## Results (1-50 of 154 matches)

Label Dim $A$ Field CM RM Traces Fricke sign $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
312.1.b.a $4$ $0.156$ $$\Q(\zeta_{8})$$ $$\Q(\sqrt{-39})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{8}q^{2}-\zeta_{8}^{2}q^{3}+\zeta_{8}^{2}q^{4}+(-\zeta_{8}+\cdots)q^{5}+\cdots$$
312.2.a.a $1$ $2.491$ $$\Q$$ None None $$0$$ $$-1$$ $$-2$$ $$4$$ $-$ $$q-q^{3}-2q^{5}+4q^{7}+q^{9}+q^{13}+2q^{15}+\cdots$$
312.2.a.b $1$ $2.491$ $$\Q$$ None None $$0$$ $$-1$$ $$0$$ $$-4$$ $+$ $$q-q^{3}-4q^{7}+q^{9}-2q^{11}-q^{13}+\cdots$$
312.2.a.c $1$ $2.491$ $$\Q$$ None None $$0$$ $$-1$$ $$4$$ $$0$$ $-$ $$q-q^{3}+4q^{5}+q^{9}-2q^{11}-q^{13}+\cdots$$
312.2.a.d $1$ $2.491$ $$\Q$$ None None $$0$$ $$1$$ $$-4$$ $$-4$$ $+$ $$q+q^{3}-4q^{5}-4q^{7}+q^{9}-2q^{11}+\cdots$$
312.2.a.e $1$ $2.491$ $$\Q$$ None None $$0$$ $$1$$ $$0$$ $$0$$ $-$ $$q+q^{3}+q^{9}+6q^{11}-q^{13}+2q^{17}+\cdots$$
312.2.a.f $1$ $2.491$ $$\Q$$ None None $$0$$ $$1$$ $$2$$ $$0$$ $-$ $$q+q^{3}+2q^{5}+q^{9}+q^{13}+2q^{15}+\cdots$$
312.2.c.a $2$ $2.491$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$-2$$ $$0$$ $$0$$ $$q-q^{3}+iq^{7}+q^{9}+iq^{11}+(3+i)q^{13}+\cdots$$
312.2.c.b $2$ $2.491$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$2$$ $$0$$ $$0$$ $$q+q^{3}+iq^{5}+iq^{7}+q^{9}+2iq^{11}+\cdots$$
312.2.c.c $2$ $2.491$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$2$$ $$0$$ $$0$$ $$q+q^{3}+2iq^{5}-iq^{7}+q^{9}+iq^{11}+\cdots$$
312.2.g.a $8$ $2.491$ $$\Q(\zeta_{20})$$ None None $$2$$ $$0$$ $$0$$ $$4$$ $$q+\zeta_{20}^{7}q^{2}-\zeta_{20}^{3}q^{3}+\zeta_{20}q^{4}+(-1+\cdots)q^{5}+\cdots$$
312.2.g.b $16$ $2.491$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None None $$2$$ $$0$$ $$0$$ $$4$$ $$q+\beta _{10}q^{2}+\beta _{9}q^{3}-\beta _{2}q^{4}+\beta _{14}q^{5}+\cdots$$
312.2.h.a $8$ $2.491$ 8.0.$$\cdots$$.21 $$\Q(\sqrt{-39})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+\beta _{3}q^{3}+\beta _{2}q^{4}+(-\beta _{4}-\beta _{7})q^{5}+\cdots$$
312.2.h.b $12$ $2.491$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ $$\Q(\sqrt{-26})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{3}q^{2}+\beta _{7}q^{3}-2q^{4}-\beta _{9}q^{5}-\beta _{4}q^{6}+\cdots$$
312.2.h.c $32$ $2.491$ None None $$0$$ $$-4$$ $$0$$ $$0$$
312.2.j.a $48$ $2.491$ None None $$0$$ $$0$$ $$0$$ $$0$$
312.2.m.a $2$ $2.491$ $$\Q(\sqrt{-1})$$ None None $$-2$$ $$0$$ $$-4$$ $$0$$ $$q+(-1+i)q^{2}-iq^{3}-2iq^{4}-2q^{5}+\cdots$$
312.2.m.b $2$ $2.491$ $$\Q(\sqrt{-1})$$ None None $$2$$ $$0$$ $$4$$ $$0$$ $$q+(1+i)q^{2}+iq^{3}+2iq^{4}+2q^{5}+\cdots$$
312.2.m.c $24$ $2.491$ None None $$0$$ $$0$$ $$0$$ $$0$$
312.2.q.a $2$ $2.491$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$-1$$ $$6$$ $$0$$ $$q+(-1+\zeta_{6})q^{3}+3q^{5}-\zeta_{6}q^{9}+(3+\cdots)q^{13}+\cdots$$
312.2.q.b $2$ $2.491$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$1$$ $$-4$$ $$-1$$ $$q+(1-\zeta_{6})q^{3}-2q^{5}-\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots$$
312.2.q.c $2$ $2.491$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$1$$ $$6$$ $$4$$ $$q+(1-\zeta_{6})q^{3}+3q^{5}+4\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots$$
