta _{3})q^{3}-\beta _{3}q^{7}+(-1-\beta _{2}+\cdots)q^{9}+\cdots$
4000.1.b.b	$4000$	$1$	4000.b	4.b	$2$	$4$	$4$	$1.996$	$\Q(i, \sqrt{5})$	$A_{5}$	None	None		✓			4000.1.b.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta _{1}q^{3}+\beta _{3}q^{7}+\beta _{2}q^{9}-\beta _{3}q^{11}+\cdots$
4000.1.e.a	$4000$	$1$	4000.e	40.e	$2$	$2$	$2$	$1.996$	$\Q(\sqrt{5})$	$D_{5}$	$\Q(\sqrt{-10})$	None	✓				1000.1.g.a	$2$	$0$	$0$	$0$	$0$	$-1$		$1$		$q-\beta q^{7}+q^{9}+(1-\beta )q^{11}+(1-\beta )q^{13}+\cdots$
4000.1.e.b	$4000$	$1$	4000.e	40.e	$2$	$2$	$2$	$1.996$	$\Q(\sqrt{5})$	$D_{5}$	$\Q(\sqrt{-10})$	None	✓				1000.1.g.a	$2$	$0$	$0$	$0$	$0$	$1$		$1$		$q+\beta q^{7}+q^{9}+(1-\beta )q^{11}+(-1+\beta )q^{13}+\cdots$
4000.1.g.a	$4000$	$1$	4000.g	8.d	$2$	$4$	$4$	$1.996$	$\Q(i, \sqrt{5})$	$D_{5}$	$\Q(\sqrt{-10})$	None			✓	✓	1000.1.g.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\beta _{1}+\beta _{3})q^{7}-q^{9}-\beta _{2}q^{11}-\beta _{1}q^{13}+\cdots$
4000.1.h.a	$4000$	$1$	4000.h	20.d	$2$	$4$	$4$	$1.996$	$\Q(i, \sqrt{5})$	$A_{5}$	None	None		✓			4000.1.b.a	$2$	$0$	$0$	$-2$	$0$	$4$		$1$		$q+(-1-\beta _{2})q^{3}+q^{7}+(1+\beta _{2})q^{9}+\cdots$
4000.1.h.b	$4000$	$1$	4000.h	20.d	$2$	$4$	$4$	$1.996$	$\Q(i, \sqrt{5})$	$A_{5}$	None	None		✓			4000.1.b.a	$2$	$0$	$0$	$2$	$0$	$-4$		$1$		$q+(1+\beta _{2})q^{3}-q^{7}+(1+\beta _{2})q^{9}+\beta _{3}q^{11}+\cdots$
4000.1.p.a	$4000$	$1$	4000.p	5.c	$4$	$8$	$4$	$1.996$	$\Q(\zeta_{20})$	$D_{20}$	$\Q(\sqrt{-5})$	None		✓			4000.1.p.a	$4$	$0$	$0$	$-2$	$0$	$2$		$2^{2}$		$q+(-\zeta_{20}+\zeta_{20}^{4})q^{3}+(\zeta_{20}^{7}-\zeta_{20}^{8}+\cdots)q^{7}+\cdots$
4000.1.p.b	$4000$	$1$	4000.p	5.c	$4$	$8$	$4$	$1.996$	$\Q(\zeta_{20})$	$D_{20}$	$\Q(\sqrt{-5})$	None		✓			4000.1.p.a	$4$	$0$	$0$	$2$	$0$	$-2$		$2^{2}$		$q+(\zeta_{20}^{6}+\zeta_{20}^{9})q^{3}+(-\zeta_{20}^{2}-\zeta_{20}^{3}+\cdots)q^{7}+\cdots$
4000.1.bf.a	$4000$	$1$	4000.bf	100.h	$10$	$8$	$2$	$1.996$	$\Q(\zeta_{20})$	$A_{5}$	None	None					800.1.bh.a	$4$	$0$	$0$	$-2$	$0$	$4$		$1$		$q-\zeta_{20}^{2}q^{3}+(-\zeta_{20}^{4}+\zeta_{20}^{6})q^{7}+\cdots$
4000.1.bf.b	$4000$	$1$	4000.bf	100.h	$10$	$8$	$2$	$1.996$	$\Q(\zeta_{20})$	$A_{5}$	None	None					800.1.bh.a	$4$	$0$	$0$	$2$	$0$	$-4$		$1$		$q+\zeta_{20}^{2}q^{3}+(\zeta_{20}^{4}-\zeta_{20}^{6})q^{7}+(-\zeta_{20}^{3}+\cdots)q^{13}+\cdots$
4000.1.bh.a	$4000$	$1$	4000.bh	100.j	$10$	$8$	$2$	$1.996$	$\Q(\zeta_{20})$	$A_{5}$	None	None			✓	✓	800.1.bh.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{20}q^{3}+(\zeta_{20}^{3}+\zeta_{20}^{7})q^{7}+(-1+\cdots)q^{13}+\cdots$
4000.1.bo.a	$4000$	$1$	4000.bo	25.f	$20$	$8$	$1$	$1.996$	$\Q(\zeta_{20})$	$D_{20}$	$\Q(\sqrt{-1})$	None					800.1.bo.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{20}^{9}q^{9}+(-\zeta_{20}^{6}-\zeta_{20}^{7})q^{13}+\cdots$
4000.1.bo.b	$4000$	$1$	4000.bo	25.f	$20$	$8$	$1$	$1.996$	$\Q(\zeta_{20})$	$D_{20}$	$\Q(\sqrt{-1})$	None					800.1.bo.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{20}^{9}q^{9}+(\zeta_{20}-\zeta_{20}^{2})q^{13}+(\zeta_{20}^{4}+\cdots)q^{17}+\cdots$
