## Results (1-50 of 77 matches)

Label Dim $A$ Field CM RM Traces Fricke sign $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1900.1.e.a $1$ $0.948$ $$\Q$$ $$\Q(\sqrt{-19})$$ None $$0$$ $$0$$ $$0$$ $$1$$ $$q+q^{7}+q^{9}-q^{11}+q^{17}+q^{19}-2q^{23}+\cdots$$
1900.1.e.b $2$ $0.948$ $$\Q(\sqrt{3})$$ $$\Q(\sqrt{-19})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta q^{7}+q^{9}+q^{11}+\beta q^{17}-q^{19}+\cdots$$
1900.1.g.a $2$ $0.948$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-19})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{7}-q^{9}-q^{11}-iq^{17}-q^{19}+\cdots$$
1900.1.j.a $8$ $0.948$ $$\Q(\zeta_{16})$$ $$\Q(\sqrt{-95})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{16}^{5}q^{2}+(-\zeta_{16}^{5}+\zeta_{16}^{7})q^{3}+\cdots$$
1900.1.j.b $8$ $0.948$ $$\Q(\zeta_{16})$$ $$\Q(\sqrt{-95})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{16}^{3}q^{2}+(\zeta_{16}+\zeta_{16}^{3})q^{3}+\zeta_{16}^{6}q^{4}+\cdots$$
1900.1.u.a $2$ $0.948$ $$\Q(\sqrt{-3})$$ None $$\Q(\sqrt{5})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{6}q^{9}+q^{11}+\zeta_{6}q^{19}+(1-\zeta_{6}^{2}+\cdots)q^{29}+\cdots$$
1900.1.w.a $8$ $0.948$ $$\Q(\zeta_{15})$$ $$\Q(\sqrt{-19})$$ None $$0$$ $$0$$ $$1$$ $$0$$ $$q+\zeta_{30}^{8}q^{5}+(\zeta_{30}^{2}+\zeta_{30}^{13})q^{7}+\zeta_{30}^{3}q^{9}+\cdots$$
1900.1.bb.a $8$ $0.948$ $$\Q(\zeta_{15})$$ $$\Q(\sqrt{-19})$$ None $$0$$ $$0$$ $$1$$ $$2$$ $$q-\zeta_{30}^{7}q^{5}+(\zeta_{30}^{2}-\zeta_{30}^{13})q^{7}+\zeta_{30}^{12}q^{9}+\cdots$$
1900.1.bf.a $4$ $0.948$ $$\Q(\zeta_{12})$$ None None $$0$$ $$2$$ $$0$$ $$0$$ $$q+(\zeta_{12}-\zeta_{12}^{4})q^{3}-\zeta_{12}^{5}q^{9}+q^{11}+\cdots$$
1900.2.a.a $1$ $15.172$ $$\Q$$ None None $$0$$ $$-2$$ $$0$$ $$-2$$ $-$ $$q-2q^{3}-2q^{7}+q^{9}-6q^{13}-2q^{17}+\cdots$$
1900.2.a.b $1$ $15.172$ $$\Q$$ None None $$0$$ $$-2$$ $$0$$ $$3$$ $-$ $$q-2q^{3}+3q^{7}+q^{9}+5q^{11}+4q^{13}+\cdots$$
1900.2.a.c $1$ $15.172$ $$\Q$$ None None $$0$$ $$0$$ $$0$$ $$2$$ $+$ $$q+2q^{7}-3q^{9}-4q^{11}+4q^{13}-6q^{17}+\cdots$$
1900.2.a.d $2$ $15.172$ $$\Q(\sqrt{3})$$ None None $$0$$ $$-2$$ $$0$$ $$-4$$ $+$ $$q+(-1+\beta )q^{3}-2q^{7}+(1-2\beta )q^{9}+\cdots$$
1900.2.a.e $2$ $15.172$ $$\Q(\sqrt{2})$$ None None $$0$$ $$4$$ $$0$$ $$4$$ $-$ $$q+(2+\beta )q^{3}+(2-2\beta )q^{7}+(3+4\beta )q^{9}+\cdots$$
1900.2.a.f $3$ $15.172$ 3.3.257.1 None None $$0$$ $$-2$$ $$0$$ $$-2$$ $+$ $$q+(-1+\beta _{1})q^{3}+(-1+\beta _{1})q^{7}+(1+\cdots)q^{9}+\cdots$$
1900.2.a.g $3$ $15.172$ 3.3.321.1 None None $$0$$ $$-2$$ $$0$$ $$-2$$ $+$ $$q+(-1-\beta _{2})q^{3}+(-1+2\beta _{1}+\beta _{2})q^{7}+\cdots$$
