## Results (displaying all 47 matches)

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 $$6$$ $$7$$ $$8$$ $$38$$ $$-$$