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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2415.1.p.a \(2\) \(1.205\) \(\Q(\sqrt{5}) \) \(\Q(\sqrt{-2415}) \) None \(-1\) \(-2\) \(-2\) \(2\) \(q+(-1+\beta )q^{2}-q^{3}+(1-\beta )q^{4}-q^{5}+\cdots\)
2415.1.p.b \(2\) \(1.205\) \(\Q(\sqrt{5}) \) \(\Q(\sqrt{-2415}) \) None \(-1\) \(-2\) \(2\) \(-2\) \(q+(-1+\beta )q^{2}-q^{3}+(1-\beta )q^{4}+q^{5}+\cdots\)
2415.1.p.c \(2\) \(1.205\) \(\Q(\sqrt{5}) \) \(\Q(\sqrt{-2415}) \) None \(-1\) \(2\) \(-2\) \(-2\) \(q+(-1+\beta )q^{2}+q^{3}+(1-\beta )q^{4}-q^{5}+\cdots\)
2415.1.p.d \(2\) \(1.205\) \(\Q(\sqrt{5}) \) \(\Q(\sqrt{-2415}) \) None \(-1\) \(2\) \(2\) \(2\) \(q-\beta q^{2}+q^{3}+\beta q^{4}+q^{5}-\beta q^{6}+q^{7}+\cdots\)
2415.1.p.e \(2\) \(1.205\) \(\Q(\sqrt{5}) \) \(\Q(\sqrt{-2415}) \) None \(1\) \(-2\) \(-2\) \(-2\) \(q+\beta q^{2}-q^{3}+\beta q^{4}-q^{5}-\beta q^{6}-q^{7}+\cdots\)
2415.1.p.f \(2\) \(1.205\) \(\Q(\sqrt{5}) \) \(\Q(\sqrt{-2415}) \) None \(1\) \(-2\) \(2\) \(2\) \(q+(1-\beta )q^{2}-q^{3}+(1-\beta )q^{4}+q^{5}+\cdots\)
2415.1.p.g \(2\) \(1.205\) \(\Q(\sqrt{5}) \) \(\Q(\sqrt{-2415}) \) None \(1\) \(2\) \(-2\) \(2\) \(q+(1-\beta )q^{2}+q^{3}+(1-\beta )q^{4}-q^{5}+\cdots\)
2415.1.p.h \(2\) \(1.205\) \(\Q(\sqrt{5}) \) \(\Q(\sqrt{-2415}) \) None \(1\) \(2\) \(2\) \(-2\) \(q+\beta q^{2}+q^{3}+\beta q^{4}+q^{5}+\beta q^{6}-q^{7}+\cdots\)
2415.1.bq.a \(8\) \(1.205\) \(\Q(\zeta_{24})\) None None \(-4\) \(0\) \(0\) \(0\) \(q+(-\zeta_{24}^{4}-\zeta_{24}^{10})q^{2}-\zeta_{24}^{2}q^{3}+\cdots\)
2415.1.bq.b \(8\) \(1.205\) \(\Q(\zeta_{24})\) None None \(4\) \(-4\) \(0\) \(0\) \(q+(\zeta_{24}^{4}+\zeta_{24}^{10})q^{2}+\zeta_{24}^{8}q^{3}-\zeta_{24}^{2}q^{4}+\cdots\)
2415.2.a.a \(1\) \(19.284\) \(\Q\) None None \(-1\) \(-1\) \(-1\) \(-1\) \(+\) \(q-q^{2}-q^{3}-q^{4}-q^{5}+q^{6}-q^{7}+\cdots\)
2415.2.a.b \(1\) \(19.284\) \(\Q\) None None \(-1\) \(1\) \(-1\) \(1\) \(-\) \(q-q^{2}+q^{3}-q^{4}-q^{5}-q^{6}+q^{7}+\cdots\)
2415.2.a.c \(1\) \(19.284\) \(\Q\) None None \(-1\) \(1\) \(1\) \(-1\) \(+\) \(q-q^{2}+q^{3}-q^{4}+q^{5}-q^{6}-q^{7}+\cdots\)
2415.2.a.d \(1\) \(19.284\) \(\Q\) None None \(-1\) \(1\) \(1\) \(1\) \(+\) \(q-q^{2}+q^{3}-q^{4}+q^{5}-q^{6}+q^{7}+\cdots\)
2415.2.a.e \(1\) \(19.284\) \(\Q\) None None \(0\) \(-1\) \(-1\) \(1\) \(+\) \(q-q^{3}-2q^{4}-q^{5}+q^{7}+q^{9}-3q^{11}+\cdots\)
2415.2.a.f \(1\) \(19.284\) \(\Q\) None None \(0\) \(1\) \(-1\) \(-1\) \(+\) \(q+q^{3}-2q^{4}-q^{5}-q^{7}+q^{9}+q^{11}+\cdots\)
2415.2.a.g \(1\) \(19.284\) \(\Q\) None None \(0\) \(1\) \(-1\) \(1\) \(+\) \(q+q^{3}-2q^{4}-q^{5}+q^{7}+q^{9}+3q^{11}+\cdots\)
2415.2.a.h \(1\) \(19.284\) \(\Q\) None None \(1\) \(1\) \(-1\) \(1\) \(-\) \(q+q^{2}+q^{3}-q^{4}-q^{5}+q^{6}+q^{7}+\cdots\)
