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Results (45 matches)

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Label Char Prim Dim $A$ Field CM RM Minimal twist Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
103.1.b.a 103.b 103.b $2$ $0.051$ \(\Q(\sqrt{5}) \) \(\Q(\sqrt{-103}) \) None 103.1.b.a \(-1\) \(0\) \(0\) \(-1\) \(q+(-1+\beta )q^{2}+(1-\beta )q^{4}-\beta q^{7}-q^{8}+\cdots\)
103.2.a.a 103.a 1.a $2$ $0.822$ \(\Q(\sqrt{5}) \) None None 103.2.a.a \(-3\) \(-2\) \(-3\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{2}-q^{3}+3\beta q^{4}+(-2+\cdots)q^{5}+\cdots\)
103.2.a.b 103.a 1.a $6$ $0.822$ 6.6.6999257.1 None None 103.2.a.b \(4\) \(0\) \(3\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(-\beta _{2}-\beta _{3}+\beta _{5})q^{3}+\cdots\)
103.2.c.a 103.c 103.c $16$ $0.822$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None 103.2.c.a \(-1\) \(-4\) \(3\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{2}+\beta _{12}q^{3}+(-1+\beta _{4}-\beta _{5}+\cdots)q^{4}+\cdots\)
103.2.e.a 103.e 103.e $112$ $0.822$ None None 103.2.e.a \(-15\) \(-11\) \(-11\) \(-5\) $\mathrm{SU}(2)[C_{17}]$
103.2.g.a 103.g 103.g $256$ $0.822$ None None 103.2.g.a \(-33\) \(-30\) \(-37\) \(-29\) $\mathrm{SU}(2)[C_{51}]$
103.3.b.a 103.b 103.b $5$ $2.807$ 5.5.33153125.1 \(\Q(\sqrt{-103}) \) None 103.3.b.a \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{2}q^{2}+(4+\beta _{1}+\beta _{4})q^{4}+(-4\beta _{1}+\cdots)q^{7}+\cdots\)
103.3.b.b 103.b 103.b $12$ $2.807$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None 103.3.b.b \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{9}q^{2}-\beta _{1}q^{3}+(1+\beta _{8})q^{4}+\beta _{2}q^{5}+\cdots\)
103.3.d.a 103.d 103.d $32$ $2.807$ None None 103.3.d.a \(-1\) \(0\) \(-3\) \(5\) $\mathrm{SU}(2)[C_{6}]$
103.3.f.a 103.f 103.f $272$ $2.807$ None None 103.3.f.a \(-15\) \(-17\) \(-17\) \(-17\) $\mathrm{SU}(2)[C_{34}]$
103.3.h.a 103.h 103.h $512$ $2.807$ None None 103.3.h.a \(-33\) \(-34\) \(-31\) \(-39\) $\mathrm{SU}(2)[C_{102}]$
103.4.a.a 103.a 1.a $10$ $6.077$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None 103.4.a.a \(-11\) \(-8\) \(-30\) \(-33\) $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{1})q^{2}+(-1-\beta _{6})q^{3}+(3+\cdots)q^{4}+\cdots\)
103.4.a.b 103.a 1.a $15$ $6.077$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None None 103.4.a.b \(9\) \(10\) \(30\) \(23\) $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(1+\beta _{9})q^{3}+(5-\beta _{1}+\cdots)q^{4}+\cdots\)
103.4.c.a 103.c 103.c $50$ $6.077$ None None 103.4.c.a \(-1\) \(4\) \(-3\) \(13\) $\mathrm{SU}(2)[C_{3}]$
103.4.e.a 103.e 103.e $400$ $6.077$ None None 103.4.e.a \(-15\) \(-19\) \(-17\) \(-7\) $\mathrm{SU}(2)[C_{17}]$
103.4.g.a 103.g 103.g $800$ $6.077$ None None 103.4.g.a \(-33\) \(-38\) \(-31\) \(-47\) $\mathrm{SU}(2)[C_{51}]$
103.5.b.a 103.b 103.b $5$ $10.647$ 5.5.33153125.1 \(\Q(\sqrt{-103}) \) None 103.5.b.a \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{4}q^{2}+(2^{4}+6\beta _{2}-\beta _{3})q^{4}+(11\beta _{2}+\cdots)q^{7}+\cdots\)
103.5.b.b 103.b 103.b $28$ $10.647$ None None 103.5.b.b \(-2\) \(0\) \(0\) \(28\) $\mathrm{SU}(2)[C_{2}]$
103.5.d.a 103.d 103.d $68$ $10.647$ None None 103.5.d.a \(-1\) \(0\) \(-3\) \(69\) $\mathrm{SU}(2)[C_{6}]$
103.5.f.a 103.f 103.f $528$ $10.647$ None None 103.5.f.a \(-15\) \(-17\) \(-17\) \(-45\) $\mathrm{SU}(2)[C_{34}]$
