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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
825.1.l.a \(2\) \(0.412\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}+iq^{4}-q^{9}+iq^{11}-q^{12}+\cdots\)
825.1.l.b \(2\) \(0.412\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-11}) \) None \(0\) \(2\) \(0\) \(0\) \(q+q^{3}+iq^{4}+q^{9}-iq^{11}+iq^{12}+\cdots\)
825.1.co.a \(8\) \(0.412\) \(\Q(\zeta_{20})\) \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{20}^{3}q^{3}-\zeta_{20}q^{4}+\zeta_{20}^{5}q^{5}+\zeta_{20}^{6}q^{9}+\cdots\)
825.1.co.b \(8\) \(0.412\) \(\Q(\zeta_{20})\) \(\Q(\sqrt{-11}) \) None \(0\) \(2\) \(0\) \(0\) \(q-\zeta_{20}^{4}q^{3}-\zeta_{20}q^{4}-\zeta_{20}^{5}q^{5}+\zeta_{20}^{8}q^{9}+\cdots\)
825.2.a.a \(1\) \(6.588\) \(\Q\) None None \(-1\) \(1\) \(0\) \(-4\) \(+\) \(q-q^{2}+q^{3}-q^{4}-q^{6}-4q^{7}+3q^{8}+\cdots\)
825.2.a.b \(1\) \(6.588\) \(\Q\) None None \(0\) \(-1\) \(0\) \(1\) \(+\) \(q-q^{3}-2q^{4}+q^{7}+q^{9}-q^{11}+2q^{12}+\cdots\)
825.2.a.c \(1\) \(6.588\) \(\Q\) None None \(0\) \(1\) \(0\) \(-1\) \(+\) \(q+q^{3}-2q^{4}-q^{7}+q^{9}-q^{11}-2q^{12}+\cdots\)
825.2.a.d \(2\) \(6.588\) \(\Q(\sqrt{2}) \) None None \(-2\) \(-2\) \(0\) \(2\) \(-\) \(q+(-1+\beta )q^{2}-q^{3}+(1-2\beta )q^{4}+(1+\cdots)q^{6}+\cdots\)
825.2.a.e \(2\) \(6.588\) \(\Q(\sqrt{3}) \) None None \(0\) \(-2\) \(0\) \(-4\) \(+\) \(q+\beta q^{2}-q^{3}+q^{4}-\beta q^{6}-2q^{7}-\beta q^{8}+\cdots\)
825.2.a.f \(2\) \(6.588\) \(\Q(\sqrt{2}) \) None None \(2\) \(2\) \(0\) \(-2\) \(-\) \(q+(1+\beta )q^{2}+q^{3}+(1+2\beta )q^{4}+(1+\beta )q^{6}+\cdots\)
825.2.a.g \(2\) \(6.588\) \(\Q(\sqrt{2}) \) None None \(2\) \(2\) \(0\) \(4\) \(-\) \(q+(1+\beta )q^{2}+q^{3}+(1+2\beta )q^{4}+(1+\beta )q^{6}+\cdots\)
825.2.a.h \(3\) \(6.588\) 3.3.148.1 None None \(-3\) \(3\) \(0\) \(-8\) \(+\) \(q+(-1-\beta _{2})q^{2}+q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
825.2.a.i \(3\) \(6.588\) 3.3.568.1 None None \(-2\) \(-3\) \(0\) \(3\) \(-\) \(q+(-1+\beta _{1})q^{2}-q^{3}+(3+\beta _{2})q^{4}+\cdots\)
825.2.a.j \(3\) \(6.588\) 3.3.148.1 None None \(-1\) \(-3\) \(0\) \(-4\) \(+\) \(q-\beta _{1}q^{2}-q^{3}+(\beta _{1}+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
825.2.a.k \(3\) \(6.588\) 3.3.148.1 None None \(1\) \(-3\) \(0\) \(0\) \(-\) \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{1}+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
825.2.a.l \(3\) \(6.588\) 3.3.148.1 None None \(1\) \(3\) \(0\) \(4\) \(-\) \(q+\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
825.2.a.m \(3\) \(6.588\) 3.3.568.1 None None \(2\) \(3\) \(0\) \(-3\) \(-\) \(q+(1-\beta _{1})q^{2}+q^{3}+(3+\beta _{2})q^{4}+(1+\cdots)q^{6}+\cdots\)
