# Learn more

## Results (46 matches)

Download to
Label Dim $A$ Field CM RM Traces Fricke sign $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3344.1.p.a $1$ $1.669$ $$\Q$$ $$\Q(\sqrt{-19})$$, $$\Q(\sqrt{-209})$$ $$\Q(\sqrt{11})$$ $$0$$ $$0$$ $$-2$$ $$-2$$ $$q-2q^{5}-2q^{7}-q^{9}-q^{11}+q^{19}+\cdots$$
3344.1.p.b $1$ $1.669$ $$\Q$$ $$\Q(\sqrt{-19})$$, $$\Q(\sqrt{-209})$$ $$\Q(\sqrt{11})$$ $$0$$ $$0$$ $$-2$$ $$2$$ $$q-2q^{5}+2q^{7}-q^{9}+q^{11}-q^{19}+\cdots$$
3344.1.p.c $2$ $1.669$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-19})$$ None $$0$$ $$0$$ $$2$$ $$-2$$ $$q+q^{5}-q^{7}-q^{9}+\zeta_{6}^{2}q^{11}+(\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{17}+\cdots$$
3344.1.p.d $2$ $1.669$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-19})$$ None $$0$$ $$0$$ $$2$$ $$2$$ $$q+q^{5}+q^{7}-q^{9}-\zeta_{6}^{2}q^{11}+(\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{17}+\cdots$$
3344.1.p.e $4$ $1.669$ $$\Q(\zeta_{20})^+$$ $$\Q(\sqrt{-209})$$ None $$0$$ $$0$$ $$2$$ $$-2$$ $$q+\beta _{3}q^{3}+(1+\beta _{2})q^{5}+\beta _{2}q^{7}+(1-\beta _{2}+\cdots)q^{9}+\cdots$$
3344.1.p.f $4$ $1.669$ $$\Q(\zeta_{20})^+$$ $$\Q(\sqrt{-209})$$ None $$0$$ $$0$$ $$2$$ $$2$$ $$q-\beta _{1}q^{3}-\beta _{2}q^{5}+(1+\beta _{2})q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots$$
3344.1.bb.a $4$ $1.669$ $$\Q(\zeta_{12})$$ None None $$0$$ $$2$$ $$-2$$ $$0$$ $$q-\zeta_{12}^{4}q^{3}+\zeta_{12}^{4}q^{5}-\zeta_{12}^{3}q^{11}+\cdots$$
3344.1.bc.a $2$ $1.669$ $$\Q(\sqrt{-3})$$ None $$\Q(\sqrt{11})$$ $$0$$ $$0$$ $$-1$$ $$-2$$ $$q+\zeta_{6}^{2}q^{5}-q^{7}+\zeta_{6}q^{9}+q^{11}-\zeta_{6}^{2}q^{19}+\cdots$$
3344.1.bc.b $2$ $1.669$ $$\Q(\sqrt{-3})$$ None $$\Q(\sqrt{11})$$ $$0$$ $$0$$ $$-1$$ $$2$$ $$q+\zeta_{6}^{2}q^{5}+q^{7}+\zeta_{6}q^{9}-q^{11}+\zeta_{6}^{2}q^{19}+\cdots$$
3344.1.bq.a $4$ $1.669$ $$\Q(\zeta_{10})$$ $$\Q(\sqrt{-19})$$ None $$0$$ $$0$$ $$2$$ $$-3$$ $$q+(\zeta_{10}-\zeta_{10}^{2})q^{5}+(-1-\zeta_{10}^{4})q^{7}+\cdots$$
3344.1.bq.b $4$ $1.669$ $$\Q(\zeta_{10})$$ $$\Q(\sqrt{-19})$$ None $$0$$ $$0$$ $$2$$ $$3$$ $$q+(\zeta_{10}-\zeta_{10}^{2})q^{5}+(1+\zeta_{10}^{4})q^{7}+\cdots$$
3344.1.bq.c $8$ $1.669$ $$\Q(\zeta_{15})$$ $$\Q(\sqrt{-19})$$ None $$0$$ $$0$$ $$-2$$ $$-3$$ $$q+(\zeta_{30}^{11}+\zeta_{30}^{13})q^{5}+(\zeta_{30}^{2}+\zeta_{30}^{10}+\cdots)q^{7}+\cdots$$
3344.1.bq.d $8$ $1.669$ $$\Q(\zeta_{15})$$ $$\Q(\sqrt{-19})$$ None $$0$$ $$0$$ $$-2$$ $$3$$ $$q+(\zeta_{30}-\zeta_{30}^{8})q^{5}+(\zeta_{30}^{5}+\zeta_{30}^{7}+\cdots)q^{7}+\cdots$$
