## Results (1-50 of 136 matches)

Label Dim $A$ Field CM RM Traces Fricke sign $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
540.1.f.a $4$ $0.269$ $$\Q(\zeta_{12})$$ $$\Q(\sqrt{-15})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{3}q^{5}-\zeta_{12}^{3}q^{8}+\cdots$$
540.1.p.a $2$ $0.269$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-5})$$ None $$-1$$ $$0$$ $$1$$ $$-1$$ $$q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{5}-\zeta_{6}q^{7}+\cdots$$
540.1.p.b $2$ $0.269$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-5})$$ None $$1$$ $$0$$ $$1$$ $$1$$ $$q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{5}+\zeta_{6}q^{7}+\cdots$$
540.1.bf.a $6$ $0.269$ $$\Q(\zeta_{18})$$ $$\Q(\sqrt{-5})$$ None $$0$$ $$0$$ $$0$$ $$-3$$ $$q-\zeta_{18}q^{2}-\zeta_{18}^{5}q^{3}+\zeta_{18}^{2}q^{4}-\zeta_{18}^{5}q^{5}+\cdots$$
540.1.bf.b $6$ $0.269$ $$\Q(\zeta_{18})$$ $$\Q(\sqrt{-5})$$ None $$0$$ $$0$$ $$0$$ $$3$$ $$q+\zeta_{18}q^{2}+\zeta_{18}^{5}q^{3}+\zeta_{18}^{2}q^{4}-\zeta_{18}^{5}q^{5}+\cdots$$
540.2.a.a $1$ $4.312$ $$\Q$$ None None $$0$$ $$0$$ $$-1$$ $$-4$$ $+$ $$q-q^{5}-4q^{7}+6q^{11}-4q^{13}-3q^{17}+\cdots$$
540.2.a.b $1$ $4.312$ $$\Q$$ None None $$0$$ $$0$$ $$-1$$ $$-1$$ $+$ $$q-q^{5}-q^{7}-6q^{11}-q^{13}-q^{19}+\cdots$$
540.2.a.c $1$ $4.312$ $$\Q$$ None None $$0$$ $$0$$ $$-1$$ $$2$$ $-$ $$q-q^{5}+2q^{7}+2q^{13}+3q^{17}+5q^{19}+\cdots$$
540.2.a.d $1$ $4.312$ $$\Q$$ None None $$0$$ $$0$$ $$1$$ $$-4$$ $+$ $$q+q^{5}-4q^{7}-6q^{11}-4q^{13}+3q^{17}+\cdots$$
540.2.a.e $1$ $4.312$ $$\Q$$ None None $$0$$ $$0$$ $$1$$ $$-1$$ $-$ $$q+q^{5}-q^{7}+6q^{11}-q^{13}-q^{19}+\cdots$$
540.2.a.f $1$ $4.312$ $$\Q$$ None None $$0$$ $$0$$ $$1$$ $$2$$ $-$ $$q+q^{5}+2q^{7}+2q^{13}-3q^{17}+5q^{19}+\cdots$$
540.2.d.a $2$ $4.312$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+(-2+i)q^{5}-2iq^{7}+2q^{11}-6iq^{13}+\cdots$$
540.2.d.b $2$ $4.312$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$4$$ $$0$$ $$q+(2+i)q^{5}+2iq^{7}-2q^{11}+6iq^{13}+\cdots$$
540.2.d.c $4$ $4.312$ $$\Q(i, \sqrt{10})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{5}+\beta _{2}q^{7}+(\beta _{1}-\beta _{3})q^{11}-3\beta _{2}q^{13}+\cdots$$
540.2.e.a $16$ $4.312$ 16.0.$$\cdots$$.1 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{11}q^{2}+\beta _{2}q^{4}+\beta _{3}q^{5}+(\beta _{4}+\beta _{6}+\cdots)q^{7}+\cdots$$
540.2.e.b $16$ $4.312$ 16.0.$$\cdots$$.1 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(\beta _{2}+\beta _{7})q^{4}+\beta _{3}q^{5}+(\beta _{6}+\cdots)q^{7}+\cdots$$
540.2.h.a $4$ $4.312$ $$\Q(\sqrt{-3}, \sqrt{5})$$ $$\Q(\sqrt{-15})$$ None $$-3$$ $$0$$ $$0$$ $$0$$ $$q+(-1+\beta _{1})q^{2}+(-\beta _{1}+\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots$$
540.2.h.b $4$ $4.312$ $$\Q(\sqrt{-3}, \sqrt{5})$$ $$\Q(\sqrt{-15})$$ None $$3$$ $$0$$ $$0$$ $$0$$ $$q+(1-\beta _{1})q^{2}+(-\beta _{1}+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$$
540.2.h.c $16$ $4.312$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{7}q^{2}-\beta _{11}q^{4}+(-\beta _{6}-\beta _{10})q^{5}+\cdots$$
540.2.h.d $24$ $4.312$ None None $$0$$ $$0$$ $$0$$ $$0$$
540.2.i.a $2$ $4.312$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$0$$ $$1$$ $$1$$ $$q+\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+4\zeta_{6}q^{13}+6q^{17}+\cdots$$
