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Pari/GP
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Label
Level
Weight
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Prim
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Dim
Rel. Dim
$A$
Field
Image
CM
RM
Self-dual
Twist minimal
Largest
Maximal
Minimal twist
Inner twists
Rank*
Traces
Fricke sign
Coefficient ring index
Sato-Tate
$q$-expansion
$a_{2}$
$a_{3}$
$a_{5}$
$a_{7}$
3328.1.c.a
$3328$
$1$
3328.c
52.b
$2$
$2$
$2$
$1.661$
\(\Q(\sqrt{-1}) \)
$D_{3}$
\(\Q(\sqrt{-26}) \)
None
104.1.h.a
$4$
$0$
\(0\)
\(0\)
\(0\)
\(-2\)
$1$
\(q-i q^{3}-i q^{5}-q^{7}-i q^{13}-q^{15}+\cdots\)
3328.1.c.b
$3328$
$1$
3328.c
52.b
$2$
$2$
$2$
$1.661$
\(\Q(\sqrt{2}) \)
$D_{4}$
\(\Q(\sqrt{-13}) \)
None
✓
1664.1.h.e
$4$
$0$
\(0\)
\(0\)
\(0\)
\(0\)
$1$
\(q+\beta q^{7}+q^{9}-\beta q^{11}-q^{13}+\beta q^{19}+\cdots\)
3328.1.c.c
$3328$
$1$
3328.c
52.b
$2$
$2$
$2$
$1.661$
\(\Q(\sqrt{-1}) \)
$D_{2}$
\(\Q(\sqrt{-1}) \)
,
\(\Q(\sqrt{-26}) \)
\(\Q(\sqrt{26}) \)
1664.1.h.a
$8$
$0$
\(0\)
\(0\)
\(0\)
\(0\)
$1$
\(q-2 i q^{5}+q^{9}-i q^{13}+2 q^{17}-3 q^{25}+\cdots\)
3328.1.c.d
$3328$
$1$
3328.c
52.b
$2$
$2$
$2$
$1.661$
\(\Q(\sqrt{2}) \)
$D_{4}$
\(\Q(\sqrt{-13}) \)
None
✓
1664.1.h.e
$4$
$0$
\(0\)
\(0\)
\(0\)
\(0\)
$1$
\(q-\beta q^{7}+q^{9}-\beta q^{11}+q^{13}+\beta q^{19}+\cdots\)
3328.1.c.e
$3328$
$1$
3328.c
52.b
$2$
$2$
$2$
$1.661$
\(\Q(\sqrt{-1}) \)
$D_{3}$
\(\Q(\sqrt{-26}) \)
None
104.1.h.a
$4$
$0$
\(0\)
\(0\)
\(0\)
\(2\)
$1$
\(q+i q^{3}-i q^{5}+q^{7}-i q^{13}+q^{15}+\cdots\)
3328.1.c.f
$3328$
$1$
3328.c
52.b
$2$
$4$
$4$
$1.661$
\(\Q(\zeta_{12})\)
$D_{6}$
\(\Q(\sqrt{-26}) \)
None
✓
1664.1.h.c
$8$
$0$
\(0\)
\(0\)
\(0\)
\(0\)
$2^{2}$
\(q+(-\zeta_{12}^{2}-\zeta_{12}^{4})q^{3}-\zeta_{12}^{3}q^{5}+\cdots\)
3328.1.h.a
$3328$
$1$
3328.h
104.h
$2$
$2$
$2$
$1.661$
\(\Q(\sqrt{-1}) \)
$D_{2}$
\(\Q(\sqrt{-1}) \)
,
\(\Q(\sqrt{-13}) \)
\(\Q(\sqrt{13}) \)
✓
✓
208.1.c.a
$8$
$0$
\(0\)
\(0\)
\(0\)
\(0\)
$1$
\(q-q^{9}-i q^{13}-2 q^{17}-q^{25}-2 i q^{29}+\cdots\)
3328.1.j.a
$3328$
$1$
3328.j
104.j
$4$
$2$
$1$
$1.661$
\(\Q(\sqrt{-1}) \)
$D_{4}$
\(\Q(\sqrt{-1}) \)
None
416.1.t.a
$4$
$0$
\(0\)