1900.2.a.h $3$ $15.172$ 3.3.257.1 None None $$0$$ $$2$$ $$0$$ $$2$$ $-$ $$q+(1-\beta _{1})q^{3}+(1-\beta _{1})q^{7}+(1-2\beta _{1}+\cdots)q^{9}+\cdots$$
1900.2.a.i $3$ $15.172$ 3.3.321.1 None None $$0$$ $$2$$ $$0$$ $$2$$ $-$ $$q+(1+\beta _{2})q^{3}+(1-2\beta _{1}-\beta _{2})q^{7}+(2+\cdots)q^{9}+\cdots$$
1900.2.a.j $4$ $15.172$ $$\Q(\sqrt{2}, \sqrt{5})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $+$ $$q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{3})q^{7}+\beta _{2}q^{9}+\cdots$$
1900.2.a.k $6$ $15.172$ 6.6.56310016.1 None None $$0$$ $$0$$ $$0$$ $$0$$ $-$ $$q+\beta _{3}q^{3}-\beta _{4}q^{7}+(2-\beta _{1}+\beta _{5})q^{9}+\cdots$$
1900.2.c.a $2$ $15.172$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}-iq^{7}-q^{9}+3iq^{13}-iq^{17}+\cdots$$
1900.2.c.b $2$ $15.172$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2iq^{3}+3iq^{7}-q^{9}+5q^{11}-4iq^{13}+\cdots$$
1900.2.c.c $2$ $15.172$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{7}+3q^{9}-4q^{11}+2iq^{13}+3iq^{17}+\cdots$$
1900.2.c.d $4$ $15.172$ $$\Q(\zeta_{8})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\zeta_{8}-\zeta_{8}^{2})q^{3}+(-\zeta_{8}-2\zeta_{8}^{2})q^{7}+\cdots$$
1900.2.c.e $4$ $15.172$ $$\Q(\zeta_{12})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{12}^{2}q^{3}+(-\zeta_{12}+\zeta_{12}^{2})q^{7}+(-1+\cdots)q^{9}+\cdots$$
1900.2.c.f $6$ $15.172$ 6.0.6594624.1 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{4}-\beta _{5})q^{3}+(2\beta _{1}-\beta _{4}-\beta _{5})q^{7}+\cdots$$
1900.2.c.g $6$ $15.172$ 6.0.4227136.2 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{3}+\beta _{1}q^{7}+\beta _{5}q^{9}-\beta _{2}q^{11}+\cdots$$
1900.2.i.a $2$ $15.172$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$-1$$ $$0$$ $$0$$ $$q+(-1+\zeta_{6})q^{3}+2\zeta_{6}q^{9}-4q^{11}+\cdots$$
1900.2.i.b $2$ $15.172$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$2$$ $$0$$ $$8$$ $$q+(2-2\zeta_{6})q^{3}+4q^{7}-\zeta_{6}q^{9}-3q^{11}+\cdots$$
1900.2.i.c $6$ $15.172$ 6.0.1783323.2 None None $$0$$ $$-1$$ $$0$$ $$-4$$ $$q+(-\beta _{3}+\beta _{5})q^{3}+(-1+\beta _{3})q^{7}+(\beta _{1}+\cdots)q^{9}+\cdots$$
1900.2.i.d $8$ $15.172$ $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ None None $$0$$ $$1$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}-\beta _{7}q^{7}+(-1+\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots$$
1900.2.i.e $12$ $15.172$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None None $$0$$ $$-3$$ $$0$$ $$0$$ $$q+(-1+\beta _{1}-\beta _{6})q^{3}+\beta _{4}q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots$$
1900.2.i.f $12$ $15.172$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None None $$0$$ $$3$$ $$0$$ $$0$$ $$q+(1-\beta _{1}+\beta _{6})q^{3}-\beta _{4}q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots$$