540.2.i.b $6$ $4.312$ 6.0.954288.1 None None $$0$$ $$0$$ $$-3$$ $$-3$$ $$q+(-1-\beta _{2})q^{5}+(\beta _{2}+\beta _{4})q^{7}+(\beta _{3}+\cdots)q^{11}+\cdots$$
540.2.j.a $8$ $4.312$ 8.0.$$\cdots$$.8 None None $$0$$ $$0$$ $$0$$ $$-8$$ $$q+\beta _{2}q^{5}+(-1-\beta _{1}+\beta _{4})q^{7}+(-\beta _{5}+\cdots)q^{11}+\cdots$$
540.2.j.b $8$ $4.312$ 8.0.$$\cdots$$.1 None None $$0$$ $$0$$ $$0$$ $$4$$ $$q+(-\beta _{1}+\beta _{4}+\beta _{7})q^{5}+(1+\beta _{6})q^{7}+\cdots$$
540.2.k.a $4$ $4.312$ $$\Q(\zeta_{8})$$ None None $$0$$ $$0$$ $$0$$ $$-8$$ $$q+(\zeta_{8}+\zeta_{8}^{3})q^{2}-2q^{4}+(-2\zeta_{8}+\zeta_{8}^{3})q^{5}+\cdots$$
540.2.k.b $4$ $4.312$ $$\Q(\zeta_{8})$$ None None $$0$$ $$0$$ $$0$$ $$4$$ $$q+(\zeta_{8}+\zeta_{8}^{3})q^{2}-2q^{4}+(\zeta_{8}-2\zeta_{8}^{3})q^{5}+\cdots$$
540.2.k.c $4$ $4.312$ $$\Q(\zeta_{8})$$ None None $$0$$ $$0$$ $$0$$ $$-4$$ $$q+(-\zeta_{8}+\zeta_{8}^{3})q^{2}+2q^{4}+(-\zeta_{8}+2\zeta_{8}^{3})q^{5}+\cdots$$
540.2.k.d $4$ $4.312$ $$\Q(\zeta_{8})$$ None None $$0$$ $$0$$ $$0$$ $$8$$ $$q+(-\zeta_{8}+\zeta_{8}^{3})q^{2}+2q^{4}+(2\zeta_{8}-\zeta_{8}^{3})q^{5}+\cdots$$
540.2.k.e $32$ $4.312$ None None $$0$$ $$0$$ $$0$$ $$0$$
540.2.k.f $48$ $4.312$ None None $$0$$ $$0$$ $$0$$ $$0$$
540.2.n.a $4$ $4.312$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None None $$0$$ $$0$$ $$-6$$ $$-6$$ $$q+\beta _{1}q^{2}+2\beta _{2}q^{4}+(-2-\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots$$
540.2.n.b $4$ $4.312$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None None $$0$$ $$0$$ $$-6$$ $$6$$ $$q+\beta _{1}q^{2}+2\beta _{2}q^{4}+(-2-\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots$$
540.2.n.c $8$ $4.312$ 8.0.3317760000.8 $$\Q(\sqrt{-5})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{4}+\beta _{5})q^{2}+(2-2\beta _{3})q^{4}+\beta _{6}q^{5}+\cdots$$
540.2.n.d $48$ $4.312$ None None $$0$$ $$0$$ $$18$$ $$0$$
540.2.q.a $48$ $4.312$ None None $$0$$ $$0$$ $$0$$ $$0$$
540.2.r.a $12$ $4.312$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None None $$0$$ $$0$$ $$-1$$ $$0$$ $$q+(-\beta _{5}+\beta _{10})q^{5}+(\beta _{7}-\beta _{9}+\beta _{10}+\cdots)q^{7}+\cdots$$
540.2.u.a $30$ $4.312$ None None $$0$$ $$-3$$ $$0$$ $$0$$
540.2.u.b $42$ $4.312$ None None $$0$$ $$3$$ $$0$$ $$0$$
540.2.x.a $24$ $4.312$ None None $$0$$ $$0$$ $$0$$ $$0$$
540.2.y.a $128$ $4.312$ None None $$2$$ $$0$$ $$4$$ $$0$$
540.2.bb.a $24$ $4.312$ $$\Q(\sqrt{-5})$$ None $$0$$ $$0$$ $$0$$ $$0$$
540.2.bb.b $600$ $4.312$ None None $$0$$ $$0$$ $$-12$$ $$0$$
540.2.bd.a $108$ $4.312$ None None $$0$$ $$0$$ $$-3$$ $$0$$
540.2.be.a $432$ $4.312$ None None $$0$$ $$0$$ $$0$$ $$0$$
540.2.bh.a $1248$ $4.312$ None None $$-12$$ $$0$$ $$-24$$ $$0$$
540.2.bj.a $216$ $4.312$ None None $$0$$ $$0$$ $$0$$ $$0$$
540.3.b.a $4$ $14.714$ $$\Q(\sqrt{-11}, \sqrt{-19})$$ None None $$0$$ $$0$$ $$-3$$ $$0$$ $$q+(-1-\beta _{3})q^{5}-\beta _{2}q^{7}+(-2\beta _{1}-3\beta _{2}+\cdots)q^{11}+\cdots$$
540.3.b.b $4$ $14.714$ $$\Q(\sqrt{-11}, \sqrt{-19})$$ None None $$0$$ $$0$$ $$3$$ $$0$$ $$q+(1+\beta _{3})q^{5}-\beta _{2}q^{7}+(2\beta _{1}+3\beta _{2}+\cdots)q^{11}+\cdots$$
540.3.b.c $8$ $14.714$ 8.0.$$\cdots$$.13 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{5}+(-\beta _{1}-\beta _{3})q^{7}-\beta _{6}q^{11}+\cdots$$
540.3.c.a $32$ $14.714$ None None $$0$$ $$0$$ $$0$$ $$0$$