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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2624.1.h.a \(1\) \(1.310\) \(\Q\) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-41}) \) \(\Q(\sqrt{41}) \) \(0\) \(0\) \(2\) \(0\) \(q+2q^{5}-q^{9}+3q^{25}+2q^{37}+q^{41}+\cdots\)
2624.1.h.b \(2\) \(1.310\) \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-41}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta q^{3}-\beta q^{7}+q^{9}+\beta q^{11}-\beta q^{19}+\cdots\)
2624.1.h.c \(4\) \(1.310\) \(\Q(\zeta_{16})^+\) \(\Q(\sqrt{-41}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{3}-\beta _{2}q^{5}-\beta _{1}q^{7}+(1-\beta _{2}+\cdots)q^{9}+\cdots\)
2624.1.k.a \(2\) \(1.310\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{5}+iq^{9}+(1+i)q^{13}+(1-i+\cdots)q^{17}+\cdots\)
2624.1.m.a \(2\) \(1.310\) \(\Q(\sqrt{-1}) \) None \(\Q(\sqrt{41}) \) \(0\) \(0\) \(2\) \(0\) \(q+(1+i)q^{5}+iq^{9}+iq^{25}+iq^{31}+\cdots\)
2624.1.bh.a \(4\) \(1.310\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+(-1+\zeta_{8}-\zeta_{8}^{2}+\cdots)q^{9}+\cdots\)
2624.1.bh.b \(4\) \(1.310\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+(-1+\zeta_{8}-\zeta_{8}^{2}+\cdots)q^{9}+\cdots\)
2624.1.bi.a \(4\) \(1.310\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{3}q^{9}+(-\zeta_{8}+\zeta_{8}^{2})q^{13}+(1+\zeta_{8}+\cdots)q^{17}+\cdots\)
2624.1.bt.a \(4\) \(1.310\) \(\Q(\zeta_{10})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q+(\zeta_{10}^{3}-\zeta_{10}^{4})q^{5}+q^{9}+(-\zeta_{10}^{2}+\cdots)q^{13}+\cdots\)
2624.1.bx.a \(4\) \(1.310\) \(\Q(\zeta_{10})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q+(-\zeta_{10}^{3}+\zeta_{10}^{4})q^{5}-q^{9}+(\zeta_{10}^{2}+\cdots)q^{13}+\cdots\)
2624.1.bz.a \(8\) \(1.310\) \(\Q(\zeta_{20})\) None None \(0\) \(-4\) \(0\) \(0\) \(q+(\zeta_{20}^{4}-\zeta_{20}^{6})q^{3}+(\zeta_{20}^{3}-\zeta_{20}^{9}+\cdots)q^{5}+\cdots\)
2624.1.bz.b \(8\) \(1.310\) \(\Q(\zeta_{20})\) None None \(0\) \(4\) \(0\) \(0\) \(q+(-\zeta_{20}^{4}+\zeta_{20}^{6})q^{3}+(\zeta_{20}^{3}-\zeta_{20}^{9}+\cdots)q^{5}+\cdots\)
2624.1.cj.a \(8\) \(1.310\) \(\Q(\zeta_{16})\) None \(\Q(\sqrt{41}) \) \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{16}^{5}q^{2}-\zeta_{16}^{2}q^{4}+(-\zeta_{16}+\zeta_{16}^{6}+\cdots)q^{5}+\cdots\)
2624.1.cz.a \(8\) \(1.310\) \(\Q(\zeta_{20})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{20}-\zeta_{20}^{7})q^{5}+\zeta_{20}^{5}q^{9}+(-\zeta_{20}^{3}+\cdots)q^{13}+\cdots\)
2624.1.dq.a \(16\) \(1.310\) \(\Q(\zeta_{40})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{40}^{3}+\zeta_{40}^{19})q^{5}-\zeta_{40}^{5}q^{9}+\cdots\)