1900.2.i.g $20$ $15.172$ $$\mathbb{Q}[x]/(x^{20} + \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{14}q^{3}+(\beta _{15}+\beta _{18})q^{7}+(-1+\beta _{4}+\cdots)q^{9}+\cdots$$
1900.2.l.a $8$ $15.172$ 8.0.2702336256.1 $$\Q(\sqrt{-19})$$ None $$0$$ $$0$$ $$0$$ $$6$$ $$q+(1+\beta _{1}+\beta _{5})q^{7}-3\beta _{1}q^{9}+(-1+\cdots)q^{11}+\cdots$$
1900.2.l.b $12$ $15.172$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$-4$$ $$q-\beta _{2}q^{3}-\beta _{6}q^{7}+(\beta _{3}+4\beta _{5}-\beta _{6}+\cdots)q^{9}+\cdots$$
1900.2.l.c $16$ $15.172$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{4}q^{3}+\beta _{9}q^{7}+(-\beta _{2}-\beta _{11})q^{9}+\cdots$$
1900.2.l.d $24$ $15.172$ None None $$0$$ $$0$$ $$0$$ $$0$$
1900.2.s.a $4$ $15.172$ $$\Q(\zeta_{12})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{12}q^{3}-2\zeta_{12}^{2}q^{9}-4q^{11}+(-\zeta_{12}+\cdots)q^{13}+\cdots$$
1900.2.s.b $4$ $15.172$ $$\Q(\zeta_{12})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{12}q^{3}-2\zeta_{12}^{3}q^{7}+\zeta_{12}^{2}q^{9}+\cdots$$
1900.2.s.c $12$ $15.172$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{6}+\beta _{11})q^{3}+(\beta _{10}+\beta _{11})q^{7}+(-2\beta _{1}+\cdots)q^{9}+\cdots$$
1900.2.s.d $16$ $15.172$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{6}q^{3}+\beta _{14}q^{7}+(\beta _{4}-\beta _{5}+\beta _{10}+\cdots)q^{9}+\cdots$$
1900.2.s.e $24$ $15.172$ None None $$0$$ $$0$$ $$0$$ $$0$$
1900.3.e.a $2$ $51.771$ $$\Q(\sqrt{57})$$ $$\Q(\sqrt{-19})$$ None $$0$$ $$0$$ $$0$$ $$-5$$ $$q+(-1-3\beta )q^{7}+9q^{9}+(1-5\beta )q^{11}+\cdots$$
1900.3.e.b $2$ $51.771$ $$\Q(\sqrt{-29})$$ None None $$0$$ $$0$$ $$0$$ $$2$$ $$q+\beta q^{3}+q^{7}-20q^{9}+14q^{11}+3\beta q^{13}+\cdots$$
1900.3.e.c $4$ $51.771$ $$\Q(\sqrt{6}, \sqrt{-14})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{3}+\beta _{2}q^{7}-5q^{9}+4q^{11}-3\beta _{1}q^{13}+\cdots$$
1900.3.e.d $4$ $51.771$ $$\Q(\sqrt{3}, \sqrt{19})$$ $$\Q(\sqrt{-19})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{7}+9q^{9}+(1-\beta _{3})q^{11}+(\beta _{1}+\cdots)q^{17}+\cdots$$
1900.3.e.e $12$ $51.771$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{6}q^{3}+\beta _{8}q^{7}+(-6-\beta _{1}+\beta _{3}+\cdots)q^{9}+\cdots$$
1900.3.e.f $12$ $51.771$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$12$$ $$q+\beta _{1}q^{3}+(1+\beta _{9})q^{7}+(-1+\beta _{2})q^{9}+\cdots$$
1900.3.e.g $14$ $51.771$ $$\mathbb{Q}[x]/(x^{14} + \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$-4$$ $$q+\beta _{1}q^{3}-\beta _{7}q^{7}+(-4+\beta _{2})q^{9}-\beta _{3}q^{11}+\cdots$$