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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
3311.1.h.a \(1\) \(1.652\) \(\Q\) \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-3311}) \) \(\Q(\sqrt{473}) \) \(-2\) \(0\) \(0\) \(-1\) \(q-2q^{2}+3q^{4}-q^{7}-4q^{8}-q^{9}-q^{11}+\cdots\)
3311.1.h.b \(1\) \(1.652\) \(\Q\) \(\Q(\sqrt{-3311}) \) None \(-1\) \(-1\) \(-1\) \(1\) \(q-q^{2}-q^{3}-q^{5}+q^{6}+q^{7}+q^{8}+\cdots\)
3311.1.h.c \(1\) \(1.652\) \(\Q\) \(\Q(\sqrt{-3311}) \) None \(-1\) \(1\) \(1\) \(1\) \(q-q^{2}+q^{3}+q^{5}-q^{6}+q^{7}+q^{8}+\cdots\)
3311.1.h.d \(1\) \(1.652\) \(\Q\) \(\Q(\sqrt{-3311}) \) None \(1\) \(-1\) \(-1\) \(-1\) \(q+q^{2}-q^{3}-q^{5}-q^{6}-q^{7}-q^{8}+\cdots\)
3311.1.h.e \(1\) \(1.652\) \(\Q\) \(\Q(\sqrt{-3311}) \) None \(1\) \(1\) \(1\) \(-1\) \(q+q^{2}+q^{3}+q^{5}+q^{6}-q^{7}-q^{8}+\cdots\)
3311.1.h.f \(1\) \(1.652\) \(\Q\) \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-3311}) \) \(\Q(\sqrt{473}) \) \(2\) \(0\) \(0\) \(1\) \(q+2q^{2}+3q^{4}+q^{7}+4q^{8}-q^{9}-q^{11}+\cdots\)
3311.1.h.g \(2\) \(1.652\) \(\Q(\sqrt{-3}) \) None \(\Q(\sqrt{473}) \) \(-2\) \(0\) \(0\) \(-1\) \(q-q^{2}+\zeta_{6}^{2}q^{7}+q^{8}-q^{9}-q^{11}+\cdots\)
3311.1.h.h \(2\) \(1.652\) \(\Q(\sqrt{3}) \) \(\Q(\sqrt{-3311}) \) None \(-2\) \(0\) \(0\) \(2\) \(q-q^{2}-\beta q^{3}-\beta q^{5}+\beta q^{6}+q^{7}+q^{8}+\cdots\)
3311.1.h.i \(2\) \(1.652\) \(\Q(\sqrt{3}) \) \(\Q(\sqrt{-3311}) \) None \(2\) \(0\) \(0\) \(-2\) \(q+q^{2}-\beta q^{3}-\beta q^{5}-\beta q^{6}-q^{7}-q^{8}+\cdots\)
3311.1.h.j \(2\) \(1.652\) \(\Q(\sqrt{-3}) \) None \(\Q(\sqrt{473}) \) \(2\) \(0\) \(0\) \(1\) \(q+q^{2}-\zeta_{6}^{2}q^{7}-q^{8}-q^{9}-q^{11}+\cdots\)
3311.1.h.k \(3\) \(1.652\) \(\Q(\zeta_{18})^+\) \(\Q(\sqrt{-3311}) \) None \(0\) \(0\) \(0\) \(-3\) \(q+(-\beta _{1}+\beta _{2})q^{2}+\beta _{1}q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots\)
3311.1.h.l \(3\) \(1.652\) \(\Q(\zeta_{18})^+\) \(\Q(\sqrt{-3311}) \) None \(0\) \(0\) \(0\) \(3\) \(q+(\beta _{1}-\beta _{2})q^{2}-\beta _{1}q^{3}+(1-\beta _{1})q^{4}+\cdots\)
3311.1.h.m \(3\) \(1.652\) \(\Q(\zeta_{18})^+\) \(\Q(\sqrt{-3311}) \) None \(0\) \(0\) \(0\) \(-3\) \(q+(-\beta _{1}+\beta _{2})q^{2}-\beta _{1}q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots\)
3311.1.h.n \(3\) \(1.652\) \(\Q(\zeta_{18})^+\) \(\Q(\sqrt{-3311}) \) None \(0\) \(0\) \(0\) \(3\) \(q+(\beta _{1}-\beta _{2})q^{2}+\beta _{1}q^{3}+(1-\beta _{1})q^{4}+\cdots\)
3311.1.h.o \(6\) \(1.652\) \(\Q(\zeta_{36})^+\) \(\Q(\sqrt{-3311}) \) None \(0\) \(0\) \(0\) \(-6\) \(q+(-\beta _{2}-\beta _{4})q^{2}-\beta _{1}q^{3}+(1-\beta _{4}+\cdots)q^{4}+\cdots\)