\(0\)
\(-2\)
\(0\)
$1$
\(q+(-i-1)q^{5}+q^{9}+q^{13}+2 i q^{17}+\cdots\)
3328.1.j.b
$3328$
$1$
3328.j
104.j
$4$
$2$
$1$
$1.661$
\(\Q(\sqrt{-1}) \)
$D_{4}$
\(\Q(\sqrt{-1}) \)
None
416.1.t.a
$4$
$0$
\(0\)
\(0\)
\(2\)
\(0\)
$1$
\(q+(i+1)q^{5}+q^{9}-q^{13}+2 i q^{17}+\cdots\)
3328.1.m.a
$3328$
$1$
3328.m
208.m
$4$
$4$
$2$
$1.661$
\(\Q(\zeta_{8})\)
$S_{4}$
None
None
✓
3328.1.m.a
$4$
$0$
\(0\)
\(0\)
\(0\)
\(0\)
$1$
\(q-\zeta_{8}q^{3}-\zeta_{8}^{2}q^{5}-\zeta_{8}^{3}q^{7}-q^{13}+\cdots\)
3328.1.m.b
$3328$
$1$
3328.m
208.m
$4$
$4$
$2$
$1.661$
\(\Q(\zeta_{8})\)
$S_{4}$
None
None
✓
3328.1.m.a
$4$
$0$
\(0\)
\(0\)
\(0\)
\(0\)
$1$
\(q-\zeta_{8}q^{3}+\zeta_{8}^{2}q^{5}+\zeta_{8}^{3}q^{7}+q^{13}+\cdots\)
3328.1.o.a
$3328$
$1$
3328.o
208.o
$4$
$4$
$2$
$1.661$
\(\Q(\zeta_{8})\)
$S_{4}$
None
None
✓
3328.1.o.a
$4$
$0$
\(0\)
\(0\)
\(0\)
\(0\)
$1$
\(q-\zeta_{8}q^{3}-\zeta_{8}^{3}q^{5}+\zeta_{8}^{2}q^{7}+(-1+\cdots)q^{11}+\cdots\)
3328.1.o.b
$3328$
$1$
3328.o
208.o
$4$
$4$
$2$
$1.661$
\(\Q(\zeta_{8})\)
$S_{4}$
None
None
✓
3328.1.o.a
$4$
$0$
\(0\)
\(0\)
\(0\)
\(0\)
$1$
\(q-\zeta_{8}q^{3}+\zeta_{8}^{3}q^{5}-\zeta_{8}^{2}q^{7}+(-1+\cdots)q^{11}+\cdots\)
3328.1.o.c
$3328$
$1$
3328.o
208.o
$4$
$4$
$2$
$1.661$
\(\Q(\zeta_{8})\)
$S_{4}$
None
None
✓
3328.1.o.a
$4$
$0$
\(0\)
\(0\)
\(0\)
\(0\)
$1$
\(q+\zeta_{8}q^{3}+\zeta_{8}^{3}q^{5}+\zeta_{8}^{2}q^{7}+(1+\zeta_{8}^{2}+\cdots)q^{11}+\cdots\)
3328.1.o.d
$3328$
$1$
3328.o
208.o
$4$
$4$
$2$
$1.661$
\(\Q(\zeta_{8})\)
$S_{4}$
None
None
✓
3328.1.o.a
$4$
$0$
\(0\)
\(0\)
\(0\)
\(0\)
$1$
\(q+\zeta_{8}q^{3}-\zeta_{8}^{3}q^{5}-\zeta_{8}^{2}q^{7}+(1+\zeta_{8}^{2}+\cdots)q^{11}+\cdots\)
3328.1.r.a
$3328$
$1$
3328.r
208.r
$4$
$4$
$2$
$1.661$
\(\Q(\zeta_{8})\)
$S_{4}$
None
None
✓
3328.1.m.a
$4$
$0$
\(0\)
\(0\)
\(-4\)
\(0\)
$1$
\(q-\zeta_{8}^{3}q^{3}-q^{5}+\zeta_{8}^{3}q^{7}-\zeta_{8}^{2}q^{13}+\cdots\)
3328.1.r.b
$3328$
$1$
3328.r
208.r
$4$
$4$
$2$
$1.661$
\(\Q(\zeta_{8})\)
$S_{4}$
None
None
✓
3328.1.m.a
$4$
$0$
\(0\)
\(0\)
\(4\)
\(0\)
$1$
\(q-\zeta_{8}^{3}q^{3}+q^{5}-\zeta_{8}^{3}q^{7}+\zeta_{8}^{2}q^{13}+\cdots\)
3328.1.t.a
$3328$
$1$
3328.t
13.d
$4$
$2$
$1$
$1.661$
\(\Q(\sqrt{-1}) \)
$D_{4}$
\(\Q(\sqrt{-1}) \)
