## Results (1-50 of 373 matches)

Label Dim $A$ Field CM RM Traces Fricke sign $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
336.1.o.a $1$ $0.168$ $$\Q$$ $$\Q(\sqrt{-3})$$, $$\Q(\sqrt{-21})$$ $$\Q(\sqrt{7})$$ $$0$$ $$-1$$ $$0$$ $$1$$ $$q-q^{3}+q^{7}+q^{9}+2q^{19}-q^{21}-q^{25}+\cdots$$
336.1.o.b $1$ $0.168$ $$\Q$$ $$\Q(\sqrt{-3})$$, $$\Q(\sqrt{-21})$$ $$\Q(\sqrt{7})$$ $$0$$ $$1$$ $$0$$ $$-1$$ $$q+q^{3}-q^{7}+q^{9}-2q^{19}-q^{21}-q^{25}+\cdots$$
336.1.z.a $2$ $0.168$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$0$$ $$1$$ $$q-\zeta_{6}q^{3}-\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}+(-\zeta_{6}+\cdots)q^{13}+\cdots$$
336.1.z.b $2$ $0.168$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$1$$ $$0$$ $$-1$$ $$q+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}+(-\zeta_{6}+\cdots)q^{13}+\cdots$$
336.1.bn.a $2$ $0.168$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$1$$ $$0$$ $$1$$ $$q-\zeta_{6}^{2}q^{3}+\zeta_{6}q^{7}-\zeta_{6}q^{9}-q^{13}+\cdots$$
336.2.a.a $1$ $2.683$ $$\Q$$ None None $$0$$ $$-1$$ $$-2$$ $$1$$ $+$ $$q-q^{3}-2q^{5}+q^{7}+q^{9}-4q^{11}-2q^{13}+\cdots$$
336.2.a.b $1$ $2.683$ $$\Q$$ None None $$0$$ $$-1$$ $$0$$ $$-1$$ $-$ $$q-q^{3}-q^{7}+q^{9}+6q^{11}+2q^{13}+\cdots$$
336.2.a.c $1$ $2.683$ $$\Q$$ None None $$0$$ $$-1$$ $$2$$ $$1$$ $-$ $$q-q^{3}+2q^{5}+q^{7}+q^{9}-2q^{13}-2q^{15}+\cdots$$
336.2.a.d $1$ $2.683$ $$\Q$$ None None $$0$$ $$1$$ $$-2$$ $$1$$ $-$ $$q+q^{3}-2q^{5}+q^{7}+q^{9}+4q^{11}+6q^{13}+\cdots$$
336.2.a.e $1$ $2.683$ $$\Q$$ None None $$0$$ $$1$$ $$2$$ $$-1$$ $-$ $$q+q^{3}+2q^{5}-q^{7}+q^{9}+6q^{13}+2q^{15}+\cdots$$
336.2.a.f $1$ $2.683$ $$\Q$$ None None $$0$$ $$1$$ $$4$$ $$1$$ $-$ $$q+q^{3}+4q^{5}+q^{7}+q^{9}-2q^{11}-6q^{13}+\cdots$$
336.2.b.a $2$ $2.683$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$-2$$ $$0$$ $$-4$$ $$q-q^{3}+(-2-\zeta_{6})q^{7}+q^{9}-2\zeta_{6}q^{11}+\cdots$$
336.2.b.b $2$ $2.683$ $$\Q(\sqrt{-6})$$ None None $$0$$ $$-2$$ $$0$$ $$2$$ $$q-q^{3}+\beta q^{5}+(1-\beta )q^{7}+q^{9}+\beta q^{11}+\cdots$$
336.2.b.c $2$ $2.683$ $$\Q(\sqrt{-6})$$ None None $$0$$ $$2$$ $$0$$ $$-2$$ $$q+q^{3}+\beta q^{5}+(-1+\beta )q^{7}+q^{9}-\beta q^{11}+\cdots$$
336.2.b.d $2$ $2.683$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$2$$ $$0$$ $$4$$ $$q+q^{3}+(2+\zeta_{6})q^{7}+q^{9}+2\zeta_{6}q^{11}+\cdots$$
336.2.h.a $4$ $2.683$ $$\Q(\zeta_{8})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\zeta_{8}-\zeta_{8}^{3})q^{3}-\zeta_{8}^{2}q^{5}-\zeta_{8}q^{7}+\cdots$$
