## Results (1-50 of 55 matches)

Label Dim $A$ Field CM RM Traces Fricke sign $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1449.1.c.a $4$ $0.723$ $$\Q(\zeta_{8})$$ $$\Q(\sqrt{-7})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\zeta_{8}-\zeta_{8}^{3})q^{2}-q^{4}+\zeta_{8}^{2}q^{7}+\cdots$$
1449.1.bq.a $10$ $0.723$ $$\Q(\zeta_{22})$$ $$\Q(\sqrt{-7})$$ None $$2$$ $$0$$ $$0$$ $$-1$$ $$q+(\zeta_{22}^{3}-\zeta_{22}^{10})q^{2}+(\zeta_{22}^{2}+\zeta_{22}^{6}+\cdots)q^{4}+\cdots$$
1449.1.bq.b $20$ $0.723$ $$\Q(\zeta_{44})$$ $$\Q(\sqrt{-7})$$ None $$0$$ $$0$$ $$0$$ $$2$$ $$q+(-\zeta_{44}^{5}-\zeta_{44}^{7})q^{2}+(\zeta_{44}^{10}+\zeta_{44}^{12}+\cdots)q^{4}+\cdots$$
1449.1.bu.a $40$ $0.723$ $$\Q(\zeta_{88})$$ $$\Q(\sqrt{-7})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\zeta_{88}^{5}-\zeta_{88}^{7})q^{2}+(\zeta_{88}^{10}+\zeta_{88}^{12}+\cdots)q^{4}+\cdots$$
1449.2.a.a $1$ $11.570$ $$\Q$$ None None $$-2$$ $$0$$ $$-4$$ $$-1$$ $+$ $$q-2q^{2}+2q^{4}-4q^{5}-q^{7}+8q^{10}+\cdots$$
1449.2.a.b $1$ $11.570$ $$\Q$$ None None $$-2$$ $$0$$ $$-2$$ $$1$$ $+$ $$q-2q^{2}+2q^{4}-2q^{5}+q^{7}+4q^{10}+\cdots$$
1449.2.a.c $1$ $11.570$ $$\Q$$ None None $$-2$$ $$0$$ $$0$$ $$1$$ $+$ $$q-2q^{2}+2q^{4}+q^{7}-q^{11}+2q^{13}+\cdots$$
1449.2.a.d $1$ $11.570$ $$\Q$$ None None $$1$$ $$0$$ $$-2$$ $$1$$ $-$ $$q+q^{2}-q^{4}-2q^{5}+q^{7}-3q^{8}-2q^{10}+\cdots$$
1449.2.a.e $1$ $11.570$ $$\Q$$ None None $$2$$ $$0$$ $$2$$ $$1$$ $-$ $$q+2q^{2}+2q^{4}+2q^{5}+q^{7}+4q^{10}+\cdots$$
1449.2.a.f $2$ $11.570$ $$\Q(\sqrt{5})$$ None None $$-1$$ $$0$$ $$3$$ $$2$$ $+$ $$q-\beta q^{2}+(-1+\beta )q^{4}+(1+\beta )q^{5}+q^{7}+\cdots$$
1449.2.a.g $2$ $11.570$ $$\Q(\sqrt{5})$$ None None $$1$$ $$0$$ $$-5$$ $$2$$ $+$ $$q+\beta q^{2}+(-1+\beta )q^{4}+(-3+\beta )q^{5}+\cdots$$
1449.2.a.h $2$ $11.570$ $$\Q(\sqrt{5})$$ None None $$1$$ $$0$$ $$-1$$ $$-2$$ $+$ $$q+\beta q^{2}+(-1+\beta )q^{4}+(-1+\beta )q^{5}+\cdots$$
1449.2.a.i $2$ $11.570$ $$\Q(\sqrt{5})$$ None None $$1$$ $$0$$ $$2$$ $$-2$$ $+$ $$q+\beta q^{2}+(-1+\beta )q^{4}+(2-2\beta )q^{5}+\cdots$$
1449.2.a.j $2$ $11.570$ $$\Q(\sqrt{13})$$ None None $$1$$ $$0$$ $$5$$ $$-2$$ $-$ $$q+\beta q^{2}+(1+\beta )q^{4}+(3-\beta )q^{5}-q^{7}+\cdots$$
1449.2.a.k $2$ $11.570$ $$\Q(\sqrt{5})$$ None None $$3$$ $$0$$ $$5$$ $$2$$ $-$ $$q+(1+\beta )q^{2}+3\beta q^{4}+(2+\beta )q^{5}+q^{7}+\cdots$$
1449.2.a.l $3$ $11.570$ 3.3.837.1 None None $$0$$ $$0$$ $$-3$$ $$-3$$ $+$ $$q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-1+\beta _{1})q^{5}+\cdots$$
1449.2.a.m $3$ $11.570$ 3.3.148.1 None None $$1$$ $$0$$ $$-2$$ $$-3$$ $-$ $$q+(\beta _{1}+\beta _{2})q^{2}+(1+2\beta _{1})q^{4}+(-1+\cdots)q^{5}+\cdots$$