4000.1.bo.c	$4000$	$1$	4000.bo	25.f	$20$	$8$	$1$	$1.996$	$\Q(\zeta_{20})$	$D_{20}$	$\Q(\sqrt{-1})$	None					800.1.bo.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{20}^{9}q^{9}+(\zeta_{20}^{6}+\zeta_{20}^{7})q^{13}+(\zeta_{20}^{2}+\cdots)q^{17}+\cdots$
4000.1.cq.a	$4000$	$1$	4000.cq	125.i	$100$	$40$	$1$	$1.996$	$\Q(\zeta_{100})$	$D_{100}$	$\Q(\sqrt{-1})$	None		✓	✓	✓	4000.1.cq.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{100}^{13}q^{5}-\zeta_{100}^{49}q^{9}+(\zeta_{100}^{2}-\zeta_{100}^{21}+\cdots)q^{13}+\cdots$
4000.2.a.a	$4000$	$2$	4000.a	1.a	$1$	$4$	$4$	$31.940$	$\Q(\zeta_{20})^+$	$_{}$	$\Q(\sqrt{-5})$	None	✓	✓			4000.2.a.a	$2$	$1$	$0$	$-6$	$0$	$-8$	$+$	$1$	$N(\mathrm{U}(1))$	$q+(-2-\beta _{1}-\beta _{2}+\beta _{3})q^{3}+(-1+2\beta _{1}+\cdots)q^{7}+\cdots$
4000.2.a.b	$4000$	$2$	4000.a	1.a	$1$	$4$	$4$	$31.940$	$\Q(\zeta_{20})^+$	$_{}$	$\Q(\sqrt{-5})$	None	✓	✓			4000.2.a.b	$2$	$1$	$0$	$-4$	$0$	$-2$	$+$	$1$	$N(\mathrm{U}(1))$	$q+(-1+\beta _{1})q^{3}+(-1+\beta _{1}-\beta _{2}-\beta _{3})q^{7}+\cdots$
4000.2.a.c	$4000$	$2$	4000.a	1.a	$1$	$4$	$4$	$31.940$	4.4.16400.1	$_{}$	None	None	✓	✓			4000.2.a.c	$2$	$0$	$0$	$-2$	$0$	$-2$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{3}+(-1-\beta _{2})q^{7}+(-2-\beta _{2}+\cdots)q^{9}+\cdots$
4000.2.a.d	$4000$	$2$	4000.a	1.a	$1$	$4$	$4$	$31.940$	$\Q(\zeta_{20})^+$	$_{}$	None	None	✓	✓			4000.2.a.d	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{3})q^{7}+\beta _{2}q^{9}+\cdots$
4000.2.a.e	$4000$	$2$	4000.a	1.a	$1$	$4$	$4$	$31.940$	$\Q(\zeta_{20})^+$	$_{}$	None	None	✓	✓			4000.2.a.e	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+\beta _{3}q^{7}+\beta _{2}q^{9}-2\beta _{3}q^{11}+\cdots$
4000.2.a.f	$4000$	$2$	4000.a	1.a	$1$	$4$	$4$	$31.940$	$\Q(\zeta_{20})^+$	$_{}$	None	None	✓	✓			4000.2.a.e	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+\beta _{3}q^{7}+\beta _{2}q^{9}+2\beta _{3}q^{11}+\cdots$
4000.2.a.g	$4000$	$2$	4000.a	1.a	$1$	$4$	$4$	$31.940$	$\Q(\zeta_{20})^+$	$_{}$	None	None	✓	✓			4000.2.a.d	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{3})q^{7}+\beta _{2}q^{9}+\cdots$
4000.2.a.h	$4000$	$2$	4000.a	1.a	$1$	$4$	$4$	$31.940$	4.4.16400.1	$_{}$	None	None	✓	✓			4000.2.a.c	$2$	$1$	$0$	$2$	$0$	$2$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{3}+(1+\beta _{2})q^{7}+(-2-\beta _{2})q^{9}+\cdots$
4000.2.a.i	$4000$	$2$	4000.a	1.a	$1$	$4$	$4$	$31.940$	$\Q(\zeta_{20})^+$	$_{}$	$\Q(\sqrt{-5})$	None	✓	✓			4000.2.a.b	$2$	$0$	$0$	$4$	$0$	$2$	$-$	$1$	$N(\mathrm{U}(1))$	$q+(1+\beta _{1})q^{3}+(1+\beta _{1}+\beta _{2}-\beta _{3})q^{7}+\cdots$
4000.2.a.j	$4000$	$2$	4000.a	1.a	$1$	$4$	$4$	$31.940$	$\Q(\zeta_{20})^+$	$_{}$	$\Q(\sqrt{-5})$	None	✓	✓			4000.2.a.a	$2$	$0$	$0$	$6$	$0$	$8$	$-$	$1$	$N(\mathrm{U}(1))$	$q+(2-\beta _{1}+\beta _{2}+\beta _{3})q^{3}+(1+2\beta _{1}+\cdots)q^{7}+\cdots$
