Learn more

Refine search


Results (1-50 of 115 matches)

Next   Download to        
Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
31.1.b.a 31.b 31.b $1$ $0.015$ \(\Q\) \(\Q(\sqrt{-31}) \) None \(-1\) \(0\) \(-1\) \(-1\) \(q-q^{2}-q^{5}-q^{7}+q^{8}+q^{9}+q^{10}+\cdots\)
31.2.a.a 31.a 1.a $2$ $0.248$ \(\Q(\sqrt{5}) \) None None \(1\) \(-2\) \(2\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-2\beta q^{3}+(-1+\beta )q^{4}+q^{5}+\cdots\)
31.2.c.a 31.c 31.c $4$ $0.248$ \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(-4\) \(2\) \(-2\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{3})q^{2}+(1+\beta _{1}+\beta _{2})q^{3}+\cdots\)
31.2.d.a 31.d 31.d $4$ $0.248$ \(\Q(\zeta_{10})\) None None \(-3\) \(1\) \(-6\) \(-3\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1-\zeta_{10}^{2})q^{2}+(1-\zeta_{10}+\zeta_{10}^{2}+\cdots)q^{3}+\cdots\)
31.2.g.a 31.g 31.g $16$ $0.248$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(-6\) \(-12\) \(-3\) \(2\) $\mathrm{SU}(2)[C_{15}]$ \(q+(-1-\beta _{1}+\beta _{3}-\beta _{4}+\beta _{5}+\beta _{6}+\cdots)q^{2}+\cdots\)
31.3.b.a 31.b 31.b $2$ $0.845$ \(\Q(\sqrt{-26}) \) None None \(-2\) \(0\) \(4\) \(16\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+\beta q^{3}-3q^{4}+2q^{5}-\beta q^{6}+\cdots\)
31.3.b.b 31.b 31.b $3$ $0.845$ 3.3.837.1 \(\Q(\sqrt{-31}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{2}q^{2}+(4+\beta _{1}-2\beta _{2})q^{4}+(-3\beta _{1}+\cdots)q^{5}+\cdots\)
31.3.e.a 31.e 31.e $2$ $0.845$ \(\Q(\sqrt{-3}) \) None None \(-6\) \(3\) \(9\) \(1\) $\mathrm{SU}(2)[C_{6}]$ \(q-3q^{2}+(1+\zeta_{6})q^{3}+5q^{4}+9\zeta_{6}q^{5}+\cdots\)
31.3.e.b 31.e 31.e $6$ $0.845$ 6.0.954288.1 None None \(2\) \(-3\) \(-7\) \(-9\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{2}+\beta _{4})q^{2}+(-\beta _{1}-\beta _{2}-\beta _{4}+\cdots)q^{3}+\cdots\)
31.3.f.a 31.f 31.f $20$ $0.845$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(-3\) \(-5\) \(-14\) \(-1\) $\mathrm{SU}(2)[C_{10}]$ \(q-\beta _{10}q^{2}-\beta _{13}q^{3}+(3\beta _{11}+\beta _{19})q^{4}+\cdots\)
31.3.h.a 31.h 31.h $32$ $0.845$ None None \(-6\) \(-10\) \(-7\) \(-22\) $\mathrm{SU}(2)[C_{30}]$
31.4.a.a 31.a 1.a $2$ $1.829$ \(\Q(\sqrt{17}) \) None None \(-5\) \(-2\) \(-25\) \(-19\) $-$ $\mathrm{SU}(2)$ \(q+(-2-\beta )q^{2}+(-2+2\beta )q^{3}+5\beta q^{4}+\cdots\)
31.4.a.b 31.a 1.a $5$ $1.829$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None None \(3\) \(4\) \(15\) \(9\) $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(-\beta _{2}+\beta _{3}-\beta _{4})q^{3}+\cdots\)
31.4.c.a 31.c 31.c $14$ $1.829$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None None \(-4\) \(-11\) \(-5\) \(31\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}+\beta _{4})q^{2}+(-2+2\beta _{3}-\beta _{8}+\cdots)q^{3}+\cdots\)
