Refine search
Label | Dim | $A$ | Field | CM | RM | Traces | Fricke sign | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
71.1.b.a | $3$ | $0.035$ | \(\Q(\zeta_{14})^+\) | \(\Q(\sqrt{-71}) \) | None | \(-1\) | \(-1\) | \(-1\) | \(0\) | \(q-\beta _{1}q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots\) | |
71.2.a.a | $3$ | $0.567$ | 3.3.257.1 | None | None | \(-1\) | \(1\) | \(5\) | \(2\) | $-$ | \(q-\beta _{1}q^{2}+\beta _{1}q^{3}+(1+\beta _{2})q^{4}+(2-\beta _{1}+\cdots)q^{5}+\cdots\) |
71.2.a.b | $3$ | $0.567$ | 3.3.257.1 | None | None | \(0\) | \(-1\) | \(-3\) | \(2\) | $-$ | \(q+\beta _{2}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(1+\beta _{1}+\cdots)q^{4}+\cdots\) |
71.2.c.a | $20$ | $0.567$ | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) | None | None | \(-6\) | \(-1\) | \(-1\) | \(-1\) | \(q-\beta _{14}q^{2}+\beta _{17}q^{3}+(-\beta _{2}-\beta _{4}-\beta _{5}+\cdots)q^{4}+\cdots\) | |
71.2.d.a | $30$ | $0.567$ | None | None | \(-3\) | \(-10\) | \(-10\) | \(-3\) | |||
71.2.g.a | $120$ | $0.567$ | None | None | \(-22\) | \(-20\) | \(-20\) | \(-27\) | |||
71.3.b.a | $4$ | $1.935$ | 4.0.2836736.1 | None | None | \(-4\) | \(-4\) | \(-8\) | \(0\) | \(q+(-1-\beta _{1})q^{2}+(-1+\beta _{1})q^{3}+(-1+\cdots)q^{4}+\cdots\) | |
71.3.b.b | $7$ | $1.935$ | 7.7.\(\cdots\).1 | \(\Q(\sqrt{-71}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{2}q^{2}-\beta _{6}q^{3}+(4+2\beta _{3}+\beta _{4})q^{4}+\cdots\) | |
71.3.e.a | $44$ | $1.935$ | None | None | \(-6\) | \(-1\) | \(3\) | \(-5\) | |||
71.3.f.a | $66$ | $1.935$ | None | None | \(-3\) | \(-10\) | \(-6\) | \(-7\) | |||
71.3.h.a | $264$ | $1.935$ | None | None | \(-22\) | \(-20\) | \(-24\) | \(-23\) | |||
71.4.a.a | $1$ | $4.189$ | \(\Q\) | None | None | \(1\) | \(1\) | \(-16\) | \(-1\) | $-$ | \(q+q^{2}+q^{3}-7q^{4}-2^{4}q^{5}+q^{6}-q^{7}+\cdots\) |
71.4.a.b | $4$ | $4.189$ | 4.4.135041.1 | None | None | \(-3\) | \(-6\) | \(-9\) | \(-35\) | $-$ | \(q+(-1-\beta _{2})q^{2}+(-1+\beta _{1}+\beta _{2}-\beta _{3})q^{3}+\cdots\) |
71.4.a.c | $12$ | $4.189$ | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) | None | None | \(2\) | \(7\) | \(15\) | \(48\) | $+$ | \(q+\beta _{1}q^{2}+(1+\beta _{5})q^{3}+(4+\beta _{1}+\beta _{7}+\cdots)q^{4}+\cdots\) |
71.4.c.a | $68$ | $4.189$ | None | None | \(0\) | \(-7\) | \(5\) | \(-17\) | |||
71.4.d.a | $102$ | $4.189$ | None | None | \(-7\) | \(5\) | \(-4\) | \(-19\) | |||
71.4.g.a | $408$ | $4.189$ | None | None | \(-28\) | \(-35\) | \(-26\) | \(-11\) | |||
71.5.b.a | $7$ | $7.339$ | 7.7.\(\cdots\).1 | \(\Q(\sqrt{-71}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(2\beta _{3}+\beta _{4})q^{2}+(-4\beta _{2}+\beta _{5})q^{3}+\cdots\) | |
71.5.b.b | $16$ | $7.339$ | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) | None | None | \(4\) | \(8\) | \(4\) | \(0\) | \(q-\beta _{2}q^{2}+(1+\beta _{4})q^{3}+(4-\beta _{2}+\beta _{6}+\cdots)q^{4}+\cdots\) | |
71.5.e.a | $92$ | $7.339$ | None | None | \(6\) | \(-13\) | \(-9\) | \(-5\) | |||
71.5.f.a | $138$ | $7.339$ | None | None | \(-11\) | \(20\) | \(-18\) | \(-7\) | |||
71.5.h.a | $552$ | $7.339$ | None | None | \(-34\) | \(-50\) | \(-12\) | \(-23\) | |||