None
1664.1.j.a
$4$
$0$
\(0\)
\(0\)
\(-2\)
\(0\)
$1$
\(q+(i-1)q^{5}-q^{9}-q^{13}-2 i q^{17}+\cdots\)
3328.1.t.b
$3328$
$1$
3328.t
13.d
$4$
$2$
$1$
$1.661$
\(\Q(\sqrt{-1}) \)
$D_{4}$
\(\Q(\sqrt{-1}) \)
None
1664.1.j.a
$4$
$0$
\(0\)
\(0\)
\(2\)
\(0\)
$1$
\(q+(-i+1)q^{5}-q^{9}+q^{13}-2 i q^{17}+\cdots\)
3328.1.t.c
$3328$
$1$
3328.t
13.d
$4$
$4$
$2$
$1.661$
\(\Q(\zeta_{8})\)
$S_{4}$
None
None
1664.1.j.c
$4$
$0$
\(0\)
\(-4\)
\(0\)
\(0\)
$1$
\(q-q^{3}-\zeta_{8}q^{5}-\zeta_{8}^{3}q^{7}+(1-\zeta_{8}^{2}+\cdots)q^{11}+\cdots\)
3328.1.t.d
$3328$
$1$
3328.t
13.d
$4$
$4$
$2$
$1.661$
\(\Q(\zeta_{8})\)
$S_{4}$
None
None
1664.1.j.c
$4$
$0$
\(0\)
\(4\)
\(0\)
\(0\)
$1$
\(q+q^{3}-\zeta_{8}q^{5}+\zeta_{8}^{3}q^{7}+(-1+\zeta_{8}^{2}+\cdots)q^{11}+\cdots\)
3328.1.v.a
$3328$
$1$
3328.v
104.n
$6$
$4$
$2$
$1.661$
\(\Q(\zeta_{12})\)
$A_{4}$
None
None
416.1.bb.a
$4$
$0$
\(0\)
\(-2\)
\(0\)
\(0\)
$1$
\(q-\zeta_{12}^{2}q^{3}-\zeta_{12}q^{7}+\zeta_{12}^{2}q^{11}+\cdots\)
3328.1.v.b
$3328$
$1$
3328.v
104.n
$6$
$4$
$2$
$1.661$
\(\Q(\zeta_{12})\)
$D_{3}$
\(\Q(\sqrt{-1}) \)
None
52.1.j.a
$8$
$0$
\(0\)
\(0\)
\(0\)
\(0\)
$1$
\(q-\zeta_{12}^{3}q^{5}-\zeta_{12}^{4}q^{9}+\zeta_{12}^{5}q^{13}+\cdots\)
3328.1.v.c
$3328$
$1$
3328.v
104.n
$6$
$4$
$2$
$1.661$
\(\Q(\zeta_{12})\)
$A_{4}$
None
None
416.1.bb.a
$4$
$0$
\(0\)
\(2\)
\(0\)
\(0\)
$1$
\(q+\zeta_{12}^{2}q^{3}-\zeta_{12}q^{7}-\zeta_{12}^{2}q^{11}+\cdots\)
3328.1.x.a
$3328$
$1$
3328.x
104.p
$6$
$4$
$2$
$1.661$
\(\Q(\zeta_{12})\)
$D_{6}$
\(\Q(\sqrt{-1}) \)
None
✓
✓
208.1.y.a
$8$
$0$
\(0\)
\(0\)
\(0\)
\(0\)
$1$
\(q+(\zeta_{12}-\zeta_{12}^{5})q^{5}-\zeta_{12}^{4}q^{9}-\zeta_{12}^{5}q^{13}+\cdots\)
3328.1.y.a
$3328$
$1$
3328.y
52.i
$6$
$4$
$2$
$1.661$
\(\Q(\zeta_{12})\)
$D_{6}$
\(\Q(\sqrt{-1}) \)
None
✓
✓
1664.1.x.a
$8$
$0$
\(0\)
\(0\)
\(0\)
\(0\)
$1$
\(q-\zeta_{12}^{3}q^{5}-\zeta_{12}^{2}q^{9}-\zeta_{12}q^{13}+\cdots\)
3328.1.bb.a
$3328$
$1$
3328.bb
52.j
$6$
$4$
$2$
$1.661$
\(\Q(\sqrt{-2}, \sqrt{-3})\)
$S_{4}$
None
None
1664.1.v.c
$4$
$0$
\(0\)
\(0\)
\(-4\)
\(0\)
$1$
\(q+(\beta _{1}-\beta _{3})q^{3}-q^{5}+(1-\beta _{2})q^{9}+\beta _{2}q^{13}+\cdots\)
3328.1.bb.b
$3328$
$1$
3328.bb
52.j
$6$
$4$