1449.2.a.n $4$ $11.570$ 4.4.2624.1 None None $$-2$$ $$0$$ $$-2$$ $$4$$ $+$ $$q+(-1+\beta _{1}-\beta _{3})q^{2}+(2-2\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots$$
1449.2.a.o $4$ $11.570$ 4.4.15317.1 None None $$-2$$ $$0$$ $$-5$$ $$-4$$ $-$ $$q-\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(-2-\beta _{2}+\cdots)q^{5}+\cdots$$
1449.2.a.p $4$ $11.570$ 4.4.24197.1 None None $$0$$ $$0$$ $$-5$$ $$4$$ $-$ $$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1+\beta _{3})q^{5}+\cdots$$
1449.2.a.q $4$ $11.570$ 4.4.2624.1 None None $$2$$ $$0$$ $$2$$ $$4$$ $-$ $$q+(1-\beta _{1}+\beta _{3})q^{2}+(2-2\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots$$
1449.2.a.r $5$ $11.570$ 5.5.2147108.1 None None $$-2$$ $$0$$ $$4$$ $$5$$ $-$ $$q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(1+\beta _{4})q^{5}+\cdots$$
1449.2.a.s $5$ $11.570$ 5.5.1337792.1 None None $$0$$ $$0$$ $$-4$$ $$-5$$ $+$ $$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1-\beta _{2})q^{5}+\cdots$$
1449.2.a.t $5$ $11.570$ 5.5.1337792.1 None None $$0$$ $$0$$ $$4$$ $$-5$$ $-$ $$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1+\beta _{2})q^{5}+\cdots$$
1449.2.d.a $56$ $11.570$ None None $$0$$ $$0$$ $$0$$ $$0$$
1449.2.e.a $48$ $11.570$ None None $$0$$ $$0$$ $$0$$ $$0$$
1449.2.h.a $2$ $11.570$ $$\Q(\sqrt{-7})$$ $$\Q(\sqrt{-7})$$ None $$2$$ $$0$$ $$0$$ $$0$$ $$q+q^{2}-q^{4}+\beta q^{7}-3q^{8}-2\beta q^{11}+\cdots$$
1449.2.h.b $4$ $11.570$ $$\Q(\sqrt{7}, \sqrt{-23})$$ $$\Q(\sqrt{-483})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-2q^{4}+\beta _{1}q^{7}-\beta _{3}q^{11}+4q^{16}+\cdots$$
1449.2.h.c $4$ $11.570$ $$\Q(i, \sqrt{7})$$ $$\Q(\sqrt{-7})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{2}+5q^{4}+\beta _{3}q^{7}-3\beta _{2}q^{8}+\cdots$$
1449.2.h.d $8$ $11.570$ 8.0.342102016.5 None None $$8$$ $$0$$ $$0$$ $$0$$ $$q+q^{2}-q^{4}-\beta _{2}q^{5}+(-\beta _{1}-\beta _{3})q^{7}+\cdots$$
1449.2.h.e $12$ $11.570$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None None $$-4$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{2}+(3+\beta _{7})q^{4}-\beta _{5}q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$$
1449.2.h.f $12$ $11.570$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None None $$0$$ $$0$$ $$-20$$ $$0$$ $$q-\beta _{5}q^{2}+(1-\beta _{2})q^{4}+(-2+\beta _{7})q^{5}+\cdots$$
1449.2.h.g $12$ $11.570$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{4}q^{2}+(1-\beta _{3})q^{4}-\beta _{2}q^{5}+\beta _{7}q^{7}+\cdots$$
1449.2.h.h $12$ $11.570$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{8}q^{2}+(1-\beta _{7})q^{4}+(-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$$