71.6.a.a | $11$ | $11.387$ | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) | None | None | \(-4\) | \(-20\) | \(-72\) | \(-344\) | $+$ | \(q-\beta _{1}q^{2}+(-2+\beta _{1}+\beta _{3})q^{3}+(11+\cdots)q^{4}+\cdots\) |
71.6.a.b | $18$ | $11.387$ | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) | None | None | \(4\) | \(16\) | \(128\) | \(244\) | $-$ | \(q+\beta _{1}q^{2}+(1+\beta _{3})q^{3}+(19+\beta _{2})q^{4}+\cdots\) |
71.6.c.a | $116$ | $11.387$ | None | None | \(0\) | \(-1\) | \(-61\) | \(95\) | |||
71.6.d.a | $174$ | $11.387$ | None | None | \(-7\) | \(-10\) | \(-70\) | \(93\) | |||
71.6.g.a | $696$ | $11.387$ | None | None | \(-28\) | \(-20\) | \(40\) | \(-123\) | |||
71.7.b.a | $7$ | $16.334$ | 7.7.\(\cdots\).1 | \(\Q(\sqrt{-71}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(5\beta _{1}+\beta _{6})q^{2}+(15\beta _{3}-2\beta _{4})q^{3}+\cdots\) | |
71.7.b.b | $28$ | $16.334$ | None | None | \(-12\) | \(-34\) | \(142\) | \(0\) | |||
71.7.e.a | $140$ | $16.334$ | None | None | \(-18\) | \(29\) | \(-147\) | \(-5\) | |||
71.7.f.a | $210$ | $16.334$ | None | None | \(5\) | \(-85\) | \(-156\) | \(-7\) | |||
71.7.h.a | $840$ | $16.334$ | None | None | \(-10\) | \(55\) | \(126\) | \(-23\) | |||
71.8.a.a | $17$ | $22.179$ | \(\mathbb{Q}[x]/(x^{17} - \cdots)\) | None | None | \(-16\) | \(-68\) | \(-430\) | \(-1716\) | $-$ | \(q+(-1+\beta _{1})q^{2}+(-4+\beta _{4})q^{3}+(54+\cdots)q^{4}+\cdots\) |
71.8.a.b | $24$ | $22.179$ | None | None | \(0\) | \(40\) | \(570\) | \(2400\) | $+$ | ||
71.8.c.a | $164$ | $22.179$ | None | None | \(-24\) | \(23\) | \(-145\) | \(-689\) | |||
71.8.d.a | $246$ | $22.179$ | None | None | \(9\) | \(-70\) | \(-154\) | \(-691\) | |||
71.8.g.a | $984$ | $22.179$ | None | None | \(-4\) | \(40\) | \(124\) | \(661\) | |||
71.9.b.a | $7$ | $28.924$ | 7.7.\(\cdots\).1 | \(\Q(\sqrt{-71}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(-4\beta _{3}+\beta _{6})q^{2}+(2^{4}\beta _{2}-5\beta _{4})q^{3}+\cdots\) | |
71.9.b.b | $40$ | $28.924$ | None | None | \(4\) | \(68\) | \(-296\) | \(0\) | |||
71.9.e.a | $188$ | $28.924$ | None | None | \(6\) | \(-73\) | \(291\) | \(-5\) | |||
71.9.f.a | $282$ | $28.924$ | None | None | \(-11\) | \(170\) | \(282\) | \(-7\) | |||
71.9.h.a | $1128$ | $28.924$ | None | None | \(-34\) | \(-200\) | \(-312\) | \(-23\) | |||
71.10.a.a | $23$ | $36.568$ | None | None | \(0\) | \(-89\) | \(-3297\) | \(-16808\) | $+$ | ||
71.10.a.b | $30$ | $36.568$ | None | None | \(32\) | \(235\) | \(1703\) | \(12004\) | $-$ | ||
71.10.c.a | $212$ | $36.568$ | None | None | \(48\) | \(-151\) | \(1589\) | \(4799\) | |||
71.10.d.a | $318$ | $36.568$ | None | None | \(-39\) | \(365\) | \(1580\) | \(4797\) | |||
71.10.g.a | $1272$ | $36.568$ | None | None | \(-76\) | \(-395\) | \(-1610\) | \(-4827\) | |||
71.11.b.a | $7$ | $45.110$ | 7.7.\(\cdots\).1 | \(\Q(\sqrt{-71}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(5\beta _{3}+13\beta _{4})q^{2}+(-76\beta _{2}+65\beta _{5}+\cdots)q^{3}+\cdots\) | |
71.11.b.b | $52$ | $45.110$ | None | None | \(20\) | \(-64\) | \(-3308\) | \(0\) | |||
71.11.e.a | $236$ | $45.110$ | None | None | \(30\) | \(59\) | \(3303\) | \(-5\) |