4000.2.a.k	$4000$	$2$	4000.a	1.a	$1$	$6$	$6$	$31.940$	6.6.30040000.1	$_{}$	None	None	✓	✓			4000.2.a.k	$1$	$1$	$0$	$0$	$0$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(-1+\beta _{5})q^{7}+(1+\beta _{1}+\beta _{3}+\cdots)q^{9}+\cdots$
4000.2.a.l	$4000$	$2$	4000.a	1.a	$1$	$6$	$6$	$31.940$	6.6.30040000.1	$_{}$	None	None	✓	✓			4000.2.a.k	$1$	$0$	$0$	$0$	$0$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(-1+\beta _{5})q^{7}+(1+\beta _{1}+\beta _{3}+\cdots)q^{9}+\cdots$
4000.2.a.m	$4000$	$2$	4000.a	1.a	$1$	$6$	$6$	$31.940$	6.6.30040000.1	$_{}$	None	None	✓	✓	✓		4000.2.a.k	$1$	$1$	$0$	$0$	$0$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(1-\beta _{5})q^{7}+(1+\beta _{1}+\beta _{3}+\cdots)q^{9}+\cdots$
4000.2.a.n	$4000$	$2$	4000.a	1.a	$1$	$6$	$6$	$31.940$	6.6.30040000.1	$_{}$	None	None	✓	✓			4000.2.a.k	$1$	$0$	$0$	$0$	$0$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(1-\beta _{5})q^{7}+(1+\beta _{1}+\beta _{3}+\cdots)q^{9}+\cdots$
4000.2.a.o	$4000$	$2$	4000.a	1.a	$1$	$8$	$8$	$31.940$	8.8. $\cdots$ .1	$_{}$	None	None	✓	✓	✓		4000.2.a.o	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$2^{4}$	$\mathrm{SU}(2)$	$q-\beta _{4}q^{3}-\beta _{6}q^{7}+(1-\beta _{5})q^{9}+(\beta _{4}+\cdots)q^{11}+\cdots$
4000.2.a.p	$4000$	$2$	4000.a	1.a	$1$	$8$	$8$	$31.940$	8.8. $\cdots$ .1	$_{}$	None	None	✓	✓			4000.2.a.o	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$2^{4}$	$\mathrm{SU}(2)$	$q-\beta _{4}q^{3}-\beta _{6}q^{7}+(1-\beta _{5})q^{9}+(-\beta _{4}+\cdots)q^{11}+\cdots$
4000.2.a.q	$4000$	$2$	4000.a	1.a	$1$	$8$	$8$	$31.940$	8.8. $\cdots$ .1	$_{}$	None	None	✓	✓			4000.2.a.q	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+\beta _{7}q^{7}+(2+\beta _{2})q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots$
4000.2.a.r	$4000$	$2$	4000.a	1.a	$1$	$8$	$8$	$31.940$	8.8. $\cdots$ .1	$_{}$	None	None	✓	✓	✓		4000.2.a.q	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+\beta _{7}q^{7}+(2+\beta _{2})q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots$
4000.2.c.a	$4000$	$2$	4000.c	5.b	$2$	$8$	$8$	$31.940$	$\Q(\zeta_{20})$	$_{}$	$\Q(\sqrt{-5})$	None		✓			4000.2.a.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{U}(1)[D_{2}]$	$q+(\beta_{7}+\beta_{3})q^{3}+(2\beta_{7}-2\beta_{3}+\beta_{2})q^{7}+\cdots$
4000.2.c.b	$4000$	$2$	4000.c	5.b	$2$	$8$	$8$	$31.940$	$\Q(\zeta_{20})$	$_{}$	$\Q(\sqrt{-5})$	None		✓			4000.2.a.b	$4$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta_{3} q^{3}+(-\beta_{7}+\beta_{3})q^{7}+(-\beta_{6}-\beta_1-1)q^{9}+\cdots$
4000.2.c.c	$4000$	$2$	4000.c	5.b	$2$	$8$	$8$	$31.940$	$\Q(\zeta_{20})$	$_{}$	None	None		✓			4000.2.a.d	$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta_{7} q^{3}+(-\beta_{7}+\beta_{2})q^{7}+(\beta_{5}+1)q^{9}+\cdots$
4000.2.c.d	$4000$	$2$	4000.c	5.b	$2$	$8$	$8$	$31.940$	$\Q(\zeta_{20})$	$_{}$	None	None		✓			4000.2.a.e	$4$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta_{2} q^{3}-\beta_{7} q^{7}-\beta_{5} q^{9}+\beta_{4} q^{11}+\cdots$
