## Results (41 matches)

Label Dim $A$ Field CM RM Traces Fricke sign $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2075.1.c.a $1$ $1.036$ $$\Q$$ $$\Q(\sqrt{-83})$$ None $$0$$ $$-2$$ $$0$$ $$1$$ $$q-2q^{3}+q^{4}+q^{7}+3q^{9}-q^{11}-2q^{12}+\cdots$$
2075.1.c.b $1$ $1.036$ $$\Q$$ $$\Q(\sqrt{-83})$$ None $$0$$ $$-1$$ $$0$$ $$-1$$ $$q-q^{3}+q^{4}-q^{7}-q^{11}-q^{12}+q^{16}+\cdots$$
2075.1.c.c $1$ $1.036$ $$\Q$$ $$\Q(\sqrt{-83})$$ None $$0$$ $$-1$$ $$0$$ $$2$$ $$q-q^{3}+q^{4}+2q^{7}+2q^{11}-q^{12}+\cdots$$
2075.1.c.d $1$ $1.036$ $$\Q$$ $$\Q(\sqrt{-83})$$ None $$0$$ $$1$$ $$0$$ $$-2$$ $$q+q^{3}+q^{4}-2q^{7}+2q^{11}+q^{12}+\cdots$$
2075.1.c.e $1$ $1.036$ $$\Q$$ $$\Q(\sqrt{-83})$$ None $$0$$ $$1$$ $$0$$ $$1$$ $$q+q^{3}+q^{4}+q^{7}-q^{11}+q^{12}+q^{16}+\cdots$$
2075.1.c.f $1$ $1.036$ $$\Q$$ $$\Q(\sqrt{-83})$$ None $$0$$ $$1$$ $$0$$ $$1$$ $$q+q^{3}+q^{4}+q^{7}-q^{11}+q^{12}+q^{16}+\cdots$$
2075.1.c.g $1$ $1.036$ $$\Q$$ $$\Q(\sqrt{-83})$$ None $$0$$ $$2$$ $$0$$ $$-1$$ $$q+2q^{3}+q^{4}-q^{7}+3q^{9}-q^{11}+2q^{12}+\cdots$$
2075.1.c.h $4$ $1.036$ $$\Q(i, \sqrt{5})$$ $$\Q(\sqrt{-415})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{2}+\beta _{2}q^{4}-\beta _{3}q^{8}-q^{9}+\beta _{2}q^{11}+\cdots$$
2075.1.d.a $2$ $1.036$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-83})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}-q^{4}-iq^{7}-3q^{9}-q^{11}+\cdots$$
2075.1.d.b $2$ $1.036$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-83})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}-q^{4}+iq^{7}-q^{11}+iq^{12}+\cdots$$
2075.1.d.c $2$ $1.036$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-83})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}-q^{4}-iq^{7}-q^{11}-iq^{12}+\cdots$$
2075.1.d.d $2$ $1.036$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-83})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}-q^{4}-iq^{7}+q^{11}+iq^{12}+\cdots$$
2075.2.a.a $1$ $16.569$ $$\Q$$ None None $$-1$$ $$-3$$ $$0$$ $$-1$$ $-$ $$q-q^{2}-3q^{3}-q^{4}+3q^{6}-q^{7}+3q^{8}+\cdots$$
2075.2.a.b $1$ $16.569$ $$\Q$$ None None $$-1$$ $$0$$ $$0$$ $$-1$$ $-$ $$q-q^{2}-q^{4}-q^{7}+3q^{8}-3q^{9}+3q^{11}+\cdots$$
2075.2.a.c $1$ $16.569$ $$\Q$$ None None $$1$$ $$0$$ $$0$$ $$1$$ $-$ $$q+q^{2}-q^{4}+q^{7}-3q^{8}-3q^{9}+3q^{11}+\cdots$$
2075.2.a.d $1$ $16.569$ $$\Q$$ None None $$1$$ $$1$$ $$0$$ $$3$$ $-$ $$q+q^{2}+q^{3}-q^{4}+q^{6}+3q^{7}-3q^{8}+\cdots$$
2075.2.a.e $2$ $16.569$ $$\Q(\sqrt{5})$$ None None $$1$$ $$1$$ $$0$$ $$0$$ $+$ $$q+\beta q^{2}+(1-\beta )q^{3}+(-1+\beta )q^{4}-q^{6}+\cdots$$
2075.2.a.f $6$ $16.569$ 6.6.7783241.1 None None $$-2$$ $$-3$$ $$0$$ $$0$$ $+$ $$q-\beta _{1}q^{2}+(-\beta _{2}+\beta _{4})q^{3}+\beta _{2}q^{4}+\cdots$$
2075.2.a.g $6$ $16.569$ 6.6.9059636.1 None None $$-1$$ $$-1$$ $$0$$ $$-3$$ $+$ $$q+(\beta _{1}+\beta _{2})q^{2}+\beta _{3}q^{3}+(1-\beta _{5})q^{4}+\cdots$$
2075.2.a.h $7$ $16.569$ 7.7.179711353.1 None None $$3$$ $$5$$ $$0$$ $$6$$ $-$ $$q+\beta _{6}q^{2}+(1-\beta _{1})q^{3}+(1-\beta _{5}+\beta _{6})q^{4}+\cdots$$