31.4.d.a 31.d 31.d $28$ $1.829$ None None \(-3\) \(-7\) \(0\) \(35\) $\mathrm{SU}(2)[C_{5}]$
31.4.g.a 31.g 31.g $56$ $1.829$ None None \(-6\) \(1\) \(0\) \(-71\) $\mathrm{SU}(2)[C_{15}]$
31.5.b.a 31.b 31.b $3$ $3.204$ 3.3.837.1 \(\Q(\sqrt{-31}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(-\beta _{1}+\beta _{2})q^{2}+(2^{4}-6\beta _{1}+\beta _{2})q^{4}+\cdots\)
31.5.b.b 31.b 31.b $6$ $3.204$ \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None None \(-2\) \(0\) \(-8\) \(-132\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{2}+\beta _{1}q^{3}+(4+\beta _{3}+\beta _{4})q^{4}+\cdots\)
31.5.e.a 31.e 31.e $20$ $3.204$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(-4\) \(6\) \(-4\) \(-98\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{3}q^{2}+\beta _{8}q^{3}+(6+\beta _{2})q^{4}+(-\beta _{11}+\cdots)q^{5}+\cdots\)
31.5.f.a 31.f 31.f $36$ $3.204$ None None \(-3\) \(-5\) \(-2\) \(-73\) $\mathrm{SU}(2)[C_{10}]$
31.5.h.a 31.h 31.h $80$ $3.204$ None None \(-6\) \(-16\) \(-1\) \(288\) $\mathrm{SU}(2)[C_{30}]$
31.6.a.a 31.a 1.a $5$ $4.972$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None None \(-9\) \(-20\) \(-72\) \(-108\) $+$ $\mathrm{SU}(2)$ \(q+(-2+\beta _{1})q^{2}+(-4-\beta _{1}-\beta _{3})q^{3}+\cdots\)
31.6.a.b 31.a 1.a $8$ $4.972$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(7\) \(-2\) \(128\) \(88\) $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+\beta _{6}q^{3}+(19-3\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
31.6.c.a 31.c 31.c $24$ $4.972$ None None \(-4\) \(10\) \(28\) \(-134\) $\mathrm{SU}(2)[C_{3}]$
31.6.d.a 31.d 31.d $52$ $4.972$ None None \(-3\) \(17\) \(-66\) \(205\) $\mathrm{SU}(2)[C_{5}]$
31.6.g.a 31.g 31.g $96$ $4.972$ None None \(-6\) \(-20\) \(-33\) \(-66\) $\mathrm{SU}(2)[C_{15}]$
31.7.b.a 31.b 31.b $1$ $7.132$ \(\Q\) \(\Q(\sqrt{-31}) \) None \(-15\) \(0\) \(-246\) \(-430\) $\mathrm{U}(1)[D_{2}]$ \(q-15q^{2}+161q^{4}-246q^{5}-430q^{7}+\cdots\)
31.7.b.b 31.b 31.b $2$ $7.132$ \(\Q(\sqrt{93}) \) \(\Q(\sqrt{-31}) \) None \(15\) \(0\) \(246\) \(430\) $\mathrm{U}(1)[D_{2}]$ \(q+(8-\beta )q^{2}+(23-15\beta )q^{4}+(127-8\beta )q^{5}+\cdots\)
31.7.b.c 31.b 31.b $12$ $7.132$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(-2\) \(0\) \(-146\) \(6\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{8}q^{2}-\beta _{1}q^{3}+(10+\beta _{6}-\beta _{8})q^{4}+\cdots\)
31.7.e.a 31.e 31.e $30$ $7.132$ None None \(-4\) \(-3\) \(-73\) \(723\) $\mathrm{SU}(2)[C_{6}]$
31.7.f.a 31.f 31.f $60$ $7.132$ None None \(-3\) \(-5\) \(136\) \(1009\) $\mathrm{SU}(2)[C_{10}]$
