## Results (1-50 of 82 matches)

Label Dim $A$ Field CM Traces Fricke sign $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
115.2.a.a $1$ $0.918$ $$\Q$$ None $$2$$ $$0$$ $$-1$$ $$1$$ $-$ $$q+2q^{2}+2q^{4}-q^{5}+q^{7}-3q^{9}-2q^{10}+\cdots$$
115.2.a.b $2$ $0.918$ $$\Q(\sqrt{5})$$ None $$-3$$ $$-2$$ $$-2$$ $$-2$$ $+$ $$q+(-1-\beta )q^{2}-q^{3}+3\beta q^{4}-q^{5}+\cdots$$
115.2.a.c $4$ $0.918$ 4.4.15317.1 None $$2$$ $$-2$$ $$4$$ $$-3$$ $-$ $$q+\beta _{1}q^{2}+(-1-\beta _{2})q^{3}+(1+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$$
115.2.b.a $2$ $0.918$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$4$$ $$0$$ $$q+2iq^{2}-2iq^{3}-2q^{4}+(2+i)q^{5}+\cdots$$
115.2.b.b $8$ $0.918$ 8.0.527896576.2 None $$0$$ $$0$$ $$-6$$ $$0$$ $$q+\beta _{7}q^{2}+(-\beta _{1}-\beta _{3}+\beta _{5})q^{3}+(-1+\cdots)q^{4}+\cdots$$
115.2.e.a $20$ $0.918$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None $$-4$$ $$-8$$ $$0$$ $$0$$ $$q-\beta _{3}q^{2}+\beta _{2}q^{3}+\beta _{4}q^{4}+\beta _{18}q^{5}+\cdots$$
115.2.g.a $10$ $0.918$ $$\Q(\zeta_{22})$$ None $$5$$ $$1$$ $$1$$ $$5$$ $$q+(\zeta_{22}+\zeta_{22}^{3}-\zeta_{22}^{4}+\zeta_{22}^{5}+\zeta_{22}^{7}+\cdots)q^{2}+\cdots$$
115.2.g.b $20$ $0.918$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None $$-4$$ $$1$$ $$2$$ $$-4$$ $$q+(-1+\beta _{2}+\beta _{3}+\beta _{4}+\beta _{6}+\beta _{8}+\cdots)q^{2}+\cdots$$
115.2.g.c $50$ $0.918$ None $$-5$$ $$-2$$ $$-5$$ $$-5$$
115.2.j.a $100$ $0.918$ None $$0$$ $$0$$ $$-9$$ $$0$$
115.2.l.a $200$ $0.918$ None $$-18$$ $$-14$$ $$-22$$ $$-22$$
115.3.c.a $1$ $3.134$ $$\Q$$ $$\Q(\sqrt{-115})$$ $$0$$ $$0$$ $$-5$$ $$9$$ $$q+4q^{4}-5q^{5}+9q^{7}+9q^{9}+2^{4}q^{16}+\cdots$$
115.3.c.b $1$ $3.134$ $$\Q$$ $$\Q(\sqrt{-115})$$ $$0$$ $$0$$ $$5$$ $$-9$$ $$q+4q^{4}+5q^{5}-9q^{7}+9q^{9}+2^{4}q^{16}+\cdots$$
115.3.c.c $20$ $3.134$ $$\mathbb{Q}[x]/(x^{20} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{3}q^{2}-\beta _{4}q^{3}+(-3+\beta _{7}-\beta _{8}+\cdots)q^{4}+\cdots$$
115.3.d.a $6$ $3.134$ $$\mathbb{Q}[x]/(x^{6} - \cdots)$$ None $$-6$$ $$2$$ $$0$$ $$0$$ $$q-q^{2}+\beta _{4}q^{3}-3q^{4}-\beta _{3}q^{5}-\beta _{4}q^{6}+\cdots$$
115.3.d.b $10$ $3.134$ $$\mathbb{Q}[x]/(x^{10} - \cdots)$$ None $$2$$ $$-2$$ $$0$$ $$0$$ $$q+\beta _{4}q^{2}-\beta _{7}q^{3}+(3+\beta _{6})q^{4}+\beta _{5}q^{5}+\cdots$$
115.3.f.a $44$ $3.134$ None $$-4$$ $$0$$ $$-8$$ $$-16$$
115.3.h.a $160$ $3.134$ None $$4$$ $$0$$ $$0$$ $$0$$
115.3.i.a $220$ $3.134$ None $$0$$ $$0$$ $$-11$$ $$0$$
115.3.k.a $440$ $3.134$ None $$-18$$ $$-22$$ $$-14$$ $$-6$$
115.4.a.a $1$ $6.785$ $$\Q$$ None $$1$$ $$4$$ $$-5$$ $$-32$$ $-$ $$q+q^{2}+4q^{3}-7q^{4}-5q^{5}+4q^{6}+\cdots$$
115.4.a.b $1$ $6.785$ $$\Q$$ None $$2$$ $$-3$$ $$5$$ $$-2$$ $-$ $$q+2q^{2}-3q^{3}-4q^{4}+5q^{5}-6q^{6}+\cdots$$