825.2.a.n \(3\) \(6.588\) 3.3.148.1 None None \(3\) \(-3\) \(0\) \(8\) \(-\) \(q+(1+\beta _{2})q^{2}-q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
825.2.c.a \(2\) \(6.588\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+iq^{3}+q^{4}-q^{6}+4iq^{7}+\cdots\)
825.2.c.b \(2\) \(6.588\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}+2q^{4}-iq^{7}-q^{9}-q^{11}+\cdots\)
825.2.c.c \(4\) \(6.588\) \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{2}q^{2}+\zeta_{12}q^{3}-q^{4}-\zeta_{12}^{3}q^{6}+\cdots\)
825.2.c.d \(4\) \(6.588\) \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{8}+\zeta_{8}^{2})q^{2}-\zeta_{8}q^{3}+(-1-2\zeta_{8}^{3})q^{4}+\cdots\)
825.2.c.e \(4\) \(6.588\) \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{8}+\zeta_{8}^{2})q^{2}-\zeta_{8}q^{3}+(-1-2\zeta_{8}^{3})q^{4}+\cdots\)
825.2.c.f \(6\) \(6.588\) 6.0.5161984.1 None None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{3}+\beta _{4})q^{2}-\beta _{3}q^{3}+(-3-\beta _{1}+\cdots)q^{4}+\cdots\)
825.2.c.g \(6\) \(6.588\) 6.0.350464.1 None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+\beta _{3}q^{3}+(-1+\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\)
825.2.d.a \(4\) \(6.588\) \(\Q(i, \sqrt{11})\) \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{1}+\beta _{2})q^{3}+2q^{4}+(2-\beta _{3})q^{9}+\cdots\)
825.2.d.b \(8\) \(6.588\) 8.0.619810816.2 None None \(0\) \(-2\) \(0\) \(16\) \(q+(\beta _{3}-\beta _{4}+\beta _{5}-\beta _{6})q^{2}+(-\beta _{4}+\beta _{5}+\cdots)q^{3}+\cdots\)
825.2.d.c \(8\) \(6.588\) 8.0.619810816.2 None None \(0\) \(-2\) \(0\) \(-16\) \(q+(\beta _{3}-\beta _{4}+\beta _{5}-\beta _{6})q^{2}+(-\beta _{3}+\beta _{6}+\cdots)q^{3}+\cdots\)
825.2.d.d \(8\) \(6.588\) 8.0.619810816.2 None None \(0\) \(2\) \(0\) \(-16\) \(q+(\beta _{3}-\beta _{4}+\beta _{5}-\beta _{6})q^{2}+(\beta _{3}-\beta _{6}+\cdots)q^{3}+\cdots\)
825.2.d.e \(8\) \(6.588\) 8.0.619810816.2 None None \(0\) \(2\) \(0\) \(16\) \(q+(\beta _{3}-\beta _{4}+\beta _{5}-\beta _{6})q^{2}+(\beta _{4}-\beta _{5}+\cdots)q^{3}+\cdots\)
825.2.d.f \(32\) \(6.588\) None None \(0\) \(0\) \(0\) \(0\)
825.2.f.a \(2\) \(6.588\) \(\Q(\sqrt{-11}) \) \(\Q(\sqrt{-11}) \) None \(0\) \(-1\) \(0\) \(0\) \(q-\beta q^{3}-2q^{4}+(-3+\beta )q^{9}+(-1+\cdots)q^{11}+\cdots\)
825.2.f.b \(4\) \(6.588\) \(\Q(i, \sqrt{11})\) \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{3}-2q^{4}+(3+\beta _{2})q^{9}+(1+2\beta _{2}+\cdots)q^{11}+\cdots\)
825.2.f.c \(8\) \(6.588\) 8.0.619810816.2 None None \(0\) \(2\) \(0\) \(0\) \(q+(\beta _{3}+\beta _{4})q^{2}+(-\beta _{3}-\beta _{5})q^{3}+(1+\cdots)q^{4}+\cdots\)