4000.2.c.e	$4000$	$2$	4000.c	5.b	$2$	$8$	$8$	$31.940$	8.0.268960000.3	$_{}$	None	None		✓			4000.2.a.c	$4$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{1}+\beta _{3})q^{3}+\beta _{3}q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots$
4000.2.c.f	$4000$	$2$	4000.c	5.b	$2$	$12$	$12$	$31.940$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		✓			4000.2.a.k	$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}-\beta _{11}q^{7}+(\beta _{3}+\beta _{4}+\beta _{6}+\cdots)q^{9}+\cdots$
4000.2.c.g	$4000$	$2$	4000.c	5.b	$2$	$12$	$12$	$31.940$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		✓			4000.2.a.k	$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}-\beta _{11}q^{7}+(\beta _{3}+\beta _{4}+\beta _{6}+\cdots)q^{9}+\cdots$
4000.2.c.h	$4000$	$2$	4000.c	5.b	$2$	$16$	$16$	$31.940$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓			4000.2.a.q	$4$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{3}-\beta _{15}q^{7}+(-2+\beta _{4})q^{9}+\cdots$
4000.2.c.i	$4000$	$2$	4000.c	5.b	$2$	$16$	$16$	$31.940$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓			4000.2.a.o	$4$	$0$	$0$	$0$	$0$	$0$		$2^{20}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{3}-\beta _{12}q^{7}+(-1+\beta _{6})q^{9}+\cdots$
4000.2.d.a	$4000$	$2$	4000.d	8.b	$2$	$4$	$4$	$31.940$	$\Q(i, \sqrt{5})$	$_{}$	None	None					1000.2.d.a	$2$	$0$	$0$	$0$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2\beta _{1}q^{3}+(1+3\beta _{2})q^{7}+(-1+4\beta _{2}+\cdots)q^{9}+\cdots$
4000.2.d.b	$4000$	$2$	4000.d	8.b	$2$	$4$	$4$	$31.940$	$\Q(i, \sqrt{5})$	$_{}$	None	None					1000.2.d.a	$2$	$0$	$0$	$0$	$0$	$2$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2\beta _{1}q^{3}+(-1-3\beta _{2})q^{7}+(-1+4\beta _{2}+\cdots)q^{9}+\cdots$
4000.2.d.c	$4000$	$2$	4000.d	8.b	$2$	$40$	$40$	$31.940$		$_{}$	None	None					1000.2.d.c	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
4000.2.d.d	$4000$	$2$	4000.d	8.b	$2$	$48$	$48$	$31.940$		$_{}$	None	None			✓		1000.2.d.d	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
4000.2.f.a	$4000$	$2$	4000.f	40.f	$2$	$4$	$4$	$31.940$	$\Q(i, \sqrt{5})$	$_{}$	None	None					1000.2.d.a	$2$	$0$	$0$	$-4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-2-2\beta _{2})q^{3}+(3\beta _{1}+2\beta _{3})q^{7}+\cdots$
4000.2.f.b	$4000$	$2$	4000.f	40.f	$2$	$4$	$4$	$31.940$	$\Q(i, \sqrt{5})$	$_{}$	None	None					1000.2.d.a	$2$	$0$	$0$	$4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(2+2\beta _{2})q^{3}+(3\beta _{1}+2\beta _{3})q^{7}+(5+\cdots)q^{9}+\cdots$
4000.2.f.c	$4000$	$2$	4000.f	40.f	$2$	$20$	$20$	$31.940$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None					1000.2.d.c	$2$	$0$	$0$	$-4$	$0$	$0$		$2^{14}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{9}q^{3}+\beta _{5}q^{7}+(\beta _{1}-\beta _{7}+\beta _{10}+\cdots)q^{9}+\cdots$

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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.