115.4.a.c $2$ $6.785$ $$\Q(\sqrt{109})$$ None $$-6$$ $$-3$$ $$10$$ $$1$$ $-$ $$q-3q^{2}+(-1-\beta )q^{3}+q^{4}+5q^{5}+\cdots$$
115.4.a.d $5$ $6.785$ $$\mathbb{Q}[x]/(x^{5} - \cdots)$$ None $$-5$$ $$-6$$ $$-25$$ $$-15$$ $-$ $$q+(-1+\beta _{1})q^{2}+(-1-\beta _{2}-\beta _{3}-\beta _{4})q^{3}+\cdots$$
115.4.a.e $5$ $6.785$ $$\mathbb{Q}[x]/(x^{5} - \cdots)$$ None $$6$$ $$4$$ $$-25$$ $$-3$$ $+$ $$q+(1+\beta _{1})q^{2}+(1+\beta _{1}-\beta _{2}+\beta _{3})q^{3}+\cdots$$
115.4.a.f $8$ $6.785$ $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ None $$6$$ $$0$$ $$40$$ $$11$$ $+$ $$q+(1-\beta _{1})q^{2}+\beta _{6}q^{3}+(5+\beta _{2})q^{4}+\cdots$$
115.4.b.a $34$ $6.785$ None $$0$$ $$0$$ $$14$$ $$0$$
115.4.e.a $68$ $6.785$ None $$-4$$ $$4$$ $$0$$ $$0$$
115.4.g.a $110$ $6.785$ None $$-2$$ $$6$$ $$-55$$ $$-10$$
115.4.g.b $130$ $6.785$ None $$6$$ $$-6$$ $$65$$ $$38$$
115.4.j.a $340$ $6.785$ None $$0$$ $$0$$ $$-25$$ $$0$$
115.4.l.a $680$ $6.785$ None $$-18$$ $$-26$$ $$-22$$ $$-22$$
115.5.c.a $1$ $11.888$ $$\Q$$ $$\Q(\sqrt{-115})$$ $$0$$ $$0$$ $$-25$$ $$17$$ $$q+2^{4}q^{4}-5^{2}q^{5}+17q^{7}+3^{4}q^{9}+\cdots$$
115.5.c.b $1$ $11.888$ $$\Q$$ $$\Q(\sqrt{-115})$$ $$0$$ $$0$$ $$25$$ $$-17$$ $$q+2^{4}q^{4}+5^{2}q^{5}-17q^{7}+3^{4}q^{9}+\cdots$$
115.5.c.c $44$ $11.888$ None $$0$$ $$0$$ $$0$$ $$0$$
115.5.d.a $32$ $11.888$ None $$12$$ $$0$$ $$0$$ $$0$$
115.5.f.a $88$ $11.888$ None $$0$$ $$0$$ $$-48$$ $$160$$
115.5.h.a $320$ $11.888$ None $$-12$$ $$0$$ $$0$$ $$0$$
115.5.i.a $460$ $11.888$ None $$0$$ $$0$$ $$-11$$ $$0$$
115.5.k.a $920$ $11.888$ None $$-18$$ $$2$$ $$-54$$ $$-78$$
115.6.a.a $2$ $18.444$ $$\Q(\sqrt{1821})$$ None $$4$$ $$3$$ $$-50$$ $$53$$ $-$ $$q+2q^{2}+(2-\beta )q^{3}-28q^{4}-5^{2}q^{5}+\cdots$$
115.6.a.b $7$ $18.444$ $$\mathbb{Q}[x]/(x^{7} - \cdots)$$ None $$-12$$ $$4$$ $$175$$ $$-275$$ $+$ $$q+(-2+\beta _{1})q^{2}+(1-\beta _{1}-\beta _{6})q^{3}+\cdots$$
115.6.a.c $7$ $18.444$ $$\mathbb{Q}[x]/(x^{7} - \cdots)$$ None $$4$$ $$-3$$ $$-175$$ $$33$$ $-$ $$q+(1-\beta _{1})q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+\cdots$$
115.6.a.d $10$ $18.444$ $$\mathbb{Q}[x]/(x^{10} - \cdots)$$ None $$-12$$ $$-18$$ $$-250$$ $$-15$$ $+$ $$q+(-1-\beta _{1})q^{2}+(-2+\beta _{3})q^{3}+(14+\cdots)q^{4}+\cdots$$
115.6.a.e $12$ $18.444$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$8$$ $$22$$ $$300$$ $$16$$ $-$ $$q+(1-\beta _{1})q^{2}+(2-\beta _{1}-\beta _{4})q^{3}+(5^{2}+\cdots)q^{4}+\cdots$$
115.6.b.a $54$ $18.444$ None $$0$$ $$0$$ $$98$$ $$0$$
115.7.c.a $1$ $26.456$ $$\Q$$ $$\Q(\sqrt{-115})$$ $$0$$ $$0$$ $$-125$$ $$-594$$ $$q+2^{6}q^{4}-5^{3}q^{5}-594q^{7}+3^{6}q^{9}+\cdots$$
115.7.c.b $1$ $26.456$ $$\Q$$ $$\Q(\sqrt{-115})$$ $$0$$ $$0$$ $$125$$ $$594$$ $$q+2^{6}q^{4}+5^{3}q^{5}+594q^{7}+3^{6}q^{9}+\cdots$$
115.7.c.c $68$ $26.456$ None $$0$$ $$0$$ $$0$$ $$0$$
115.7.d.a $48$ $26.456$ None $$-20$$ $$0$$ $$0$$ $$0$$