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Label | Dim | $A$ | Field | CM | Traces | Fricke sign | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | |||||||
53.2.a.a | $1$ | $0.423$ | \(\Q\) | None | \(-1\) | \(-3\) | \(0\) | \(-4\) | $+$ | \(q-q^{2}-3q^{3}-q^{4}+3q^{6}-4q^{7}+3q^{8}+\cdots\) |
53.2.a.b | $3$ | $0.423$ | 3.3.148.1 | None | \(-1\) | \(3\) | \(-2\) | \(4\) | $-$ | \(q-\beta _{1}q^{2}+(1-\beta _{2})q^{3}+(\beta _{1}+\beta _{2})q^{4}+\cdots\) |
53.2.b.a | $4$ | $0.423$ | 4.0.7168.1 | None | \(0\) | \(0\) | \(0\) | \(-8\) | \(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(-1+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\) | |
53.2.d.a | $36$ | $0.423$ | None | \(-8\) | \(-9\) | \(-5\) | \(-5\) | |||
53.2.e.a | $48$ | $0.423$ | None | \(-13\) | \(-13\) | \(-13\) | \(-5\) | |||
53.3.c.a | $16$ | $1.444$ | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) | None | \(-6\) | \(-4\) | \(-10\) | \(0\) | \(q-\beta _{1}q^{2}+\beta _{11}q^{3}+(-2\beta _{6}+\beta _{14}+\cdots)q^{4}+\cdots\) | |
53.3.f.a | $192$ | $1.444$ | None | \(-20\) | \(-22\) | \(-16\) | \(-26\) | |||
53.4.a.a | $1$ | $3.127$ | \(\Q\) | None | \(0\) | \(1\) | \(-18\) | \(2\) | $-$ | \(q+q^{3}-8q^{4}-18q^{5}+2q^{7}-26q^{9}+\cdots\) |
53.4.a.b | $4$ | $3.127$ | 4.4.222004.1 | None | \(-4\) | \(-15\) | \(-1\) | \(-46\) | $-$ | \(q+(-1+\beta _{2})q^{2}+(-4-\beta _{2}+\beta _{3})q^{3}+\cdots\) |
53.4.a.c | $8$ | $3.127$ | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) | None | \(2\) | \(16\) | \(1\) | \(68\) | $+$ | \(q+\beta _{1}q^{2}+(2+\beta _{3})q^{3}+(6+\beta _{6}+\beta _{7})q^{4}+\cdots\) |
53.4.b.a | $12$ | $3.127$ | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(24\) | \(q+\beta _{1}q^{2}-\beta _{6}q^{3}+(-5+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\) | |
53.4.d.a | $156$ | $3.127$ | None | \(-11\) | \(-15\) | \(5\) | \(-37\) | |||
53.4.e.a | $144$ | $3.127$ | None | \(-13\) | \(-13\) | \(-13\) | \(-37\) | |||
53.5.c.a | $34$ | $5.479$ | None | \(4\) | \(8\) | \(64\) | \(0\) | |||
53.5.f.a | $408$ | $5.479$ | None | \(-30\) | \(-34\) | \(-90\) | \(-26\) | |||
53.6.a.a | $9$ | $8.500$ | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) | None | \(-4\) | \(-47\) | \(-14\) | \(-404\) | $+$ | \(q-\beta _{1}q^{2}+(-5-\beta _{3})q^{3}+(8+\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots\) |
53.6.a.b | $12$ | $8.500$ | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) | None | \(8\) | \(43\) | \(86\) | \(380\) | $-$ | \(q+(1-\beta _{1})q^{2}+(4-\beta _{4})q^{3}+(19-\beta _{1}+\cdots)q^{4}+\cdots\) |
53.6.b.a | $22$ | $8.500$ | None | \(0\) | \(0\) | \(0\) | \(-24\) | |||
53.6.d.a | $252$ | $8.500$ | None | \(-17\) | \(-9\) | \(-85\) | \(11\) | |||
53.6.e.a | $264$ | $8.500$ | None | \(-13\) | \(-13\) | \(-13\) | \(11\) | |||
53.7.c.a | $52$ | $12.193$ | None | \(-4\) | \(-34\) | \(120\) | \(0\) | |||