2415.2.a.i \(1\) \(19.284\) \(\Q\) None None \(1\) \(1\) \(1\) \(-1\) \(+\) \(q+q^{2}+q^{3}-q^{4}+q^{5}+q^{6}-q^{7}+\cdots\)
2415.2.a.j \(2\) \(19.284\) \(\Q(\sqrt{3}) \) None None \(0\) \(2\) \(-2\) \(-2\) \(+\) \(q+\beta q^{2}+q^{3}+q^{4}-q^{5}+\beta q^{6}-q^{7}+\cdots\)
2415.2.a.k \(2\) \(19.284\) \(\Q(\sqrt{3}) \) None None \(0\) \(2\) \(-2\) \(2\) \(+\) \(q+\beta q^{2}+q^{3}+q^{4}-q^{5}+\beta q^{6}+q^{7}+\cdots\)
2415.2.a.l \(3\) \(19.284\) 3.3.148.1 None None \(-3\) \(-3\) \(-3\) \(3\) \(+\) \(q+(-1-\beta _{2})q^{2}-q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
2415.2.a.m \(3\) \(19.284\) 3.3.148.1 None None \(-1\) \(-3\) \(3\) \(3\) \(+\) \(q-\beta _{1}q^{2}-q^{3}+(\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots\)
2415.2.a.n \(3\) \(19.284\) 3.3.148.1 None None \(1\) \(-3\) \(3\) \(-3\) \(+\) \(q+\beta _{1}q^{2}-q^{3}+(\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots\)
2415.2.a.o \(5\) \(19.284\) 5.5.2508628.1 None None \(0\) \(-5\) \(-5\) \(-5\) \(+\) \(q-\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
2415.2.a.p \(6\) \(19.284\) 6.6.42978136.1 None None \(1\) \(-6\) \(-6\) \(-6\) \(-\) \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
2415.2.a.q \(6\) \(19.284\) 6.6.15751800.1 None None \(3\) \(-6\) \(-6\) \(6\) \(-\) \(q+\beta _{2}q^{2}-q^{3}+(\beta _{2}+\beta _{5})q^{4}-q^{5}+\cdots\)
2415.2.a.r \(7\) \(19.284\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None None \(-2\) \(7\) \(-7\) \(-7\) \(-\) \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
2415.2.a.s \(7\) \(19.284\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None None \(-1\) \(-7\) \(7\) \(-7\) \(-\) \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
2415.2.a.t \(7\) \(19.284\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None None \(2\) \(7\) \(-7\) \(7\) \(-\) \(q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
2415.2.a.u \(9\) \(19.284\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None None \(1\) \(-9\) \(9\) \(9\) \(-\) \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
2415.2.a.v \(10\) \(19.284\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(2\) \(10\) \(10\) \(-10\) \(-\) \(q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
2415.2.a.w \(10\) \(19.284\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(2\) \(10\) \(10\) \(10\) \(-\) \(q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
2415.4.a.a \(1\) \(142.490\) \(\Q\) None None \(0\) \(3\) \(-5\) \(7\) \(-\) \(q+3q^{3}-8q^{4}-5q^{5}+7q^{7}+9q^{9}+\cdots\)
2415.4.a.b \(1\) \(142.490\) \(\Q\) None None \(1\) \(-3\) \(-5\) \(-7\) \(-\) \(q+q^{2}-3q^{3}-7q^{4}-5q^{5}-3q^{6}+\cdots\)