3344.1.bx.a $4$ $1.669$ $$\Q(\zeta_{10})$$ $$\Q(\sqrt{-19})$$ None $$0$$ $$0$$ $$-2$$ $$-3$$ $$q+(\zeta_{10}^{2}+\zeta_{10}^{4})q^{5}+(-1+\zeta_{10}^{3}+\cdots)q^{7}+\cdots$$
3344.1.bx.b $8$ $1.669$ $$\Q(\zeta_{15})$$ $$\Q(\sqrt{-19})$$ None $$0$$ $$0$$ $$2$$ $$3$$ $$q+(-\zeta_{30}+\zeta_{30}^{2})q^{5}+(-\zeta_{30}^{10}-\zeta_{30}^{14}+\cdots)q^{7}+\cdots$$
3344.1.ck.a $8$ $1.669$ $$\Q(\zeta_{24})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+(-\zeta_{24}^{3}+\zeta_{24}^{9}+\cdots)q^{7}+\cdots$$
3344.2.a.a $1$ $26.702$ $$\Q$$ None None $$0$$ $$-3$$ $$-2$$ $$-1$$ $-$ $$q-3q^{3}-2q^{5}-q^{7}+6q^{9}-q^{11}+\cdots$$
3344.2.a.b $1$ $26.702$ $$\Q$$ None None $$0$$ $$-2$$ $$2$$ $$0$$ $-$ $$q-2q^{3}+2q^{5}+q^{9}-q^{11}+4q^{13}+\cdots$$
3344.2.a.c $1$ $26.702$ $$\Q$$ None None $$0$$ $$-1$$ $$-3$$ $$-2$$ $+$ $$q-q^{3}-3q^{5}-2q^{7}-2q^{9}+q^{11}+\cdots$$
3344.2.a.d $1$ $26.702$ $$\Q$$ None None $$0$$ $$-1$$ $$-3$$ $$4$$ $-$ $$q-q^{3}-3q^{5}+4q^{7}-2q^{9}-q^{11}+\cdots$$
3344.2.a.e $1$ $26.702$ $$\Q$$ None None $$0$$ $$-1$$ $$2$$ $$3$$ $+$ $$q-q^{3}+2q^{5}+3q^{7}-2q^{9}+q^{11}+\cdots$$
3344.2.a.f $1$ $26.702$ $$\Q$$ None None $$0$$ $$0$$ $$-2$$ $$4$$ $-$ $$q-2q^{5}+4q^{7}-3q^{9}+q^{11}+2q^{13}+\cdots$$
3344.2.a.g $1$ $26.702$ $$\Q$$ None None $$0$$ $$0$$ $$2$$ $$-2$$ $-$ $$q+2q^{5}-2q^{7}-3q^{9}-q^{11}-2q^{13}+\cdots$$
3344.2.a.h $1$ $26.702$ $$\Q$$ None None $$0$$ $$1$$ $$-2$$ $$3$$ $+$ $$q+q^{3}-2q^{5}+3q^{7}-2q^{9}+q^{11}+\cdots$$
3344.2.a.i $1$ $26.702$ $$\Q$$ None None $$0$$ $$1$$ $$1$$ $$0$$ $+$ $$q+q^{3}+q^{5}-2q^{9}+q^{11}-2q^{13}+\cdots$$
3344.2.a.j $2$ $26.702$ $$\Q(\sqrt{13})$$ None None $$0$$ $$-1$$ $$-1$$ $$-1$$ $+$ $$q-\beta q^{3}-\beta q^{5}+(-1+\beta )q^{7}+\beta q^{9}+\cdots$$
3344.2.a.k $2$ $26.702$ $$\Q(\sqrt{17})$$ None None $$0$$ $$-1$$ $$4$$ $$-3$$ $+$ $$q-\beta q^{3}+2q^{5}+(-2+\beta )q^{7}+(1+\beta )q^{9}+\cdots$$
3344.2.a.l $2$ $26.702$ $$\Q(\sqrt{21})$$ None None $$0$$ $$1$$ $$3$$ $$5$$ $-$ $$q+\beta q^{3}+(2-\beta )q^{5}+(3-\beta )q^{7}+(2+\beta )q^{9}+\cdots$$
3344.2.a.m $2$ $26.702$ $$\Q(\sqrt{2})$$ None None $$0$$ $$2$$ $$-2$$ $$0$$ $+$ $$q+(1+\beta )q^{3}-q^{5}-\beta q^{7}+2\beta q^{9}-q^{11}+\cdots$$
3344.2.a.n $2$ $26.702$ $$\Q(\sqrt{2})$$ None None $$0$$ $$2$$ $$-2$$ $$4$$ $-$ $$q+(1+\beta )q^{3}-q^{5}+(2+\beta )q^{7}+2\beta q^{9}+\cdots$$
