## Results (1-50 of 147 matches)

Label Dim $A$ Field CM RM Traces Fricke sign $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
592.1.b.a $1$ $0.295$ $$\Q$$ $$\Q(\sqrt{-1})$$, $$\Q(\sqrt{-37})$$ $$\Q(\sqrt{37})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+q^{9}+q^{25}-q^{37}-2q^{41}+q^{49}+\cdots$$
592.1.b.b $2$ $0.295$ $$\Q(\sqrt{-3})$$ None $$\Q(\sqrt{37})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\zeta_{6}+\zeta_{6}^{2})q^{3}+(\zeta_{6}+\zeta_{6}^{2})q^{7}+(-1+\cdots)q^{9}+\cdots$$
592.1.k.a $2$ $0.295$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$-2$$ $$2$$ $$q+iq^{3}+(-1-i)q^{5}+q^{7}+iq^{11}+\cdots$$
592.1.k.b $2$ $0.295$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$0$$ $$2$$ $$q-iq^{3}+q^{7}+iq^{11}+(-1-i)q^{17}+\cdots$$
592.1.z.a $4$ $0.295$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+(\beta _{1}-\beta _{3})q^{3}-\beta _{2}q^{5}+(1-\beta _{2})q^{9}+\cdots$$
592.1.bb.a $2$ $0.295$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$3$$ $$0$$ $$q+(1+\zeta_{6})q^{5}-\zeta_{6}q^{9}+(-1+\zeta_{6}^{2}+\cdots)q^{17}+\cdots$$
592.1.bt.a $6$ $0.295$ $$\Q(\zeta_{18})$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-3$$ $$0$$ $$q+(-\zeta_{18}^{2}-\zeta_{18}^{3})q^{5}+\zeta_{18}^{8}q^{9}+\cdots$$
592.2.a.a $1$ $4.727$ $$\Q$$ None None $$0$$ $$-1$$ $$0$$ $$1$$ $+$ $$q-q^{3}+q^{7}-2q^{9}-3q^{11}-4q^{13}+\cdots$$
592.2.a.b $1$ $4.727$ $$\Q$$ None None $$0$$ $$1$$ $$-4$$ $$3$$ $+$ $$q+q^{3}-4q^{5}+3q^{7}-2q^{9}-5q^{11}+\cdots$$
592.2.a.c $1$ $4.727$ $$\Q$$ None None $$0$$ $$1$$ $$-2$$ $$-1$$ $+$ $$q+q^{3}-2q^{5}-q^{7}-2q^{9}-q^{11}-6q^{13}+\cdots$$
592.2.a.d $1$ $4.727$ $$\Q$$ None None $$0$$ $$1$$ $$0$$ $$3$$ $-$ $$q+q^{3}+3q^{7}-2q^{9}+3q^{11}+2q^{17}+\cdots$$
592.2.a.e $1$ $4.727$ $$\Q$$ None None $$0$$ $$3$$ $$-2$$ $$1$$ $-$ $$q+3q^{3}-2q^{5}+q^{7}+6q^{9}+5q^{11}+\cdots$$
592.2.a.f $2$ $4.727$ $$\Q(\sqrt{13})$$ None None $$0$$ $$-3$$ $$-1$$ $$-2$$ $+$ $$q+(-1-\beta )q^{3}-\beta q^{5}+(-2+2\beta )q^{7}+\cdots$$
592.2.a.g $2$ $4.727$ $$\Q(\sqrt{5})$$ None None $$0$$ $$1$$ $$1$$ $$2$$ $-$ $$q+\beta q^{3}+(-1+3\beta )q^{5}+2\beta q^{7}+(-2+\cdots)q^{9}+\cdots$$
592.2.a.h $2$ $4.727$ $$\Q(\sqrt{17})$$ None None $$0$$ $$1$$ $$4$$ $$-1$$ $-$ $$q+\beta q^{3}+2q^{5}-\beta q^{7}+(1+\beta )q^{9}-\beta q^{11}+\cdots$$
592.2.a.i $3$ $4.727$ 3.3.229.1 None None $$0$$ $$-2$$ $$-1$$ $$-7$$ $+$ $$q+(-1-\beta _{2})q^{3}+\beta _{2}q^{5}+(-2-\beta _{1}+\cdots)q^{7}+\cdots$$