2075.2.a.i $8$ $16.569$ $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ None None $$-1$$ $$1$$ $$0$$ $$0$$ $+$ $$q-\beta _{1}q^{2}-\beta _{5}q^{3}+\beta _{2}q^{4}+(-\beta _{1}+\beta _{5}+\cdots)q^{6}+\cdots$$
2075.2.a.j $8$ $16.569$ $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ None None $$1$$ $$-1$$ $$0$$ $$0$$ $+$ $$q+\beta _{1}q^{2}+\beta _{5}q^{3}+\beta _{2}q^{4}+(-\beta _{1}+\beta _{5}+\cdots)q^{6}+\cdots$$
2075.2.a.k $11$ $16.569$ $$\mathbb{Q}[x]/(x^{11} - \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$3$$ $-$ $$q-\beta _{1}q^{2}-\beta _{7}q^{3}+(2+\beta _{2})q^{4}+(-1+\cdots)q^{6}+\cdots$$
2075.2.a.l $19$ $16.569$ $$\mathbb{Q}[x]/(x^{19} - \cdots)$$ None None $$0$$ $$-1$$ $$0$$ $$-1$$ $-$ $$q+\beta _{1}q^{2}+\beta _{9}q^{3}+(2+\beta _{2})q^{4}+\beta _{7}q^{6}+\cdots$$
2075.2.a.m $19$ $16.569$ $$\mathbb{Q}[x]/(x^{19} - \cdots)$$ None None $$0$$ $$1$$ $$0$$ $$1$$ $-$ $$q-\beta _{1}q^{2}-\beta _{9}q^{3}+(2+\beta _{2})q^{4}+\beta _{7}q^{6}+\cdots$$
2075.2.a.n $20$ $16.569$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None None $$-5$$ $$-6$$ $$0$$ $$-14$$ $+$ $$q-\beta _{1}q^{2}+\beta _{15}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{6}+\cdots$$
2075.2.a.o $20$ $16.569$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None None $$5$$ $$6$$ $$0$$ $$14$$ $-$ $$q+\beta _{1}q^{2}-\beta _{15}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{6}+\cdots$$
2075.4.a.a $1$ $122.429$ $$\Q$$ None None $$-4$$ $$-7$$ $$0$$ $$0$$ $-$ $$q-4q^{2}-7q^{3}+8q^{4}+28q^{6}+22q^{9}+\cdots$$
2075.4.a.b $1$ $122.429$ $$\Q$$ None None $$4$$ $$7$$ $$0$$ $$0$$ $-$ $$q+4q^{2}+7q^{3}+8q^{4}+28q^{6}+22q^{9}+\cdots$$
2075.4.a.c $7$ $122.429$ $$\mathbb{Q}[x]/(x^{7} - \cdots)$$ None None $$5$$ $$11$$ $$0$$ $$46$$ $+$ $$q+(1+\beta _{4})q^{2}+(1-\beta _{1}-\beta _{4})q^{3}+(2+\cdots)q^{4}+\cdots$$
2075.4.a.d $13$ $122.429$ $$\mathbb{Q}[x]/(x^{13} - \cdots)$$ None None $$-5$$ $$-7$$ $$0$$ $$-52$$ $-$ $$q-\beta _{1}q^{2}+(-1-\beta _{8})q^{3}+(6+\beta _{2})q^{4}+\cdots$$
2075.4.a.e $15$ $122.429$ $$\mathbb{Q}[x]/(x^{15} - \cdots)$$ None None $$3$$ $$12$$ $$0$$ $$37$$ $-$ $$q+\beta _{1}q^{2}+(1-\beta _{5})q^{3}+(2+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$$
2075.4.a.f $20$ $122.429$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None None $$-5$$ $$-12$$ $$0$$ $$-31$$ $-$ $$q-\beta _{1}q^{2}+(-1-\beta _{5})q^{3}+(3+\beta _{2})q^{4}+\cdots$$
2075.4.a.g $21$ $122.429$ None None $$5$$ $$12$$ $$0$$ $$11$$ $+$
2075.4.a.h $26$ $122.429$ None None $$-7$$ $$-12$$ $$0$$ $$-5$$ $+$
2075.4.a.i $34$ $122.429$ None None $$-3$$ $$-13$$ $$0$$ $$-6$$ $-$
2075.4.a.j $34$ $122.429$ None None $$3$$ $$13$$ $$0$$ $$6$$ $-$
2075.4.a.k $47$ $122.429$ None None $$-1$$ $$6$$ $$0$$ $$6$$ $+$
2075.4.a.l $47$ $122.429$ None None $$1$$ $$-6$$ $$0$$ $$-6$$ $+$
2075.4.a.m $62$ $122.429$ None None $$-10$$ $$-18$$ $$0$$ $$-98$$ $-$
2075.4.a.n $62$ $122.429$ None None $$10$$ $$18$$ $$0$$ $$98$$ $+$