3344.2.a.o $2$ $26.702$ $$\Q(\sqrt{13})$$ None None $$0$$ $$3$$ $$-1$$ $$1$$ $-$ $$q+(1+\beta )q^{3}+(-1+\beta )q^{5}+\beta q^{7}+(1+\cdots)q^{9}+\cdots$$
3344.2.a.p $3$ $26.702$ 3.3.469.1 None None $$0$$ $$-1$$ $$5$$ $$-1$$ $-$ $$q-\beta _{1}q^{3}+(2-\beta _{1})q^{5}+\beta _{2}q^{7}+(1+\beta _{2})q^{9}+\cdots$$
3344.2.a.q $3$ $26.702$ 3.3.621.1 None None $$0$$ $$0$$ $$-3$$ $$6$$ $-$ $$q-\beta _{1}q^{3}+(-1-\beta _{1}-\beta _{2})q^{5}+(2+\beta _{1}+\cdots)q^{7}+\cdots$$
3344.2.a.r $3$ $26.702$ 3.3.229.1 None None $$0$$ $$0$$ $$0$$ $$-3$$ $+$ $$q-\beta _{1}q^{3}+\beta _{1}q^{5}+(-1-\beta _{1})q^{7}+\beta _{2}q^{9}+\cdots$$
3344.2.a.s $4$ $26.702$ 4.4.13676.1 None None $$0$$ $$1$$ $$-3$$ $$3$$ $+$ $$q+\beta _{1}q^{3}+(-1+\beta _{3})q^{5}+(1-\beta _{1})q^{7}+\cdots$$
3344.2.a.t $5$ $26.702$ 5.5.246832.1 None None $$0$$ $$-1$$ $$-5$$ $$-6$$ $+$ $$q-\beta _{3}q^{3}+(-1-\beta _{1}+\beta _{2})q^{5}+(-2+\cdots)q^{7}+\cdots$$
3344.2.a.u $5$ $26.702$ 5.5.3979184.1 None None $$0$$ $$-1$$ $$7$$ $$-8$$ $-$ $$q+\beta _{4}q^{3}+(1+\beta _{1})q^{5}+(-2+\beta _{1})q^{7}+\cdots$$
3344.2.a.v $6$ $26.702$ 6.6.576096652.1 None None $$0$$ $$-4$$ $$1$$ $$0$$ $+$ $$q+(-1+\beta _{1})q^{3}+\beta _{4}q^{5}-\beta _{3}q^{7}+(1+\cdots)q^{9}+\cdots$$
3344.2.a.w $6$ $26.702$ 6.6.744786576.1 None None $$0$$ $$-1$$ $$5$$ $$2$$ $-$ $$q-\beta _{1}q^{3}+(1+\beta _{5})q^{5}+(1-\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots$$
3344.2.a.x $6$ $26.702$ $$\mathbb{Q}[x]/(x^{6} - \cdots)$$ None None $$0$$ $$2$$ $$0$$ $$-2$$ $-$ $$q+\beta _{1}q^{3}-\beta _{5}q^{5}-\beta _{4}q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots$$
3344.2.a.y $6$ $26.702$ 6.6.57500224.1 None None $$0$$ $$4$$ $$-4$$ $$4$$ $-$ $$q+(1-\beta _{1})q^{3}+(-1-\beta _{4})q^{5}+(1-\beta _{1}+\cdots)q^{7}+\cdots$$
3344.2.a.z $6$ $26.702$ 6.6.106392688.1 None None $$0$$ $$4$$ $$-3$$ $$3$$ $-$ $$q+(1-\beta _{1})q^{3}+(-1+\beta _{5})q^{5}+\beta _{5}q^{7}+\cdots$$
3344.2.a.ba $7$ $26.702$ $$\mathbb{Q}[x]/(x^{7} - \cdots)$$ None None $$0$$ $$-2$$ $$2$$ $$-10$$ $+$ $$q+\beta _{2}q^{3}-\beta _{4}q^{5}+(-2-\beta _{2}+\beta _{5}+\cdots)q^{7}+\cdots$$
3344.2.a.bb $9$ $26.702$ $$\mathbb{Q}[x]/(x^{9} - \cdots)$$ None None $$0$$ $$-1$$ $$6$$ $$-3$$ $-$ $$q-\beta _{1}q^{3}+(1+\beta _{7})q^{5}-\beta _{8}q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots$$
3344.2.o.a $36$ $26.702$ None None $$0$$ $$0$$ $$0$$ $$0$$
3344.2.o.b $64$ $26.702$ None None $$0$$ $$0$$ $$0$$ $$0$$
Download to