Learn more

Refine search


Results (1-50 of 271 matches)

Next   Download to        
Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
8.3.d.a 8.d 8.d $1$ $0.218$ \(\Q\) \(\Q(\sqrt{-2}) \) \(-2\) \(-2\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-2q^{2}-2q^{3}+4q^{4}+4q^{6}-8q^{8}+\cdots\)
8.4.a.a 8.a 1.a $1$ $0.472$ \(\Q\) None \(0\) \(-4\) \(-2\) \(24\) $+$ $\mathrm{SU}(2)$ \(q-4q^{3}-2q^{5}+24q^{7}-11q^{9}-44q^{11}+\cdots\)
8.4.b.a 8.b 8.b $2$ $0.472$ \(\Q(\sqrt{-7}) \) None \(-2\) \(0\) \(0\) \(-16\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1-\beta )q^{2}+2\beta q^{3}+(-6+2\beta )q^{4}+\cdots\)
8.5.d.a 8.d 8.d $1$ $0.827$ \(\Q\) \(\Q(\sqrt{-2}) \) \(4\) \(-14\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+4q^{2}-14q^{3}+2^{4}q^{4}-56q^{6}+2^{6}q^{8}+\cdots\)
8.5.d.b 8.d 8.d $2$ $0.827$ \(\Q(\sqrt{-15}) \) None \(-2\) \(12\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1-\beta )q^{2}+6q^{3}+(-14+2\beta )q^{4}+\cdots\)
8.6.a.a 8.a 1.a $1$ $1.283$ \(\Q\) None \(0\) \(20\) \(-74\) \(-24\) $-$ $\mathrm{SU}(2)$ \(q+20q^{3}-74q^{5}-24q^{7}+157q^{9}+\cdots\)
8.6.b.a 8.b 8.b $4$ $1.283$ 4.0.218489.1 None \(-2\) \(0\) \(0\) \(96\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1-\beta _{1})q^{2}+(-\beta _{1}+\beta _{3})q^{3}+(5+\cdots)q^{4}+\cdots\)
8.7.d.a 8.d 8.d $1$ $1.840$ \(\Q\) \(\Q(\sqrt{-2}) \) \(-8\) \(46\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-8q^{2}+46q^{3}+2^{6}q^{4}-368q^{6}+\cdots\)
8.7.d.b 8.d 8.d $4$ $1.840$ 4.0.3803625.2 None \(2\) \(-48\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-13+2\beta _{1}+\beta _{2})q^{3}+(-12+\cdots)q^{4}+\cdots\)
8.8.a.a 8.a 1.a $1$ $2.499$ \(\Q\) None \(0\) \(-84\) \(-82\) \(-456\) $-$ $\mathrm{SU}(2)$ \(q-84q^{3}-82q^{5}-456q^{7}+4869q^{9}+\cdots\)
8.8.a.b 8.a 1.a $1$ $2.499$ \(\Q\) None \(0\) \(44\) \(430\) \(-1224\) $+$ $\mathrm{SU}(2)$ \(q+44q^{3}+430q^{5}-1224q^{7}-251q^{9}+\cdots\)
8.8.b.a 8.b 8.b $6$ $2.499$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(6\) \(0\) \(0\) \(-688\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+\beta _{1})q^{2}+\beta _{4}q^{3}+(19+\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots\)
8.9.d.a 8.d 8.d $1$ $3.259$ \(\Q\) \(\Q(\sqrt{-2}) \) \(16\) \(34\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+2^{4}q^{2}+34q^{3}+2^{8}q^{4}+544q^{6}+\cdots\)
8.9.d.b 8.d 8.d $6$ $3.259$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(-14\) \(-36\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-2+\beta _{1})q^{2}+(-6-\beta _{1}-\beta _{2})q^{3}+\cdots\)
8.10.a.a 8.a 1.a $1$ $4.120$ \(\Q\) None \(0\) \(-60\) \(-2074\) \(-4344\) $+$ $\mathrm{SU}(2)$ \(q-60q^{3}-2074q^{5}-4344q^{7}-16083q^{9}+\cdots\)
8.10.a.b 8.a 1.a $1$ $4.120$ \(\Q\) None \(0\) \(68\) \(1510\) \(10248\) $-$ $\mathrm{SU}(2)$ \(q+68q^{3}+1510q^{5}+10248q^{7}-15059q^{9}+\cdots\)
8.10.b.a 8.b 8.b $8$ $4.120$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-18\) \(0\) \(0\) \(4800\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-2-\beta _{1})q^{2}+(\beta _{1}+\beta _{3})q^{3}+(-54+\cdots)q^{4}+\cdots\)