31.7.h.a 31.h 31.h $120$ $7.132$ None None \(-6\) \(-7\) \(68\) \(-1753\) $\mathrm{SU}(2)[C_{30}]$
31.8.a.a 31.a 1.a $7$ $9.684$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None None \(-17\) \(-14\) \(-430\) \(-832\) $-$ $\mathrm{SU}(2)$ \(q+(-2-\beta _{1})q^{2}+(-2+\beta _{1}+\beta _{3})q^{3}+\cdots\)
31.8.a.b 31.a 1.a $10$ $9.684$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(15\) \(40\) \(570\) \(540\) $+$ $\mathrm{SU}(2)$ \(q+(2-\beta _{1})q^{2}+(4+\beta _{2})q^{3}+(61+\beta _{1}+\cdots)q^{4}+\cdots\)
31.8.c.a 31.c 31.c $36$ $9.684$ None None \(-4\) \(-2\) \(70\) \(-2158\) $\mathrm{SU}(2)[C_{3}]$
31.8.d.a 31.d 31.d $68$ $9.684$ None None \(-3\) \(-31\) \(-150\) \(-3083\) $\mathrm{SU}(2)[C_{5}]$
31.8.g.a 31.g 31.g $144$ $9.684$ None None \(-6\) \(-8\) \(-75\) \(5518\) $\mathrm{SU}(2)[C_{15}]$
31.9.b.a 31.b 31.b $3$ $12.629$ 3.3.837.1 \(\Q(\sqrt{-31}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(-6\beta _{1}+\beta _{2})q^{2}+(2^{8}-\beta _{1}+3^{4}\beta _{2})q^{4}+\cdots\)
31.9.b.b 31.b 31.b $18$ $12.629$ \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None None \(-2\) \(0\) \(292\) \(-5472\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}+\beta _{1}q^{3}+(140+\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)
31.9.e.a 31.e 31.e $40$ $12.629$ None None \(-4\) \(-84\) \(146\) \(272\) $\mathrm{SU}(2)[C_{6}]$
31.9.f.a 31.f 31.f $84$ $12.629$ None None \(-3\) \(-5\) \(-302\) \(5067\) $\mathrm{SU}(2)[C_{10}]$
31.9.h.a 31.h 31.h $160$ $12.629$ None None \(-6\) \(74\) \(-151\) \(118\) $\mathrm{SU}(2)[C_{30}]$
31.10.a.a 31.a 1.a $10$ $15.966$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(-33\) \(-8\) \(-3297\) \(-495\) $+$ $\mathrm{SU}(2)$ \(q+(-3-\beta _{1})q^{2}+(-1+\beta _{1}-\beta _{3})q^{3}+\cdots\)
31.10.a.b 31.a 1.a $13$ $15.966$ \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None None \(31\) \(154\) \(1703\) \(9109\) $-$ $\mathrm{SU}(2)$ \(q+(2+\beta _{1})q^{2}+(12+\beta _{3})q^{3}+(300+6\beta _{1}+\cdots)q^{4}+\cdots\)
31.10.c.a 31.c 31.c $46$ $15.966$ None None \(-4\) \(13\) \(-797\) \(6359\) $\mathrm{SU}(2)[C_{3}]$
31.10.d.a 31.d 31.d $92$ $15.966$ None None \(-3\) \(-151\) \(1584\) \(15771\) $\mathrm{SU}(2)[C_{5}]$
31.10.g.a 31.g 31.g $184$ $15.966$ None None \(-6\) \(-23\) \(792\) \(-30759\) $\mathrm{SU}(2)[C_{15}]$
31.11.b.a 31.b 31.b $3$ $19.696$ 3.3.837.1 \(\Q(\sqrt{-31}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(-15\beta _{1}+14\beta _{2})q^{2}+(2^{10}-644\beta _{1}+\cdots)q^{4}+\cdots\)
31.11.b.b 31.b 31.b $22$ $19.696$ None None \(-2\) \(0\) \(3304\) \(19916\) $\mathrm{SU}(2)[C_{2}]$
31.11.e.a 31.e 31.e $52$ $19.696$ None None \(-4\) \(-246\) \(1652\) \(-19306\) $\mathrm{SU}(2)[C_{6}]$
Next   Download to