53.7.f.a | $624$ | $12.193$ | None | \(-22\) | \(8\) | \(-146\) | \(-26\) | |||
53.8.a.a | $14$ | $16.556$ | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) | None | \(-16\) | \(-149\) | \(-374\) | \(-3076\) | $-$ | \(q+(-1-\beta _{1})q^{2}+(-11-\beta _{3})q^{3}+(55+\cdots)q^{4}+\cdots\) |
53.8.a.b | $17$ | $16.556$ | \(\mathbb{Q}[x]/(x^{17} - \cdots)\) | None | \(8\) | \(121\) | \(126\) | \(2412\) | $+$ | \(q+\beta _{1}q^{2}+(7-\beta _{4})q^{3}+(79+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\) |
53.8.b.a | $30$ | $16.556$ | None | \(0\) | \(0\) | \(0\) | \(-664\) | |||
53.8.d.a | $372$ | $16.556$ | None | \(-5\) | \(15\) | \(235\) | \(651\) | |||
53.8.e.a | $360$ | $16.556$ | None | \(-13\) | \(-13\) | \(-13\) | \(651\) | |||
53.9.c.a | $70$ | $21.591$ | None | \(4\) | \(68\) | \(-1136\) | \(0\) | |||
53.9.f.a | $840$ | $21.591$ | None | \(-30\) | \(-94\) | \(1110\) | \(-26\) | |||
53.10.a.a | $18$ | $27.297$ | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) | None | \(-16\) | \(-332\) | \(-909\) | \(-16732\) | $+$ | \(q+(-1+\beta _{1})q^{2}+(-18-\beta _{1}+\beta _{3}+\cdots)q^{3}+\cdots\) |
53.10.a.b | $21$ | $27.297$ | None | \(32\) | \(478\) | \(1591\) | \(21684\) | $-$ | ||
53.10.b.a | $40$ | $27.297$ | None | \(0\) | \(0\) | \(0\) | \(4952\) | |||
53.10.d.a | $468$ | $27.297$ | None | \(-29\) | \(-159\) | \(-695\) | \(-4965\) | |||
53.10.e.a | $480$ | $27.297$ | None | \(-13\) | \(-13\) | \(-13\) | \(-4965\) | |||
53.11.c.a | $88$ | $33.674$ | None | \(-12\) | \(-64\) | \(-1750\) | \(0\) | |||
53.11.f.a | $1056$ | $33.674$ | None | \(-14\) | \(38\) | \(1724\) | \(-26\) | |||
53.12.a.a | $22$ | $40.722$ | None | \(-64\) | \(-1721\) | \(-6844\) | \(-116660\) | $-$ | ||
53.12.a.b | $25$ | $40.722$ | None | \(32\) | \(709\) | \(5656\) | \(152252\) | $+$ | ||
53.12.b.a | $48$ | $40.722$ | None | \(0\) | \(0\) | \(0\) | \(2104\) | |||
53.12.d.a | $588$ | $40.722$ | None | \(67\) | \(495\) | \(-8485\) | \(-2117\) | |||
53.12.e.a | $576$ | $40.722$ | None | \(-13\) | \(-13\) | \(-13\) | \(-2117\) | |||
53.14.a.a | $27$ | $56.832$ | None | \(-64\) | \(-3047\) | \(-31304\) | \(-1140324\) | $+$ | ||
53.14.a.b | $30$ | $56.832$ | None | \(128\) | \(4243\) | \(31196\) | \(742060\) | $-$ | ||
53.14.b.a | $58$ | $56.832$ | None | \(0\) | \(0\) | \(0\) | \(-398264\) | |||
53.16.a.a | $31$ | $75.628$ | None | \(-256\) | \(-8306\) | \(-156539\) | \(-7000492\) | $-$ | ||
53.16.a.b | $34$ | $75.628$ | None | \(128\) | \(13564\) | \(155961\) | \(6176196\) | $+$ | ||
53.16.b.a | $66$ | $75.628$ | None | \(0\) | \(0\) | \(0\) | \(4820616\) | |||
53.18.a.a | $35$ | $97.108$ | None | \(-256\) | \(-30323\) | \(-699174\) | \(-66984244\) | $+$ | ||
53.18.a.b | $38$ | $97.108$ | None | \(512\) | \(35287\) | \(863326\) | \(25252572\) | $-$ | ||
53.18.b.a | $76$ | $97.108$ | None | \(0\) | \(0\) | \(0\) | \(-35279688\) |