592.2.a.j $4$ $4.727$ 4.4.48389.1 None None $$0$$ $$-2$$ $$5$$ $$1$$ $-$ $$q+(-1+\beta _{1})q^{3}+(1-\beta _{3})q^{5}+(\beta _{2}-\beta _{3})q^{7}+\cdots$$
592.2.g.a $2$ $4.727$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$-2$$ $$0$$ $$-2$$ $$q-q^{3}-\zeta_{6}q^{5}-q^{7}-2q^{9}-3q^{11}+\cdots$$
592.2.g.b $2$ $4.727$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$2$$ $$0$$ $$-6$$ $$q+q^{3}+iq^{5}-3q^{7}-2q^{9}+3q^{11}+\cdots$$
592.2.g.c $4$ $4.727$ $$\Q(i, \sqrt{21})$$ None None $$0$$ $$2$$ $$0$$ $$8$$ $$q+(1-\beta _{3})q^{3}-\beta _{1}q^{5}+2q^{7}+(3-\beta _{3})q^{9}+\cdots$$
592.2.g.d $10$ $4.727$ $$\mathbb{Q}[x]/(x^{10} - \cdots)$$ None None $$0$$ $$-2$$ $$0$$ $$4$$ $$q+\beta _{2}q^{3}-\beta _{7}q^{5}+\beta _{3}q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots$$
592.2.i.a $2$ $4.727$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$-2$$ $$-3$$ $$-4$$ $$q-2\zeta_{6}q^{3}-3\zeta_{6}q^{5}-4\zeta_{6}q^{7}+(-1+\cdots)q^{9}+\cdots$$
592.2.i.b $2$ $4.727$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$-1$$ $$-3$$ $$3$$ $$q-\zeta_{6}q^{3}-3\zeta_{6}q^{5}+3\zeta_{6}q^{7}+(2-2\zeta_{6})q^{9}+\cdots$$
592.2.i.c $2$ $4.727$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$0$$ $$-1$$ $$2$$ $$q-\zeta_{6}q^{5}+2\zeta_{6}q^{7}+(3-3\zeta_{6})q^{9}+2q^{11}+\cdots$$
592.2.i.d $2$ $4.727$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$2$$ $$1$$ $$0$$ $$q+2\zeta_{6}q^{3}+\zeta_{6}q^{5}+(-1+\zeta_{6})q^{9}+\cdots$$
592.2.i.e $6$ $4.727$ 6.0.4406832.1 None None $$0$$ $$0$$ $$-1$$ $$0$$ $$q+\beta _{4}q^{3}+(-\beta _{1}-\beta _{5})q^{5}-\beta _{4}q^{7}+\cdots$$
592.2.i.f $6$ $4.727$ 6.0.27870912.1 None None $$0$$ $$1$$ $$3$$ $$1$$ $$q+(-\beta _{1}-\beta _{2})q^{3}+(1-\beta _{4})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$$
592.2.i.g $6$ $4.727$ 6.0.591408.1 None None $$0$$ $$2$$ $$1$$ $$-2$$ $$q+(-\beta _{1}+\beta _{3}-\beta _{5})q^{3}+(\beta _{1}+\beta _{5})q^{5}+\cdots$$
592.2.i.h $10$ $4.727$ $$\mathbb{Q}[x]/(x^{10} - \cdots)$$ None None $$0$$ $$1$$ $$3$$ $$-3$$ $$q+\beta _{9}q^{3}+(\beta _{2}+\beta _{6}+\beta _{9})q^{5}+(-1+\cdots)q^{7}+\cdots$$
592.2.m.a $148$ $4.727$ None None $$0$$ $$0$$ $$0$$ $$-8$$
592.2.n.a $148$ $4.727$ None None $$0$$ $$-4$$ $$0$$ $$0$$
592.2.o.a $144$ $4.727$ None None $$0$$ $$0$$ $$0$$ $$0$$