1449.2.h.i $12$ $11.570$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None None $$0$$ $$0$$ $$20$$ $$0$$ $$q-\beta _{5}q^{2}+(1-\beta _{2})q^{4}+(2-\beta _{7})q^{5}+\cdots$$
1449.3.b.a $88$ $39.482$ None None $$0$$ $$0$$ $$0$$ $$0$$
1449.4.a.a $1$ $85.494$ $$\Q$$ None None $$-3$$ $$0$$ $$-3$$ $$7$$ $-$ $$q-3q^{2}+q^{4}-3q^{5}+7q^{7}+21q^{8}+\cdots$$
1449.4.a.b $1$ $85.494$ $$\Q$$ None None $$3$$ $$0$$ $$3$$ $$7$$ $+$ $$q+3q^{2}+q^{4}+3q^{5}+7q^{7}-21q^{8}+\cdots$$
1449.4.a.c $3$ $85.494$ 3.3.3877.1 None None $$4$$ $$0$$ $$-2$$ $$-21$$ $+$ $$q+(1+\beta _{1})q^{2}+(1+4\beta _{1}+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots$$
1449.4.a.d $4$ $85.494$ 4.4.8184789.1 None None $$-2$$ $$0$$ $$23$$ $$-28$$ $+$ $$q+(-1-\beta _{1})q^{2}+(3+\beta _{1})q^{4}+(6+\beta _{1}+\cdots)q^{5}+\cdots$$
1449.4.a.e $5$ $85.494$ $$\mathbb{Q}[x]/(x^{5} - \cdots)$$ None None $$4$$ $$0$$ $$4$$ $$35$$ $-$ $$q+(1-\beta _{1})q^{2}+\beta _{2}q^{4}+(1+\beta _{2}-\beta _{4})q^{5}+\cdots$$
1449.4.a.f $7$ $85.494$ $$\mathbb{Q}[x]/(x^{7} - \cdots)$$ None None $$-2$$ $$0$$ $$11$$ $$49$$ $-$ $$q-\beta _{1}q^{2}+(3+\beta _{2})q^{4}+(1+2\beta _{1}+\beta _{5}+\cdots)q^{5}+\cdots$$
1449.4.a.g $7$ $85.494$ $$\mathbb{Q}[x]/(x^{7} - \cdots)$$ None None $$2$$ $$0$$ $$11$$ $$-49$$ $-$ $$q+\beta _{1}q^{2}+(3+\beta _{4}+\beta _{5})q^{4}+(2-\beta _{2}+\cdots)q^{5}+\cdots$$
1449.4.a.h $7$ $85.494$ $$\mathbb{Q}[x]/(x^{7} - \cdots)$$ None None $$6$$ $$0$$ $$41$$ $$49$$ $+$ $$q+(1-\beta _{1})q^{2}+(3-\beta _{1}+\beta _{2})q^{4}+(6+\cdots)q^{5}+\cdots$$
1449.4.a.i $8$ $85.494$ $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ None None $$0$$ $$0$$ $$24$$ $$-56$$ $-$ $$q+\beta _{1}q^{2}+(3+\beta _{1}+\beta _{3}-\beta _{4})q^{4}+(3+\cdots)q^{5}+\cdots$$
1449.4.a.j $9$ $85.494$ $$\mathbb{Q}[x]/(x^{9} - \cdots)$$ None None $$-8$$ $$0$$ $$-39$$ $$63$$ $-$ $$q+(-1+\beta _{1})q^{2}+(4-2\beta _{1}+\beta _{2})q^{4}+\cdots$$
1449.4.a.k $9$ $85.494$ $$\mathbb{Q}[x]/(x^{9} - \cdots)$$ None None $$-4$$ $$0$$ $$-39$$ $$-63$$ $-$ $$q-\beta _{1}q^{2}+(4+\beta _{2})q^{4}+(-4-\beta _{4})q^{5}+\cdots$$
1449.4.a.l $9$ $85.494$ $$\mathbb{Q}[x]/(x^{9} - \cdots)$$ None None $$-4$$ $$0$$ $$-9$$ $$-63$$ $+$ $$q-\beta _{1}q^{2}+(4+\beta _{1}+\beta _{2})q^{4}+(-1-\beta _{7}+\cdots)q^{5}+\cdots$$
1449.4.a.m $9$ $85.494$ $$\mathbb{Q}[x]/(x^{9} - \cdots)$$ None None $$0$$ $$0$$ $$-29$$ $$63$$ $+$ $$q+\beta _{1}q^{2}+(5+\beta _{2})q^{4}+(-3-\beta _{7})q^{5}+\cdots$$
1449.4.a.n $9$ $85.494$ $$\mathbb{Q}[x]/(x^{9} - \cdots)$$ None None $$0$$ $$0$$ $$4$$ $$-63$$ $+$ $$q-\beta _{1}q^{2}+(5+\beta _{1}+\beta _{2})q^{4}-\beta _{6}q^{5}+\cdots$$