3311.1.h.p \(6\) \(1.652\) \(\Q(\zeta_{36})^+\) \(\Q(\sqrt{-3311}) \) None \(0\) \(0\) \(0\) \(6\) \(q+(\beta _{2}+\beta _{4})q^{2}-\beta _{1}q^{3}+(1-\beta _{4})q^{4}+\cdots\)
3311.1.bm.a \(2\) \(1.652\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-7}) \) None \(-2\) \(0\) \(0\) \(-1\) \(q-q^{2}-\zeta_{6}q^{7}+q^{8}+\zeta_{6}q^{9}-q^{11}+\cdots\)
3311.1.bm.b \(2\) \(1.652\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-7}) \) None \(2\) \(0\) \(0\) \(1\) \(q+q^{2}+\zeta_{6}q^{7}-q^{8}+\zeta_{6}q^{9}-q^{11}+\cdots\)
3311.1.bq.a \(4\) \(1.652\) \(\Q(\zeta_{10})\) \(\Q(\sqrt{-7}) \) None \(-2\) \(0\) \(0\) \(-1\) \(q+(\zeta_{10}^{2}+\zeta_{10}^{4})q^{2}+(-\zeta_{10}-\zeta_{10}^{3}+\cdots)q^{4}+\cdots\)
3311.1.bq.b \(4\) \(1.652\) \(\Q(\zeta_{10})\) \(\Q(\sqrt{-7}) \) None \(2\) \(0\) \(0\) \(1\) \(q+(-\zeta_{10}^{2}-\zeta_{10}^{4})q^{2}+(-\zeta_{10}-\zeta_{10}^{3}+\cdots)q^{4}+\cdots\)
3311.1.bx.a \(6\) \(1.652\) \(\Q(\zeta_{14})\) \(\Q(\sqrt{-7}) \) None \(-2\) \(0\) \(0\) \(6\) \(q+(\zeta_{14}^{4}-\zeta_{14}^{5})q^{2}+(-\zeta_{14}+\zeta_{14}^{2}+\cdots)q^{4}+\cdots\)
3311.1.bx.b \(6\) \(1.652\) \(\Q(\zeta_{14})\) \(\Q(\sqrt{-7}) \) None \(2\) \(0\) \(0\) \(-6\) \(q+(-\zeta_{14}^{4}+\zeta_{14}^{5})q^{2}+(-\zeta_{14}+\zeta_{14}^{2}+\cdots)q^{4}+\cdots\)
3311.1.cm.a \(8\) \(1.652\) \(\Q(\zeta_{15})\) \(\Q(\sqrt{-7}) \) None \(2\) \(0\) \(0\) \(1\) \(q+(\zeta_{30}^{2}+\zeta_{30}^{4})q^{2}+(\zeta_{30}^{4}+\zeta_{30}^{6}+\cdots)q^{4}+\cdots\)
3311.1.cm.b \(8\) \(1.652\) \(\Q(\zeta_{15})\) \(\Q(\sqrt{-7}) \) None \(2\) \(0\) \(0\) \(1\) \(q+(-\zeta_{30}^{7}+\zeta_{30}^{14})q^{2}+(\zeta_{30}^{6}-\zeta_{30}^{13}+\cdots)q^{4}+\cdots\)
3311.1.co.a \(8\) \(1.652\) \(\Q(\zeta_{15})\) \(\Q(\sqrt{-7}) \) None \(-2\) \(0\) \(0\) \(-1\) \(q+(\zeta_{30}-\zeta_{30}^{2})q^{2}+(\zeta_{30}^{2}-\zeta_{30}^{3}+\cdots)q^{4}+\cdots\)
3311.1.co.b \(8\) \(1.652\) \(\Q(\zeta_{15})\) \(\Q(\sqrt{-7}) \) None \(2\) \(0\) \(0\) \(1\) \(q+(-\zeta_{30}^{7}-\zeta_{30}^{11})q^{2}+(-\zeta_{30}^{3}+\cdots)q^{4}+\cdots\)
3311.1.dr.a \(12\) \(1.652\) \(\Q(\zeta_{21})\) \(\Q(\sqrt{-7}) \) None \(-2\) \(0\) \(0\) \(6\) \(q+(\zeta_{42}+\zeta_{42}^{17})q^{2}+(\zeta_{42}^{2}-\zeta_{42}^{13}+\cdots)q^{4}+\cdots\)
3311.1.dr.b \(12\) \(1.652\) \(\Q(\zeta_{21})\) \(\Q(\sqrt{-7}) \) None \(2\) \(0\) \(0\) \(-6\) \(q+(-\zeta_{42}-\zeta_{42}^{17})q^{2}+(\zeta_{42}^{2}-\zeta_{42}^{13}+\cdots)q^{4}+\cdots\)
3311.1.ev.a \(24\) \(1.652\) \(\Q(\zeta_{35})\) \(\Q(\sqrt{-7}) \) None \(2\) \(0\) \(0\) \(-6\) \(q+(\zeta_{70}^{16}-\zeta_{70}^{17})q^{2}+(\zeta_{70}^{32}-\zeta_{70}^{33}+\cdots)q^{4}+\cdots\)
3311.1.ev.b \(24\) \(1.652\) \(\Q(\zeta_{35})\) \(\Q(\sqrt{-7}) \) None \(2\) \(0\) \(0\) \(-6\) \(q+(\zeta_{70}^{2}-\zeta_{70}^{31})q^{2}+(\zeta_{70}^{4}-\zeta_{70}^{27}+\cdots)q^{4}+\cdots\)