2415.4.a.c \(1\) \(142.490\) \(\Q\) None None \(1\) \(-3\) \(-5\) \(-7\) \(+\) \(q+q^{2}-3q^{3}-7q^{4}-5q^{5}-3q^{6}+\cdots\)
2415.4.a.d \(1\) \(142.490\) \(\Q\) None None \(1\) \(-3\) \(5\) \(7\) \(-\) \(q+q^{2}-3q^{3}-7q^{4}+5q^{5}-3q^{6}+\cdots\)
2415.4.a.e \(12\) \(142.490\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(-4\) \(36\) \(60\) \(-84\) \(-\) \(q-\beta _{1}q^{2}+3q^{3}+(2+\beta _{1}+\beta _{2})q^{4}+\cdots\)
2415.4.a.f \(12\) \(142.490\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(-4\) \(36\) \(60\) \(84\) \(-\) \(q-\beta _{1}q^{2}+3q^{3}+(2+\beta _{1}+\beta _{2})q^{4}+\cdots\)
2415.4.a.g \(12\) \(142.490\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(-4\) \(36\) \(-60\) \(84\) \(-\) \(q-\beta _{1}q^{2}+3q^{3}+(3+\beta _{2})q^{4}-5q^{5}+\cdots\)
2415.4.a.h \(12\) \(142.490\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(-3\) \(-36\) \(60\) \(84\) \(-\) \(q-\beta _{1}q^{2}-3q^{3}+(4+\beta _{2})q^{4}+5q^{5}+\cdots\)
2415.4.a.i \(15\) \(142.490\) \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None None \(-3\) \(-45\) \(-75\) \(-105\) \(-\) \(q-\beta _{1}q^{2}-3q^{3}+(5+\beta _{2})q^{4}-5q^{5}+\cdots\)
2415.4.a.j \(15\) \(142.490\) \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None None \(1\) \(-45\) \(-75\) \(-105\) \(+\) \(q+\beta _{1}q^{2}-3q^{3}+(4+\beta _{2})q^{4}-5q^{5}+\cdots\)
2415.4.a.k \(15\) \(142.490\) \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None None \(2\) \(-45\) \(75\) \(-105\) \(-\) \(q+\beta _{1}q^{2}-3q^{3}+(4+\beta _{2})q^{4}+5q^{5}+\cdots\)
2415.4.a.l \(15\) \(142.490\) \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None None \(4\) \(45\) \(-75\) \(-105\) \(-\) \(q+\beta _{1}q^{2}+3q^{3}+(4+\beta _{2})q^{4}-5q^{5}+\cdots\)
2415.4.a.m \(16\) \(142.490\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(-6\) \(-48\) \(-80\) \(112\) \(-\) \(q-\beta _{1}q^{2}-3q^{3}+(4+\beta _{2})q^{4}-5q^{5}+\cdots\)
2415.4.a.n \(18\) \(142.490\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None None \(6\) \(-54\) \(-90\) \(126\) \(+\) \(q+\beta _{1}q^{2}-3q^{3}+(4+\beta _{2})q^{4}-5q^{5}+\cdots\)
2415.4.a.o \(19\) \(142.490\) \(\mathbb{Q}[x]/(x^{19} - \cdots)\) None None \(-2\) \(-57\) \(95\) \(-133\) \(+\) \(q-\beta _{1}q^{2}-3q^{3}+(4+\beta _{2})q^{4}+5q^{5}+\cdots\)
2415.4.a.p \(19\) \(142.490\) \(\mathbb{Q}[x]/(x^{19} - \cdots)\) None None \(0\) \(57\) \(-95\) \(-133\) \(+\) \(q+\beta _{1}q^{2}+3q^{3}+(5+\beta _{2})q^{4}-5q^{5}+\cdots\)
2415.4.a.q \(19\) \(142.490\) \(\mathbb{Q}[x]/(x^{19} - \cdots)\) None None \(0\) \(57\) \(-95\) \(133\) \(+\) \(q-\beta _{1}q^{2}+3q^{3}+(5+\beta _{2})q^{4}-5q^{5}+\cdots\)
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