## Results (displaying matches 1-50 of 52) Next

Label Dim. $$A$$ Field CM RM Traces Fricke sign $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
4000.1.b.a $$4$$ $$1.996$$ $$\Q(i, \sqrt{5})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\beta _{1}-\beta _{3})q^{3}-\beta _{3}q^{7}+(-1-\beta _{2}+\cdots)q^{9}+\cdots$$
4000.1.b.b $$4$$ $$1.996$$ $$\Q(i, \sqrt{5})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{3}+\beta _{3}q^{7}+\beta _{2}q^{9}-\beta _{3}q^{11}+\cdots$$
4000.1.e.a $$2$$ $$1.996$$ $$\Q(\sqrt{5})$$ $$\Q(\sqrt{-10})$$ None $$0$$ $$0$$ $$0$$ $$-1$$ $$q-\beta q^{7}+q^{9}+(1-\beta )q^{11}+(1-\beta )q^{13}+\cdots$$
4000.1.e.b $$2$$ $$1.996$$ $$\Q(\sqrt{5})$$ $$\Q(\sqrt{-10})$$ None $$0$$ $$0$$ $$0$$ $$1$$ $$q+\beta q^{7}+q^{9}+(1-\beta )q^{11}+(-1+\beta )q^{13}+\cdots$$
4000.1.g.a $$4$$ $$1.996$$ $$\Q(i, \sqrt{5})$$ $$\Q(\sqrt{-10})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{1}+\beta _{3})q^{7}-q^{9}-\beta _{2}q^{11}-\beta _{1}q^{13}+\cdots$$
4000.1.h.a $$4$$ $$1.996$$ $$\Q(i, \sqrt{5})$$ None None $$0$$ $$-2$$ $$0$$ $$4$$ $$q+(-1-\beta _{2})q^{3}+q^{7}+(1+\beta _{2})q^{9}+\cdots$$
4000.1.h.b $$4$$ $$1.996$$ $$\Q(i, \sqrt{5})$$ None None $$0$$ $$2$$ $$0$$ $$-4$$ $$q+(1+\beta _{2})q^{3}-q^{7}+(1+\beta _{2})q^{9}+\beta _{3}q^{11}+\cdots$$
4000.1.p.a $$8$$ $$1.996$$ $$\Q(\zeta_{20})$$ $$\Q(\sqrt{-5})$$ None $$0$$ $$-2$$ $$0$$ $$2$$ $$q+(-\zeta_{20}+\zeta_{20}^{4})q^{3}+(\zeta_{20}^{7}-\zeta_{20}^{8}+\cdots)q^{7}+\cdots$$
4000.1.p.b $$8$$ $$1.996$$ $$\Q(\zeta_{20})$$ $$\Q(\sqrt{-5})$$ None $$0$$ $$2$$ $$0$$ $$-2$$ $$q+(\zeta_{20}^{6}+\zeta_{20}^{9})q^{3}+(-\zeta_{20}^{2}-\zeta_{20}^{3}+\cdots)q^{7}+\cdots$$
4000.1.bf.a $$8$$ $$1.996$$ $$\Q(\zeta_{20})$$ None None $$0$$ $$-2$$ $$0$$ $$4$$ $$q-\zeta_{20}^{2}q^{3}+(-\zeta_{20}^{4}+\zeta_{20}^{6})q^{7}+\cdots$$
4000.1.bf.b $$8$$ $$1.996$$ $$\Q(\zeta_{20})$$ None None $$0$$ $$2$$ $$0$$ $$-4$$ $$q+\zeta_{20}^{2}q^{3}+(\zeta_{20}^{4}-\zeta_{20}^{6})q^{7}+(-\zeta_{20}^{3}+\cdots)q^{13}+\cdots$$
4000.1.bh.a $$8$$ $$1.996$$ $$\Q(\zeta_{20})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{20}q^{3}+(\zeta_{20}^{3}+\zeta_{20}^{7})q^{7}+(-1+\cdots)q^{13}+\cdots$$
4000.1.bo.a $$8$$ $$1.996$$ $$\Q(\zeta_{20})$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{20}^{9}q^{9}+(-\zeta_{20}^{6}-\zeta_{20}^{7})q^{13}+\cdots$$
4000.1.bo.b $$8$$ $$1.996$$ $$\Q(\zeta_{20})$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{20}^{9}q^{9}+(\zeta_{20}-\zeta_{20}^{2})q^{13}+(\zeta_{20}^{4}+\cdots)q^{17}+\cdots$$
4000.1.bo.c $$8$$ $$1.996$$ $$\Q(\zeta_{20})$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{20}^{9}q^{9}+(\zeta_{20}^{6}+\zeta_{20}^{7})q^{13}+(\zeta_{20}^{2}+\cdots)q^{17}+\cdots$$
4000.1.cq.a $$40$$ $$1.996$$ $$\Q(\zeta_{100})$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{100}^{13}q^{5}-\zeta_{100}^{49}q^{9}+(\zeta_{100}^{2}-\zeta_{100}^{21}+\cdots)q^{13}+\cdots$$