103.5.h.a 103.h 103.h $1088$ $10.647$ None None 103.5.h.a \(-33\) \(-34\) \(-31\) \(-103\) $\mathrm{SU}(2)[C_{102}]$
103.6.a.a 103.a 1.a $19$ $16.520$ \(\mathbb{Q}[x]/(x^{19} - \cdots)\) None None 103.6.a.a \(-21\) \(-38\) \(-147\) \(-206\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{1})q^{2}+(-2-\beta _{7})q^{3}+(14+\cdots)q^{4}+\cdots\)
103.6.a.b 103.a 1.a $24$ $16.520$ None None 103.6.a.b \(19\) \(16\) \(153\) \(186\) $-$ $\mathrm{SU}(2)$
103.6.c.a 103.c 103.c $84$ $16.520$ None None 103.6.c.a \(-1\) \(-20\) \(-9\) \(139\) $\mathrm{SU}(2)[C_{3}]$
103.6.e.a 103.e 103.e $688$ $16.520$ None None 103.6.e.a \(-15\) \(5\) \(-23\) \(3\) $\mathrm{SU}(2)[C_{17}]$
103.6.g.a 103.g 103.g $1344$ $16.520$ None None 103.6.g.a \(-33\) \(-14\) \(-25\) \(-173\) $\mathrm{SU}(2)[C_{51}]$
103.7.b.a 103.b 103.b $5$ $23.696$ 5.5.33153125.1 \(\Q(\sqrt{-103}) \) None 103.7.b.a \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(-\beta _{2}+\beta _{3})q^{2}+(2^{6}-19\beta _{1}-4\beta _{4})q^{4}+\cdots\)
103.7.b.b 103.b 103.b $46$ $23.696$ None None 103.7.b.b \(-2\) \(0\) \(0\) \(-810\) $\mathrm{SU}(2)[C_{2}]$
103.8.a.a 103.a 1.a $27$ $32.176$ None None 103.8.a.a \(-41\) \(-68\) \(-555\) \(-1518\) $-$ $\mathrm{SU}(2)$
103.8.a.b 103.a 1.a $32$ $32.176$ None None 103.8.a.b \(39\) \(94\) \(945\) \(1226\) $+$ $\mathrm{SU}(2)$
103.9.b.a 103.b 103.b $5$ $41.960$ 5.5.33153125.1 \(\Q(\sqrt{-103}) \) None 103.9.b.a \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(6\beta _{2}-\beta _{3})q^{2}+(2^{8}-65\beta _{1}+14\beta _{4})q^{4}+\cdots\)
103.9.b.b 103.b 103.b $64$ $41.960$ None None 103.9.b.b \(-2\) \(0\) \(0\) \(-5152\) $\mathrm{SU}(2)[C_{2}]$
103.10.a.a 103.a 1.a $36$ $53.049$ None None 103.10.a.a \(-81\) \(-170\) \(-5172\) \(-5297\) $+$ $\mathrm{SU}(2)$
103.10.a.b 103.a 1.a $41$ $53.049$ None None 103.10.a.b \(79\) \(316\) \(2328\) \(13911\) $-$ $\mathrm{SU}(2)$
103.11.b.a 103.b 103.b $1$ $65.442$ \(\Q\) \(\Q(\sqrt{-103}) \) None 103.11.b.a \(-39\) \(0\) \(0\) \(242\) $\mathrm{U}(1)[D_{2}]$ \(q-39q^{2}+497q^{4}+242q^{7}+20553q^{8}+\cdots\)
103.11.b.b 103.b 103.b $4$ $65.442$ 4.4.1326125.1 \(\Q(\sqrt{-103}) \) None 103.11.b.b \(39\) \(0\) \(0\) \(-242\) $\mathrm{U}(1)[D_{2}]$ \(q+(17+17\beta _{2}-5\beta _{3})q^{2}+(2^{10}+195\beta _{1}+\cdots)q^{4}+\cdots\)
103.11.b.c 103.b 103.b $80$ $65.442$ None None 103.11.b.c \(-2\) \(0\) \(0\) \(56700\) $\mathrm{SU}(2)[C_{2}]$
103.12.a.a 103.a 1.a $44$ $79.139$ None None 103.12.a.a \(-137\) \(-992\) \(-21435\) \(-103218\) $-$ $\mathrm{SU}(2)$
103.12.a.b 103.a 1.a $49$ $79.139$ None None 103.12.a.b \(183\) \(466\) \(16065\) \(31238\) $+$ $\mathrm{SU}(2)$
103.14.a.a 103.a 1.a $53$ $110.448$ None None 103.14.a.a \(-321\) \(-2318\) \(-88497\) \(-350426\) $+$ $\mathrm{SU}(2)$
103.14.a.b 103.a 1.a $58$ $110.448$ None None 103.14.a.b \(319\) \(2056\) \(99003\) \(590766\) $-$ $\mathrm{SU}(2)$
103.16.a.a 103.a 1.a $61$ $146.974$ None None 103.16.a.a \(-857\) \(-3932\) \(-439140\) \(-3190353\) $-$ $\mathrm{SU}(2)$
103.16.a.b 103.a 1.a $66$ $146.974$ None None 103.16.a.b \(423\) \(9190\) \(498360\) \(3397991\) $+$ $\mathrm{SU}(2)$
103.18.a.a 103.a 1.a $70$ $188.719$ None None 103.18.a.a \(-753\) \(-23762\) \(-2234097\) \(-22054742\) $+$ $\mathrm{SU}(2)$
103.18.a.b 103.a 1.a $75$ $188.719$ None None 103.18.a.b \(1807\) \(15604\) \(2453403\) \(24063666\) $-$ $\mathrm{SU}(2)$
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