2624.1.dr.a \(16\) \(1.310\) \(\Q(\zeta_{40})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{40}+\zeta_{40}^{14})q^{3}+(\zeta_{40}^{2}-\zeta_{40}^{8}+\cdots)q^{9}+\cdots\)
2624.1.dr.b \(16\) \(1.310\) \(\Q(\zeta_{40})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{40}-\zeta_{40}^{14})q^{3}+(\zeta_{40}^{2}-\zeta_{40}^{8}+\cdots)q^{9}+\cdots\)
2624.2.a.a \(1\) \(20.953\) \(\Q\) None None \(0\) \(-2\) \(-2\) \(-2\) \(-\) \(q-2q^{3}-2q^{5}-2q^{7}+q^{9}-2q^{11}+\cdots\)
2624.2.a.b \(1\) \(20.953\) \(\Q\) None None \(0\) \(-2\) \(2\) \(0\) \(-\) \(q-2q^{3}+2q^{5}+q^{9}+6q^{11}+4q^{13}+\cdots\)
2624.2.a.c \(1\) \(20.953\) \(\Q\) None None \(0\) \(-2\) \(2\) \(4\) \(-\) \(q-2q^{3}+2q^{5}+4q^{7}+q^{9}-2q^{11}+\cdots\)
2624.2.a.d \(1\) \(20.953\) \(\Q\) None None \(0\) \(0\) \(2\) \(-2\) \(+\) \(q+2q^{5}-2q^{7}-3q^{9}+4q^{13}-2q^{17}+\cdots\)
2624.2.a.e \(1\) \(20.953\) \(\Q\) None None \(0\) \(0\) \(2\) \(2\) \(-\) \(q+2q^{5}+2q^{7}-3q^{9}+4q^{13}-2q^{17}+\cdots\)
2624.2.a.f \(1\) \(20.953\) \(\Q\) None None \(0\) \(2\) \(-2\) \(2\) \(+\) \(q+2q^{3}-2q^{5}+2q^{7}+q^{9}+2q^{11}+\cdots\)
2624.2.a.g \(1\) \(20.953\) \(\Q\) None None \(0\) \(2\) \(2\) \(-4\) \(+\) \(q+2q^{3}+2q^{5}-4q^{7}+q^{9}+2q^{11}+\cdots\)
2624.2.a.h \(1\) \(20.953\) \(\Q\) None None \(0\) \(2\) \(2\) \(0\) \(-\) \(q+2q^{3}+2q^{5}+q^{9}-6q^{11}+4q^{13}+\cdots\)
2624.2.a.i \(2\) \(20.953\) \(\Q(\sqrt{3}) \) None None \(0\) \(-2\) \(0\) \(2\) \(+\) \(q+(-1+\beta )q^{3}+(1+\beta )q^{7}+(1-2\beta )q^{9}+\cdots\)
2624.2.a.j \(2\) \(20.953\) \(\Q(\sqrt{2}) \) None None \(0\) \(0\) \(0\) \(-4\) \(+\) \(q+\beta q^{3}-2\beta q^{5}+(-2+\beta )q^{7}-q^{9}+\cdots\)
2624.2.a.k \(2\) \(20.953\) \(\Q(\sqrt{2}) \) None None \(0\) \(0\) \(0\) \(0\) \(+\) \(q+\beta q^{3}+\beta q^{7}-q^{9}-\beta q^{11}+2q^{13}+\cdots\)
2624.2.a.l \(2\) \(20.953\) \(\Q(\sqrt{2}) \) None None \(0\) \(0\) \(0\) \(4\) \(-\) \(q+\beta q^{3}+2\beta q^{5}+(2+\beta )q^{7}-q^{9}+3\beta q^{11}+\cdots\)
2624.2.a.m \(2\) \(20.953\) \(\Q(\sqrt{3}) \) None None \(0\) \(2\) \(0\) \(-2\) \(-\) \(q+(1+\beta )q^{3}+(-1+\beta )q^{7}+(1+2\beta )q^{9}+\cdots\)
2624.2.a.n \(3\) \(20.953\) 3.3.148.1 None None \(0\) \(-4\) \(2\) \(2\) \(+\) \(q+(-1-\beta _{1})q^{3}+(1-\beta _{1}+\beta _{2})q^{5}+\cdots\)
2624.2.a.o \(3\) \(20.953\) 3.3.788.1 None None \(0\) \(-2\) \(-2\) \(-4\) \(+\) \(q+(-1+\beta _{1})q^{3}+(-1+\beta _{2})q^{5}+(-1+\cdots)q^{7}+\cdots\)
2624.2.a.p \(3\) \(20.953\) 3.3.148.1 None None \(0\) \(-2\) \(-2\) \(2\) \(+\) \(q+(-1+\beta _{1})q^{3}+(-1+\beta _{1}+\beta _{2})q^{5}+\cdots\)
2624.2.a.q \(3\) \(20.953\) 3.3.148.1 None None \(0\) \(0\) \(2\) \(-6\) \(+\) \(q+\beta _{2}q^{3}+(1-\beta _{1}-\beta _{2})q^{5}+(-2+\beta _{2})q^{7}+\cdots\)