4000.2.a.a $$4$$ $$31.940$$ $$\Q(\zeta_{20})^+$$ $$\Q(\sqrt{-5})$$ None $$0$$ $$-6$$ $$0$$ $$-8$$ $$+$$ $$q+(-2-\beta _{1}-\beta _{2}+\beta _{3})q^{3}+(-1+2\beta _{1}+\cdots)q^{7}+\cdots$$
4000.2.a.b $$4$$ $$31.940$$ $$\Q(\zeta_{20})^+$$ $$\Q(\sqrt{-5})$$ None $$0$$ $$-4$$ $$0$$ $$-2$$ $$+$$ $$q+(-1+\beta _{1})q^{3}+(-1+\beta _{1}-\beta _{2}-\beta _{3})q^{7}+\cdots$$
4000.2.a.c $$4$$ $$31.940$$ 4.4.16400.1 None None $$0$$ $$-2$$ $$0$$ $$-2$$ $$-$$ $$q+\beta _{2}q^{3}+(-1-\beta _{2})q^{7}+(-2-\beta _{2}+\cdots)q^{9}+\cdots$$
4000.2.a.d $$4$$ $$31.940$$ $$\Q(\zeta_{20})^+$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$+$$ $$q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{3})q^{7}+\beta _{2}q^{9}+\cdots$$
4000.2.a.e $$4$$ $$31.940$$ $$\Q(\zeta_{20})^+$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$+$$ $$q+\beta _{1}q^{3}+\beta _{3}q^{7}+\beta _{2}q^{9}-2\beta _{3}q^{11}+\cdots$$
4000.2.a.f $$4$$ $$31.940$$ $$\Q(\zeta_{20})^+$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$-$$ $$q+\beta _{1}q^{3}+\beta _{3}q^{7}+\beta _{2}q^{9}+2\beta _{3}q^{11}+\cdots$$
4000.2.a.g $$4$$ $$31.940$$ $$\Q(\zeta_{20})^+$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$+$$ $$q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{3})q^{7}+\beta _{2}q^{9}+\cdots$$
4000.2.a.h $$4$$ $$31.940$$ 4.4.16400.1 None None $$0$$ $$2$$ $$0$$ $$2$$ $$+$$ $$q-\beta _{2}q^{3}+(1+\beta _{2})q^{7}+(-2-\beta _{2})q^{9}+\cdots$$
4000.2.a.i $$4$$ $$31.940$$ $$\Q(\zeta_{20})^+$$ $$\Q(\sqrt{-5})$$ None $$0$$ $$4$$ $$0$$ $$2$$ $$-$$ $$q+(1+\beta _{1})q^{3}+(1+\beta _{1}+\beta _{2}-\beta _{3})q^{7}+\cdots$$
4000.2.a.j $$4$$ $$31.940$$ $$\Q(\zeta_{20})^+$$ $$\Q(\sqrt{-5})$$ None $$0$$ $$6$$ $$0$$ $$8$$ $$-$$ $$q+(2-\beta _{1}+\beta _{2}+\beta _{3})q^{3}+(1+2\beta _{1}+\cdots)q^{7}+\cdots$$
4000.2.a.k $$6$$ $$31.940$$ 6.6.30040000.1 None None $$0$$ $$0$$ $$0$$ $$-3$$ $$+$$ $$q+\beta _{1}q^{3}+(-1+\beta _{5})q^{7}+(1+\beta _{1}+\beta _{3}+\cdots)q^{9}+\cdots$$
4000.2.a.l $$6$$ $$31.940$$ 6.6.30040000.1 None None $$0$$ $$0$$ $$0$$ $$-3$$ $$-$$ $$q+\beta _{1}q^{3}+(-1+\beta _{5})q^{7}+(1+\beta _{1}+\beta _{3}+\cdots)q^{9}+\cdots$$
4000.2.a.m $$6$$ $$31.940$$ 6.6.30040000.1 None None $$0$$ $$0$$ $$0$$ $$3$$ $$+$$ $$q-\beta _{1}q^{3}+(1-\beta _{5})q^{7}+(1+\beta _{1}+\beta _{3}+\cdots)q^{9}+\cdots$$
4000.2.a.n $$6$$ $$31.940$$ 6.6.30040000.1 None None $$0$$ $$0$$ $$0$$ $$3$$ $$-$$ $$q-\beta _{1}q^{3}+(1-\beta _{5})q^{7}+(1+\beta _{1}+\beta _{3}+\cdots)q^{9}+\cdots$$
4000.2.a.o $$8$$ $$31.940$$ 8.8.$$\cdots$$.1 None None $$0$$ $$0$$ $$0$$ $$0$$ $$+$$ $$q-\beta _{4}q^{3}-\beta _{6}q^{7}+(1-\beta _{5})q^{9}+(\beta _{4}+\cdots)q^{11}+\cdots$$
4000.2.a.p $$8$$ $$31.940$$ 8.8.$$\cdots$$.1 None None $$0$$ $$0$$ $$0$$ $$0$$ $$-$$ $$q-\beta _{4}q^{3}-\beta _{6}q^{7}+(1-\beta _{5})q^{9}+(-\beta _{4}+\cdots)q^{11}+\cdots$$