592.2.s.a $148$ $4.727$ None None $$-4$$ $$0$$ $$-4$$ $$-8$$
592.2.t.a $2$ $4.727$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+(-1+i)q^{5}-3q^{9}+(-1+i)q^{13}+\cdots$$
592.2.t.b $4$ $4.727$ $$\Q(i, \sqrt{7})$$ None None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+\beta _{2}q^{3}+(-1+\beta _{1})q^{5}+\beta _{3}q^{7}+4q^{9}+\cdots$$
592.2.t.c $4$ $4.727$ $$\Q(\zeta_{12})$$ None None $$0$$ $$0$$ $$8$$ $$0$$ $$q+\zeta_{12}^{3}q^{3}+(2-2\zeta_{12})q^{5}-\zeta_{12}^{2}q^{7}+\cdots$$
592.2.t.d $28$ $4.727$ None None $$0$$ $$0$$ $$-8$$ $$0$$
592.2.w.a $2$ $4.727$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$-2$$ $$-3$$ $$-2$$ $$q-2\zeta_{6}q^{3}+(-2+\zeta_{6})q^{5}-2\zeta_{6}q^{7}+\cdots$$
592.2.w.b $2$ $4.727$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$1$$ $$3$$ $$1$$ $$q+\zeta_{6}q^{3}+(2-\zeta_{6})q^{5}+\zeta_{6}q^{7}+(2-2\zeta_{6})q^{9}+\cdots$$
592.2.w.c $4$ $4.727$ $$\Q(\zeta_{12})$$ None None $$0$$ $$-2$$ $$-6$$ $$0$$ $$q+(\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+(-2-2\zeta_{12}+\cdots)q^{5}+\cdots$$
592.2.w.d $4$ $4.727$ $$\Q(\zeta_{12})$$ None None $$0$$ $$2$$ $$-6$$ $$8$$ $$q+(\zeta_{12}-\zeta_{12}^{2})q^{3}+(-2+\zeta_{12})q^{5}+\cdots$$
592.2.w.e $4$ $4.727$ $$\Q(\zeta_{12})$$ None None $$0$$ $$2$$ $$6$$ $$-4$$ $$q+(\zeta_{12}-\zeta_{12}^{2})q^{3}+(2-\zeta_{12})q^{5}-2\zeta_{12}q^{7}+\cdots$$
592.2.w.f $20$ $4.727$ $$\mathbb{Q}[x]/(x^{20} + \cdots)$$ None None $$0$$ $$2$$ $$6$$ $$2$$ $$q+(\beta _{5}+\beta _{14})q^{3}+\beta _{4}q^{5}+(-\beta _{2}-\beta _{10}+\cdots)q^{7}+\cdots$$
592.2.bc.a $6$ $4.727$ $$\Q(\zeta_{18})$$ None None $$0$$ $$-3$$ $$-6$$ $$-3$$ $$q+(-\zeta_{18}+\zeta_{18}^{2}-\zeta_{18}^{3})q^{3}+(-2\zeta_{18}^{3}+\cdots)q^{5}+\cdots$$
592.2.bc.b $6$ $4.727$ $$\Q(\zeta_{18})$$ None None $$0$$ $$3$$ $$3$$ $$-6$$ $$q+(\zeta_{18}+\zeta_{18}^{3})q^{3}+(1+\zeta_{18}+2\zeta_{18}^{2}+\cdots)q^{5}+\cdots$$
592.2.bc.c $6$ $4.727$ $$\Q(\zeta_{18})$$ None None $$0$$ $$6$$ $$6$$ $$12$$ $$q+(1+\zeta_{18}^{4})q^{3}+(1+\zeta_{18}-\zeta_{18}^{2}+\cdots)q^{5}+\cdots$$
592.2.bc.d $12$ $4.727$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None None $$0$$ $$3$$ $$-6$$ $$-6$$ $$q+(\beta _{1}+\beta _{9})q^{3}+(-1+\beta _{1}+\beta _{5})q^{5}+\cdots$$
592.2.bc.e $24$ $4.727$ None None $$0$$ $$-3$$ $$-3$$ $$9$$
592.2.bc.f $24$ $4.727$ None None $$0$$ $$0$$ $$3$$ $$3$$
592.2.bc.g $30$ $4.727$ None None $$0$$ $$0$$ $$-6$$ $$3$$