3311.1.ex.a \(24\) \(1.652\) \(\Q(\zeta_{35})\) \(\Q(\sqrt{-7}) \) None \(-2\) \(0\) \(0\) \(6\) \(q+(\zeta_{70}^{23}+\zeta_{70}^{31})q^{2}+(-\zeta_{70}^{11}+\cdots)q^{4}+\cdots\)
3311.1.ex.b \(24\) \(1.652\) \(\Q(\zeta_{35})\) \(\Q(\sqrt{-7}) \) None \(2\) \(0\) \(0\) \(-6\) \(q+(-\zeta_{70}^{3}+\zeta_{70}^{16})q^{2}+(\zeta_{70}^{6}-\zeta_{70}^{19}+\cdots)q^{4}+\cdots\)
3311.1.gb.a \(48\) \(1.652\) \(\Q(\zeta_{210})\) \(\Q(\sqrt{-7}) \) None \(-2\) \(0\) \(0\) \(6\) \(q+(-\zeta_{210}^{43}-\zeta_{210}^{101})q^{2}+(-\zeta_{210}^{39}+\cdots)q^{4}+\cdots\)
3311.1.gb.b \(48\) \(1.652\) \(\Q(\zeta_{210})\) \(\Q(\sqrt{-7}) \) None \(2\) \(0\) \(0\) \(-6\) \(q+(\zeta_{210}-\zeta_{210}^{38})q^{2}+(\zeta_{210}^{2}-\zeta_{210}^{39}+\cdots)q^{4}+\cdots\)
3311.1.gd.a \(48\) \(1.652\) \(\Q(\zeta_{210})\) \(\Q(\sqrt{-7}) \) None \(-2\) \(0\) \(0\) \(6\) \(q+(\zeta_{210}^{2}+\zeta_{210}^{34})q^{2}+(\zeta_{210}^{4}+\zeta_{210}^{36}+\cdots)q^{4}+\cdots\)
3311.1.gd.b \(48\) \(1.652\) \(\Q(\zeta_{210})\) \(\Q(\sqrt{-7}) \) None \(-2\) \(0\) \(0\) \(6\) \(q+(\zeta_{210}^{44}-\zeta_{210}^{97})q^{2}+(\zeta_{210}^{36}+\zeta_{210}^{88}+\cdots)q^{4}+\cdots\)
3311.2.a.a \(1\) \(26.438\) \(\Q\) None None \(1\) \(2\) \(-4\) \(-1\) \(-\) \(q+q^{2}+2q^{3}-q^{4}-4q^{5}+2q^{6}-q^{7}+\cdots\)
3311.2.a.b \(1\) \(26.438\) \(\Q\) None None \(1\) \(2\) \(0\) \(1\) \(+\) \(q+q^{2}+2q^{3}-q^{4}+2q^{6}+q^{7}-3q^{8}+\cdots\)
3311.2.a.c \(1\) \(26.438\) \(\Q\) None None \(2\) \(1\) \(-1\) \(-1\) \(+\) \(q+2q^{2}+q^{3}+2q^{4}-q^{5}+2q^{6}-q^{7}+\cdots\)
3311.2.a.d \(15\) \(26.438\) \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None None \(-2\) \(-4\) \(1\) \(15\) \(+\) \(q-\beta _{1}q^{2}-\beta _{14}q^{3}+(1+\beta _{2})q^{4}-\beta _{7}q^{5}+\cdots\)
3311.2.a.e \(16\) \(26.438\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(-4\) \(-3\) \(-4\) \(16\) \(+\) \(q-\beta _{1}q^{2}+\beta _{14}q^{3}+\beta _{2}q^{4}-\beta _{11}q^{5}+\cdots\)
3311.2.a.f \(18\) \(26.438\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None None \(-4\) \(3\) \(4\) \(-18\) \(+\) \(q-\beta _{1}q^{2}-\beta _{5}q^{3}+(1+\beta _{2})q^{4}-\beta _{6}q^{5}+\cdots\)
3311.2.a.g \(19\) \(26.438\) \(\mathbb{Q}[x]/(x^{19} - \cdots)\) None None \(1\) \(-9\) \(-6\) \(-19\) \(+\) \(q+\beta _{1}q^{2}+\beta _{15}q^{3}+(1+\beta _{2})q^{4}+\beta _{3}q^{5}+\cdots\)
3311.2.a.h \(32\) \(26.438\) None None \(3\) \(2\) \(1\) \(-32\) \(-\)
3311.2.a.i \(35\) \(26.438\) None None \(-5\) \(3\) \(16\) \(-35\) \(-\)
3311.2.a.j \(35\) \(26.438\) None None \(2\) \(-4\) \(-1\) \(35\) \(-\)
3311.2.a.k \(38\) \(26.438\) None None \(6\) \(7\) \(8\) \(38\) \(-\)


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