8.11.d.a 8.d 8.d $1$ $5.083$ \(\Q\) \(\Q(\sqrt{-2}) \) \(-32\) \(-482\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-2^{5}q^{2}-482q^{3}+2^{10}q^{4}+15424q^{6}+\cdots\)
8.11.d.b 8.d 8.d $8$ $5.083$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(42\) \(480\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(5-\beta _{1})q^{2}+(60+\beta _{1}+\beta _{2})q^{3}+(5^{2}+\cdots)q^{4}+\cdots\)
8.12.a.a 8.a 1.a $1$ $6.147$ \(\Q\) None \(0\) \(-36\) \(-3490\) \(-55464\) $-$ $\mathrm{SU}(2)$ \(q-6^{2}q^{3}-3490q^{5}-55464q^{7}-175851q^{9}+\cdots\)
8.12.a.b 8.a 1.a $2$ $6.147$ \(\Q(\sqrt{109}) \) None \(0\) \(56\) \(7868\) \(91056\) $+$ $\mathrm{SU}(2)$ \(q+(28+\beta )q^{3}+(3934-12\beta )q^{5}+(45528+\cdots)q^{7}+\cdots\)
8.12.b.a 8.b 8.b $10$ $6.147$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(22\) \(0\) \(0\) \(-33616\) $\mathrm{SU}(2)[C_{2}]$ \(q+(2+\beta _{1})q^{2}+(\beta _{1}+\beta _{3})q^{3}+(43+2\beta _{1}+\cdots)q^{4}+\cdots\)
8.13.d.a 8.d 8.d $1$ $7.312$ \(\Q\) \(\Q(\sqrt{-2}) \) \(64\) \(658\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+2^{6}q^{2}+658q^{3}+2^{12}q^{4}+42112q^{6}+\cdots\)
8.13.d.b 8.d 8.d $10$ $7.312$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-110\) \(-660\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-11-\beta _{1})q^{2}+(-66+3\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)
8.14.a.a 8.a 1.a $1$ $8.578$ \(\Q\) None \(0\) \(-12\) \(-4330\) \(-139992\) $+$ $\mathrm{SU}(2)$ \(q-12q^{3}-4330q^{5}-139992q^{7}+\cdots\)
8.14.a.b 8.a 1.a $2$ $8.578$ \(\Q(\sqrt{781}) \) None \(0\) \(872\) \(18476\) \(110928\) $-$ $\mathrm{SU}(2)$ \(q+(436-\beta )q^{3}+(9238-12\beta )q^{5}+(55464+\cdots)q^{7}+\cdots\)
8.14.b.a 8.b 8.b $2$ $8.578$ \(\Q(\sqrt{-79}) \) None \(-112\) \(0\) \(0\) \(-351664\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-56-4\beta )q^{2}+129\beta q^{3}+(-1920+\cdots)q^{4}+\cdots\)
8.14.b.b 8.b 8.b $10$ $8.578$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(110\) \(0\) \(0\) \(586960\) $\mathrm{SU}(2)[C_{2}]$ \(q+(11+\beta _{1})q^{2}+(3\beta _{1}+\beta _{3})q^{3}+(-472+\cdots)q^{4}+\cdots\)
8.15.d.a 8.d 8.d $1$ $9.946$ \(\Q\) \(\Q(\sqrt{-2}) \) \(-128\) \(3022\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-2^{7}q^{2}+3022q^{3}+2^{14}q^{4}-386816q^{6}+\cdots\)
8.15.d.b 8.d 8.d $12$ $9.946$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(218\) \(-3024\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(18+\beta _{1})q^{2}+(-252+3\beta _{1}+\beta _{3}+\cdots)q^{3}+\cdots\)
8.16.a.a 8.a 1.a $1$ $11.415$ \(\Q\) None \(0\) \(-3444\) \(313358\) \(-2324616\) $-$ $\mathrm{SU}(2)$ \(q-3444q^{3}+313358q^{5}-2324616q^{7}+\cdots\)
8.16.a.b 8.a 1.a $1$ $11.415$ \(\Q\) None \(0\) \(2700\) \(-251890\) \(1374072\) $-$ $\mathrm{SU}(2)$ \(q+2700q^{3}-251890q^{5}+1374072q^{7}+\cdots\)
8.16.a.c 8.a 1.a $2$ $11.415$ \(\Q(\sqrt{58}) \) None \(0\) \(-4072\) \(-140260\) \(126192\) $+$ $\mathrm{SU}(2)$ \(q+(-2036+\beta )q^{3}+(-70130+6^{2}\beta )q^{5}+\cdots\)
8.16.b.a 8.b 8.b $14$ $11.415$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(-90\) \(0\) \(0\) \(-1647088\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-6-\beta _{1})q^{2}+\beta _{2}q^{3}+(3672+5\beta _{1}+\cdots)q^{4}+\cdots\)