2624.2.a.r \(3\) \(20.953\) 3.3.148.1 None None \(0\) \(0\) \(2\) \(6\) \(-\) \(q-\beta _{2}q^{3}+(1-\beta _{1}-\beta _{2})q^{5}+(2-\beta _{2})q^{7}+\cdots\)
2624.2.a.s \(3\) \(20.953\) 3.3.148.1 None None \(0\) \(2\) \(-2\) \(-2\) \(+\) \(q+(1-\beta _{1})q^{3}+(-1+\beta _{1}+\beta _{2})q^{5}+\cdots\)
2624.2.a.t \(3\) \(20.953\) 3.3.788.1 None None \(0\) \(2\) \(-2\) \(4\) \(-\) \(q+(1-\beta _{1})q^{3}+(-1+\beta _{2})q^{5}+(1+\beta _{1}+\cdots)q^{7}+\cdots\)
2624.2.a.u \(3\) \(20.953\) 3.3.148.1 None None \(0\) \(4\) \(2\) \(-2\) \(-\) \(q+(1+\beta _{1})q^{3}+(1-\beta _{1}+\beta _{2})q^{5}+(-1+\cdots)q^{7}+\cdots\)
2624.2.a.v \(4\) \(20.953\) 4.4.25808.1 None None \(0\) \(-2\) \(-4\) \(0\) \(+\) \(q+(\beta _{1}-\beta _{2})q^{3}+(-2+\beta _{2}-\beta _{3})q^{5}+\cdots\)
2624.2.a.w \(4\) \(20.953\) \(\Q(\sqrt{2}, \sqrt{5})\) None None \(0\) \(0\) \(-4\) \(0\) \(+\) \(q+\beta _{1}q^{3}+(-1-\beta _{2})q^{5}+\beta _{3}q^{7}+\beta _{2}q^{9}+\cdots\)
2624.2.a.x \(4\) \(20.953\) 4.4.25088.1 None None \(0\) \(0\) \(4\) \(0\) \(-\) \(q+\beta _{1}q^{3}+(1+\beta _{2})q^{5}+(2\beta _{1}-\beta _{3})q^{7}+\cdots\)
2624.2.a.y \(4\) \(20.953\) 4.4.25808.1 None None \(0\) \(2\) \(-4\) \(0\) \(-\) \(q+(-\beta _{1}+\beta _{2})q^{3}+(-2+\beta _{2}-\beta _{3})q^{5}+\cdots\)
2624.2.a.z \(7\) \(20.953\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None None \(0\) \(-4\) \(2\) \(6\) \(-\) \(q+(-1-\beta _{2})q^{3}-\beta _{5}q^{5}+(1-\beta _{3}+\beta _{5}+\cdots)q^{7}+\cdots\)
2624.2.a.ba \(7\) \(20.953\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None None \(0\) \(4\) \(2\) \(-6\) \(-\) \(q+(1+\beta _{2})q^{3}-\beta _{5}q^{5}+(-1+\beta _{3}-\beta _{5}+\cdots)q^{7}+\cdots\)
2624.2.a.bb \(8\) \(20.953\) 8.8.\(\cdots\).1 None None \(0\) \(0\) \(-4\) \(0\) \(-\) \(q-\beta _{3}q^{3}-\beta _{5}q^{5}+\beta _{2}q^{7}+(2+\beta _{1}+\cdots)q^{9}+\cdots\)
2624.2.b.a \(2\) \(20.953\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}-q^{9}+iq^{11}-2iq^{13}+2q^{17}+\cdots\)
2624.2.b.b \(2\) \(20.953\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}-q^{9}+iq^{11}+2iq^{13}+2q^{17}+\cdots\)
2624.2.b.c \(4\) \(20.953\) \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(-12\) \(q-\zeta_{12}^{3}q^{3}+(\zeta_{12}^{2}+2\zeta_{12}^{3})q^{5}+(-3+\cdots)q^{7}+\cdots\)
2624.2.b.d \(4\) \(20.953\) \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(12\) \(q-\zeta_{12}^{3}q^{3}+(-\zeta_{12}^{2}-2\zeta_{12}^{3})q^{5}+\cdots\)
2624.2.b.e \(12\) \(20.953\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{7}q^{3}+\beta _{5}q^{5}+(-\beta _{1}+\beta _{6})q^{7}+\cdots\)
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