336.2.h.b $8$ $2.683$ 8.0.56070144.2 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{6}q^{3}+(\beta _{3}+\beta _{5})q^{5}+\beta _{4}q^{7}+(2+\cdots)q^{9}+\cdots$$
336.2.k.a $2$ $2.683$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$-4$$ $$q-\zeta_{6}q^{3}+(-2-\zeta_{6})q^{7}-3q^{9}-4\zeta_{6}q^{13}+\cdots$$
336.2.k.b $4$ $2.683$ $$\Q(i, \sqrt{6})$$ None None $$0$$ $$0$$ $$0$$ $$4$$ $$q+\beta _{1}q^{3}+(\beta _{1}-\beta _{3})q^{5}+(1-\beta _{1}-\beta _{3})q^{7}+\cdots$$
336.2.k.c $8$ $2.683$ 8.0.342102016.5 None None $$0$$ $$0$$ $$0$$ $$4$$ $$q+\beta _{1}q^{3}+\beta _{2}q^{5}+(1+\beta _{5})q^{7}+(-\beta _{5}+\cdots)q^{9}+\cdots$$
336.2.q.a $2$ $2.683$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$-1$$ $$-2$$ $$-5$$ $$q+(-1+\zeta_{6})q^{3}-2\zeta_{6}q^{5}+(-2-\zeta_{6})q^{7}+\cdots$$
336.2.q.b $2$ $2.683$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$-1$$ $$-1$$ $$-1$$ $$q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{5}+(1-3\zeta_{6})q^{7}+\cdots$$
336.2.q.c $2$ $2.683$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$-1$$ $$2$$ $$-1$$ $$q+(-1+\zeta_{6})q^{3}+2\zeta_{6}q^{5}+(-2+3\zeta_{6})q^{7}+\cdots$$
336.2.q.d $2$ $2.683$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$1$$ $$-3$$ $$-5$$ $$q+(1-\zeta_{6})q^{3}-3\zeta_{6}q^{5}+(-3+\zeta_{6})q^{7}+\cdots$$
336.2.q.e $2$ $2.683$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$1$$ $$1$$ $$-1$$ $$q+(1-\zeta_{6})q^{3}+\zeta_{6}q^{5}+(1-3\zeta_{6})q^{7}+\cdots$$
336.2.q.f $2$ $2.683$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$1$$ $$2$$ $$5$$ $$q+(1-\zeta_{6})q^{3}+2\zeta_{6}q^{5}+(2+\zeta_{6})q^{7}+\cdots$$
336.2.q.g $4$ $2.683$ $$\Q(\sqrt{-3}, \sqrt{-19})$$ None None $$0$$ $$-2$$ $$1$$ $$6$$ $$q+(-1+\beta _{2})q^{3}+(-1+2\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$$
336.2.s.a $4$ $2.683$ $$\Q(\zeta_{8})$$ None None $$-4$$ $$-4$$ $$-4$$ $$-4$$ $$q+(-1+\zeta_{8})q^{2}+(-1+\zeta_{8}^{2})q^{3}-2\zeta_{8}q^{4}+\cdots$$
336.2.s.b $4$ $2.683$ $$\Q(\zeta_{8})$$ None None $$4$$ $$0$$ $$4$$ $$-4$$ $$q+(1+\zeta_{8})q^{2}+(-\zeta_{8}-\zeta_{8}^{3})q^{3}+2\zeta_{8}q^{4}+\cdots$$
336.2.s.c $40$ $2.683$ None None $$0$$ $$4$$ $$0$$ $$-40$$
336.2.s.d $48$ $2.683$ None None $$0$$ $$0$$ $$0$$ $$48$$
336.2.u.a $64$ $2.683$ None None $$0$$ $$0$$ $$0$$ $$0$$
336.2.w.a $20$ $2.683$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{3}q^{2}-\beta _{7}q^{3}+(\beta _{1}-\beta _{3}-\beta _{6}-\beta _{16}+\cdots)q^{4}+\cdots$$
336.2.w.b $28$ $2.683$ None None $$0$$ $$0$$ $$0$$ $$0$$