312.2.q.d $4$ $2.491$ $$\Q(\sqrt{-3}, \sqrt{13})$$ None None $$0$$ $$-2$$ $$-4$$ $$-2$$ $$q+(-1+\beta _{1})q^{3}-q^{5}+(-\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots$$
312.2.q.e $6$ $2.491$ 6.0.2101707.2 None None $$0$$ $$3$$ $$0$$ $$-3$$ $$q+(1+\beta _{3})q^{3}+\beta _{2}q^{5}+(-2-\beta _{4}+2\beta _{5})q^{7}+\cdots$$
312.2.t.a $2$ $2.491$ $$\Q(\sqrt{-1})$$ None None $$-2$$ $$-2$$ $$-4$$ $$2$$ $$q+(-1+i)q^{2}-q^{3}-2iq^{4}+(-2+\cdots)q^{5}+\cdots$$
312.2.t.b $2$ $2.491$ $$\Q(\sqrt{-1})$$ None None $$-2$$ $$2$$ $$-4$$ $$-6$$ $$q+(-1-i)q^{2}+q^{3}+2iq^{4}+(-2+\cdots)q^{5}+\cdots$$
312.2.t.c $2$ $2.491$ $$\Q(\sqrt{-1})$$ None None $$-2$$ $$2$$ $$4$$ $$6$$ $$q+(-1-i)q^{2}+q^{3}+2iq^{4}+(2-2i)q^{5}+\cdots$$
312.2.t.d $2$ $2.491$ $$\Q(\sqrt{-1})$$ None None $$2$$ $$-2$$ $$4$$ $$-2$$ $$q+(1-i)q^{2}-q^{3}-2iq^{4}+(2-2i)q^{5}+\cdots$$
312.2.t.e $24$ $2.491$ None None $$0$$ $$-24$$ $$0$$ $$0$$
312.2.t.f $24$ $2.491$ None None $$4$$ $$24$$ $$0$$ $$0$$
312.2.x.a $4$ $2.491$ $$\Q(\zeta_{8})$$ None None $$0$$ $$4$$ $$0$$ $$12$$ $$q+(1+\zeta_{8}^{2})q^{3}+(-\zeta_{8}^{2}-\zeta_{8}^{3})q^{5}+\cdots$$
312.2.x.b $8$ $2.491$ $$\Q(\zeta_{24})$$ None None $$0$$ $$-8$$ $$0$$ $$8$$ $$q+(-1-\zeta_{24}^{2})q^{3}-\zeta_{24}^{7}q^{5}+(1+\zeta_{24}+\cdots)q^{7}+\cdots$$
312.2.x.c $16$ $2.491$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None None $$0$$ $$4$$ $$0$$ $$-24$$ $$q-\beta _{12}q^{3}+(\beta _{6}-\beta _{7}-\beta _{13}+\beta _{14}+\cdots)q^{5}+\cdots$$
312.2.y.a $104$ $2.491$ None None $$0$$ $$0$$ $$0$$ $$-8$$
312.2.ba.a $104$ $2.491$ None None $$0$$ $$-2$$ $$0$$ $$0$$
312.2.bb.a $56$ $2.491$ None None $$0$$ $$0$$ $$0$$ $$0$$
312.2.bf.a $4$ $2.491$ $$\Q(\zeta_{12})$$ None None $$0$$ $$2$$ $$0$$ $$6$$ $$q+(1-\zeta_{12}^{2})q^{3}+(1-2\zeta_{12}^{2})q^{5}+(2+\cdots)q^{7}+\cdots$$
312.2.bf.b $8$ $2.491$ 8.0.649638144.4 None None $$0$$ $$-4$$ $$0$$ $$0$$ $$q+\beta _{2}q^{3}+(-\beta _{2}-\beta _{6})q^{5}+(1+\beta _{1}+\cdots)q^{7}+\cdots$$
312.2.bk.a $8$ $2.491$ 8.0.12960000.1 None None $$0$$ $$0$$ $$0$$ $$12$$ $$q+(\beta _{6}+\beta _{7})q^{2}+(\beta _{3}+\beta _{7})q^{3}+(-1+\cdots)q^{4}+\cdots$$
312.2.bk.b $48$ $2.491$ None None $$0$$ $$0$$ $$0$$ $$-12$$
312.2.bn.a $104$ $2.491$ None None $$0$$ $$-2$$ $$0$$ $$0$$
312.2.bo.a $208$ $2.491$ None None $$0$$ $$0$$ $$0$$ $$-16$$
312.2.bp.a $56$ $2.491$ None None $$0$$ $$0$$ $$0$$ $$4$$
312.2.bt.a $4$ $2.491$ $$\Q(\zeta_{12})$$ None None $$-4$$ $$-2$$ $$-2$$ $$-6$$ $$q+(-1+\zeta_{12}^{3})q^{2}-\zeta_{12}^{2}q^{3}-2\zeta_{12}^{3}q^{4}+\cdots$$
312.2.bt.b $4$ $2.491$ $$\Q(\zeta_{12})$$ None None $$2$$ $$-2$$ $$2$$ $$6$$ $$q+(1-\zeta_{12}-\zeta_{12}^{2})q^{2}-\zeta_{12}^{2}q^{3}+\cdots$$
312.2.bt.c $48$ $2.491$ None None $$2$$ $$-24$$ $$0$$ $$0$$
312.2.bt.d $56$ $2.491$ None None $$0$$ $$28$$ $$0$$ $$0$$
312.3.b.a $1$ $8.501$ $$\Q$$ $$\Q(\sqrt{-78})$$ None $$-2$$ $$-3$$ $$0$$ $$0$$ $$q-2q^{2}-3q^{3}+4q^{4}+6q^{6}-8q^{8}+\cdots$$
312.3.b.b $1$ $8.501$ $$\Q$$ $$\Q(\sqrt{-78})$$ None $$-2$$ $$3$$ $$0$$ $$0$$ $$q-2q^{2}+3q^{3}+4q^{4}-6q^{6}-8q^{8}+\cdots$$
312.3.b.c $1$ $8.501$ $$\Q$$ $$\Q(\sqrt{-78})$$ None $$2$$ $$-3$$ $$0$$ $$0$$ $$q+2q^{2}-3q^{3}+4q^{4}-6q^{6}+8q^{8}+\cdots$$