4000.2.a.q $$8$$ $$31.940$$ 8.8.$$\cdots$$.1 None None $$0$$ $$0$$ $$0$$ $$0$$ $$-$$ $$q-\beta _{1}q^{3}+\beta _{7}q^{7}+(2+\beta _{2})q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots$$
4000.2.a.r $$8$$ $$31.940$$ 8.8.$$\cdots$$.1 None None $$0$$ $$0$$ $$0$$ $$0$$ $$-$$ $$q-\beta _{1}q^{3}+\beta _{7}q^{7}+(2+\beta _{2})q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots$$
4000.2.c.a $$8$$ $$31.940$$ $$\Q(\zeta_{20})$$ $$\Q(\sqrt{-5})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\zeta_{20}^{3}+\zeta_{20}^{7})q^{3}+(\zeta_{20}^{2}-2\zeta_{20}^{3}+\cdots)q^{7}+\cdots$$
4000.2.c.b $$8$$ $$31.940$$ $$\Q(\zeta_{20})$$ $$\Q(\sqrt{-5})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{20}^{3}q^{3}+(\zeta_{20}^{3}-\zeta_{20}^{7})q^{7}+(-1+\cdots)q^{9}+\cdots$$
4000.2.c.c $$8$$ $$31.940$$ $$\Q(\zeta_{20})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{20}^{7}q^{3}+(\zeta_{20}^{2}-\zeta_{20}^{7})q^{7}+(1+\cdots)q^{9}+\cdots$$
4000.2.c.d $$8$$ $$31.940$$ $$\Q(\zeta_{20})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{20}^{2}q^{3}-\zeta_{20}^{7}q^{7}-\zeta_{20}^{5}q^{9}+\cdots$$
4000.2.c.e $$8$$ $$31.940$$ 8.0.268960000.3 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\beta _{1}+\beta _{3})q^{3}+\beta _{3}q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots$$
4000.2.c.f $$12$$ $$31.940$$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}-\beta _{11}q^{7}+(\beta _{3}+\beta _{4}+\beta _{6}+\cdots)q^{9}+\cdots$$
4000.2.c.g $$12$$ $$31.940$$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}-\beta _{11}q^{7}+(\beta _{3}+\beta _{4}+\beta _{6}+\cdots)q^{9}+\cdots$$
4000.2.c.h $$16$$ $$31.940$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{3}q^{3}-\beta _{15}q^{7}+(-2+\beta _{4})q^{9}+\cdots$$
4000.2.c.i $$16$$ $$31.940$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{3}-\beta _{12}q^{7}+(-1+\beta _{6})q^{9}+\cdots$$
4000.2.d.a $$4$$ $$31.940$$ $$\Q(i, \sqrt{5})$$ None None $$0$$ $$0$$ $$0$$ $$-2$$ $$q+2\beta _{1}q^{3}+(1+3\beta _{2})q^{7}+(-1+4\beta _{2}+\cdots)q^{9}+\cdots$$
4000.2.d.b $$4$$ $$31.940$$ $$\Q(i, \sqrt{5})$$ None None $$0$$ $$0$$ $$0$$ $$2$$ $$q+2\beta _{1}q^{3}+(-1-3\beta _{2})q^{7}+(-1+4\beta _{2}+\cdots)q^{9}+\cdots$$
4000.2.d.c $$40$$ $$31.940$$ None None $$0$$ $$0$$ $$0$$ $$0$$
4000.2.d.d $$48$$ $$31.940$$ None None $$0$$ $$0$$ $$0$$ $$0$$
4000.2.f.a $$4$$ $$31.940$$ $$\Q(i, \sqrt{5})$$ None None $$0$$ $$-4$$ $$0$$ $$0$$ $$q+(-2-2\beta _{2})q^{3}+(3\beta _{1}+2\beta _{3})q^{7}+\cdots$$
4000.2.f.b $$4$$ $$31.940$$ $$\Q(i, \sqrt{5})$$ None None $$0$$ $$4$$ $$0$$ $$0$$ $$q+(2+2\beta _{2})q^{3}+(3\beta _{1}+2\beta _{3})q^{7}+(5+\cdots)q^{9}+\cdots$$
4000.2.f.c $$20$$ $$31.940$$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None None $$0$$ $$-4$$ $$0$$ $$0$$ $$q-\beta _{9}q^{3}+\beta _{5}q^{7}+(\beta _{1}-\beta _{7}+\beta _{10}+\cdots)q^{9}+\cdots$$
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