336.2.y.a $120$ $2.683$ None None $$0$$ $$0$$ $$0$$ $$0$$
336.2.bc.a $2$ $2.683$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-3$$ $$0$$ $$5$$ $$q+(-1-\zeta_{6})q^{3}+(2+\zeta_{6})q^{7}+3\zeta_{6}q^{9}+\cdots$$
336.2.bc.b $2$ $2.683$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$0$$ $$-3$$ $$-4$$ $$q+(-1+2\zeta_{6})q^{3}-3\zeta_{6}q^{5}+(-1-2\zeta_{6})q^{7}+\cdots$$
336.2.bc.c $2$ $2.683$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$3$$ $$0$$ $$-1$$ $$q+(1+\zeta_{6})q^{3}+(-2+3\zeta_{6})q^{7}+3\zeta_{6}q^{9}+\cdots$$
336.2.bc.d $2$ $2.683$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$3$$ $$3$$ $$-4$$ $$q+(2-\zeta_{6})q^{3}+3\zeta_{6}q^{5}+(-1-2\zeta_{6})q^{7}+\cdots$$
336.2.bc.e $4$ $2.683$ $$\Q(\zeta_{12})$$ None None $$0$$ $$0$$ $$0$$ $$10$$ $$q-\zeta_{12}^{2}q^{3}+(-\zeta_{12}^{2}+\zeta_{12}^{3})q^{5}+\cdots$$
336.2.bc.f $16$ $2.683$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$-4$$ $$q+(-\beta _{5}+\beta _{8})q^{3}-\beta _{14}q^{5}+\beta _{10}q^{7}+\cdots$$
336.2.bj.a $2$ $2.683$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-3$$ $$0$$ $$-5$$ $$q+(-2+\zeta_{6})q^{3}+(-3+\zeta_{6})q^{7}+(3+\cdots)q^{9}+\cdots$$
336.2.bj.b $2$ $2.683$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-3$$ $$0$$ $$-1$$ $$q+(-2+\zeta_{6})q^{3}+(1-3\zeta_{6})q^{7}+(3-3\zeta_{6})q^{9}+\cdots$$
336.2.bj.c $2$ $2.683$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$3$$ $$0$$ $$1$$ $$q+(2-\zeta_{6})q^{3}+(-1+3\zeta_{6})q^{7}+(3-3\zeta_{6})q^{9}+\cdots$$
336.2.bj.d $2$ $2.683$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$3$$ $$0$$ $$5$$ $$q+(2-\zeta_{6})q^{3}+(3-\zeta_{6})q^{7}+(3-3\zeta_{6})q^{9}+\cdots$$
336.2.bj.e $8$ $2.683$ 8.0.8275904784.2 None None $$0$$ $$-3$$ $$0$$ $$-6$$ $$q+(1-\beta _{1}-\beta _{5}+\beta _{6})q^{3}+(1-\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots$$
336.2.bj.f $8$ $2.683$ 8.0.303595776.1 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}+(1-2\beta _{2}+\beta _{4}+2\beta _{6})q^{5}+\cdots$$
336.2.bj.g $8$ $2.683$ 8.0.8275904784.2 None None $$0$$ $$3$$ $$0$$ $$6$$ $$q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{4}-\beta _{7})q^{5}+(3+\cdots)q^{7}+\cdots$$
336.2.bl.a $2$ $2.683$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$-1$$ $$-6$$ $$1$$ $$q+(-1+\zeta_{6})q^{3}+(-4+2\zeta_{6})q^{5}+(2+\cdots)q^{7}+\cdots$$
336.2.bl.b $2$ $2.683$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$-1$$ $$-3$$ $$-5$$ $$q+(-1+\zeta_{6})q^{3}+(-2+\zeta_{6})q^{5}+(-3+\cdots)q^{7}+\cdots$$