825.2.f.d \(8\) \(6.588\) 8.0.619810816.2 None None \(0\) \(2\) \(0\) \(0\) \(q+(-\beta _{3}-\beta _{4})q^{2}-\beta _{4}q^{3}+(1-\beta _{4}+\cdots)q^{4}+\cdots\)
825.2.f.e \(16\) \(6.588\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(-2\) \(0\) \(0\) \(q+\beta _{3}q^{2}+\beta _{4}q^{3}+(1+\beta _{1})q^{4}+\beta _{5}q^{6}+\cdots\)
825.2.f.f \(16\) \(6.588\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{6}q^{2}-\beta _{5}q^{3}+(2-\beta _{2})q^{4}+\beta _{14}q^{6}+\cdots\)
825.2.f.g \(16\) \(6.588\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(2\) \(0\) \(0\) \(q+\beta _{3}q^{2}-\beta _{4}q^{3}+(1+\beta _{1})q^{4}-\beta _{5}q^{6}+\cdots\)
825.2.j.a \(8\) \(6.588\) \(\Q(\zeta_{24})\) None None \(-4\) \(0\) \(0\) \(-8\) \(q-\zeta_{24}^{2}q^{2}-\zeta_{24}q^{3}+(-1+\zeta_{24}^{2}+\cdots)q^{4}+\cdots\)
825.2.j.b \(8\) \(6.588\) \(\Q(\zeta_{24})\) None None \(4\) \(0\) \(0\) \(8\) \(q+(1-\zeta_{24}^{2}+\zeta_{24}^{3})q^{2}-\zeta_{24}q^{3}+\cdots\)
825.2.j.c \(24\) \(6.588\) None None \(0\) \(0\) \(0\) \(0\)
825.2.j.d \(32\) \(6.588\) None None \(0\) \(0\) \(0\) \(0\)
825.2.k.a \(4\) \(6.588\) \(\Q(\zeta_{8})\) None None \(-4\) \(-4\) \(0\) \(-8\) \(q+(-1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{2}+(-1-\zeta_{8}^{2}+\cdots)q^{3}+\cdots\)
825.2.k.b \(4\) \(6.588\) \(\Q(\zeta_{8})\) None None \(-4\) \(-4\) \(0\) \(8\) \(q+(-1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{2}+(-1-\zeta_{8}^{2}+\cdots)q^{3}+\cdots\)
825.2.k.c \(4\) \(6.588\) \(\Q(\zeta_{8})\) None None \(-4\) \(0\) \(0\) \(8\) \(q+(-1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{2}+(-\zeta_{8}-\zeta_{8}^{2}+\cdots)q^{3}+\cdots\)
825.2.k.d \(4\) \(6.588\) \(\Q(i, \sqrt{6})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}-\beta _{1}q^{3}+\beta _{2}q^{4}-3\beta _{2}q^{6}+\cdots\)
825.2.k.e \(4\) \(6.588\) \(\Q(i, \sqrt{6})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+\beta _{1}q^{3}+\beta _{2}q^{4}+3\beta _{2}q^{6}+\cdots\)
825.2.k.f \(4\) \(6.588\) \(\Q(\zeta_{8})\) None None \(4\) \(4\) \(0\) \(8\) \(q+(1-\zeta_{8}^{2}-\zeta_{8}^{3})q^{2}+(1-\zeta_{8}-\zeta_{8}^{3})q^{3}+\cdots\)
825.2.k.g \(4\) \(6.588\) \(\Q(\zeta_{8})\) None None \(4\) \(4\) \(0\) \(-8\) \(q+(1-\zeta_{8}^{2}-\zeta_{8}^{3})q^{2}+(1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+\cdots\)
825.2.k.h \(4\) \(6.588\) \(\Q(\zeta_{8})\) None None \(4\) \(4\) \(0\) \(8\) \(q+(1-\zeta_{8}^{2}-\zeta_{8}^{3})q^{2}+(1+\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+\cdots\)
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