8.17.d.a 8.d 8.d $1$ $12.986$ \(\Q\) \(\Q(\sqrt{-2}) \) \(256\) \(-11966\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+2^{8}q^{2}-11966q^{3}+2^{16}q^{4}-3063296q^{6}+\cdots\)
8.17.d.b 8.d 8.d $14$ $12.986$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(-350\) \(11964\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-5^{2}-\beta _{1})q^{2}+(855-6\beta _{1}+\beta _{3}+\cdots)q^{3}+\cdots\)
8.18.a.a 8.a 1.a $2$ $14.658$ \(\Q(\sqrt{2146}) \) None \(0\) \(-952\) \(-53620\) \(-333168\) $-$ $\mathrm{SU}(2)$ \(q+(-476+\beta )q^{3}+(-26810+60\beta )q^{5}+\cdots\)
8.18.a.b 8.a 1.a $2$ $14.658$ \(\Q(\sqrt{114}) \) None \(0\) \(11592\) \(-791924\) \(-18932592\) $+$ $\mathrm{SU}(2)$ \(q+(5796+\beta )q^{3}+(-395962-68\beta )q^{5}+\cdots\)
8.18.b.a 8.b 8.b $16$ $14.658$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(270\) \(0\) \(0\) \(11529600\) $\mathrm{SU}(2)[C_{2}]$ \(q+(17-\beta _{1})q^{2}+(3\beta _{1}-\beta _{2})q^{3}+(-1712+\cdots)q^{4}+\cdots\)
8.19.d.a 8.d 8.d $1$ $16.431$ \(\Q\) \(\Q(\sqrt{-2}) \) \(-512\) \(-3266\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-2^{9}q^{2}-3266q^{3}+2^{18}q^{4}+1672192q^{6}+\cdots\)
8.19.d.b 8.d 8.d $16$ $16.431$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(426\) \(3264\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(3^{3}+\beta _{1})q^{2}+(203-4\beta _{1}-\beta _{2})q^{3}+\cdots\)
8.20.a.a 8.a 1.a $2$ $18.305$ \(\Q(\sqrt{1453}) \) None \(0\) \(-27912\) \(1226620\) \(88510512\) $-$ $\mathrm{SU}(2)$ \(q+(-13956-\beta )q^{3}+(613310+44\beta )q^{5}+\cdots\)
8.20.a.b 8.a 1.a $3$ $18.305$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(0\) \(23732\) \(2140218\) \(55851720\) $+$ $\mathrm{SU}(2)$ \(q+(7911-\beta _{1})q^{3}+(713429-70\beta _{1}+\cdots)q^{5}+\cdots\)
8.20.b.a 8.b 8.b $18$ $18.305$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(-458\) \(0\) \(0\) \(-80707216\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-5^{2}+\beta _{1})q^{2}+(2+5\beta _{1}-\beta _{2})q^{3}+\cdots\)
8.21.d.a 8.d 8.d $1$ $20.281$ \(\Q\) \(\Q(\sqrt{-2}) \) \(1024\) \(114226\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+2^{10}q^{2}+114226q^{3}+2^{20}q^{4}+\cdots\)
8.21.d.b 8.d 8.d $18$ $20.281$ \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None \(-398\) \(-114228\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-22+\beta _{1})q^{2}+(-6347-5\beta _{1}+\cdots)q^{3}+\cdots\)
8.22.a.a 8.a 1.a $2$ $22.358$ \(\Q(\sqrt{358549}) \) None \(0\) \(-105432\) \(2108140\) \(444771792\) $+$ $\mathrm{SU}(2)$ \(q+(-52716-\beta )q^{3}+(1054070+20\beta )q^{5}+\cdots\)
8.22.a.b 8.a 1.a $3$ $22.358$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(0\) \(96764\) \(-24111774\) \(295988280\) $-$ $\mathrm{SU}(2)$ \(q+(32255-\beta _{1})q^{3}+(-8037261+9\beta _{1}+\cdots)q^{5}+\cdots\)
8.22.b.a 8.b 8.b $20$ $22.358$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(286\) \(0\) \(0\) \(564950496\) $\mathrm{SU}(2)[C_{2}]$ \(q+(14-\beta _{1})q^{2}+(1+3\beta _{1}-\beta _{2})q^{3}+\cdots\)
8.23.d.a 8.d 8.d $1$ $24.537$ \(\Q\) \(\Q(\sqrt{-2}) \) \(-2048\) \(-199058\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-2^{11}q^{2}-199058q^{3}+2^{22}q^{4}+\cdots\)
Next   Download to