$2$
$1.661$
\(\Q(\zeta_{12})\)
$D_{6}$
\(\Q(\sqrt{-1}) \)
None
1664.1.v.a
$8$
$0$
\(0\)
\(0\)
\(0\)
\(0\)
$1$
\(q+(\zeta_{12}-\zeta_{12}^{5})q^{5}-\zeta_{12}^{2}q^{9}-\zeta_{12}q^{13}+\cdots\)
3328.1.bb.c
$3328$
$1$
3328.bb
52.j
$6$
$4$
$2$
$1.661$
\(\Q(\sqrt{-2}, \sqrt{-3})\)
$S_{4}$
None
None
1664.1.v.c
$4$
$0$
\(0\)
\(0\)
\(4\)
\(0\)
$1$
\(q+(\beta _{1}-\beta _{3})q^{3}+q^{5}+(1-\beta _{2})q^{9}-\beta _{2}q^{13}+\cdots\)
3328.1.bl.a
$3328$
$1$
3328.bl
13.f
$12$
$4$
$1$
$1.661$
\(\Q(\zeta_{12})\)
$D_{12}$
\(\Q(\sqrt{-1}) \)
None
1664.1.bv.a
$4$
$0$
\(0\)
\(0\)
\(-2\)
\(0\)
$1$
\(q+(-\zeta_{12}-\zeta_{12}^{2})q^{5}+\zeta_{12}^{2}q^{9}+\zeta_{12}^{4}q^{13}+\cdots\)
3328.1.bl.b
$3328$
$1$
3328.bl
13.f
$12$
$4$
$1$
$1.661$
\(\Q(\zeta_{12})\)
$D_{12}$
\(\Q(\sqrt{-1}) \)
None
1664.1.bv.a
$4$
$0$
\(0\)
\(0\)
\(2\)
\(0\)
$1$
\(q+(\zeta_{12}+\zeta_{12}^{2})q^{5}+\zeta_{12}^{2}q^{9}-\zeta_{12}^{4}q^{13}+\cdots\)
3328.1.bv.a
$3328$
$1$
3328.bv
104.x
$12$
$4$
$1$
$1.661$
\(\Q(\zeta_{12})\)
$D_{12}$
\(\Q(\sqrt{-1}) \)
None
416.1.bl.a
$4$
$0$
\(0\)
\(0\)
\(-2\)
\(0\)
$1$
\(q+(\zeta_{12}-\zeta_{12}^{2})q^{5}-\zeta_{12}^{2}q^{9}-\zeta_{12}^{4}q^{13}+\cdots\)
3328.1.bv.b
$3328$
$1$
3328.bv
104.x
$12$
$4$
$1$
$1.661$
\(\Q(\zeta_{12})\)
$D_{12}$
\(\Q(\sqrt{-1}) \)
None
416.1.bl.a
$4$
$0$
\(0\)
\(0\)
\(2\)
\(0\)
$1$
\(q+(-\zeta_{12}+\zeta_{12}^{2})q^{5}-\zeta_{12}^{2}q^{9}+\zeta_{12}^{4}q^{13}+\cdots\)
3328.2.a.a
$3328$
$2$
3328.a
1.a
$1$
$1$
$1$
$26.574$
\(\Q\)
$_{}$
None
None
✓
1664.2.b.a
$1$
$2$
\(0\)
\(-3\)
\(-1\)
\(-3\)
$-$
$1$
$\mathrm{SU}(2)$
\(q-3q^{3}-q^{5}-3q^{7}+6q^{9}-6q^{11}+\cdots\)
3328.2.a.b
$3328$
$2$
3328.a
1.a
$1$
$1$
$1$
$26.574$
\(\Q\)
$_{}$
None
None
✓
1664.2.b.a
$1$
$0$
\(0\)
\(-3\)
\(1\)
\(3\)
$-$
$1$
$\mathrm{SU}(2)$
\(q-3q^{3}+q^{5}+3q^{7}+6q^{9}-6q^{11}+\cdots\)
3328.2.a.c
$3328$
$2$
3328.a
1.a
$1$
$1$
$1$
$26.574$
\(\Q\)
$_{}$
None
None
✓
104.2.b.a
$1$
$2$
\(0\)
\(-1\)
\(-3\)
\(-3\)
$-$
$1$
$\mathrm{SU}(2)$
\(q-q^{3}-3q^{5}-3q^{7}-2q^{9}+q^{13}+\cdots\)
3328.2.a.d
$3328$
$2$
3328.a
1.a
$1$
$1$
$1$
$26.574$
\(\Q\)
$_{}$
None
None
✓
1664.2.b.b
$1$
$1$
\(0\)
\(-1\)
\(-1\)
\(-1\)
$+$
$1$
$\mathrm{SU}(2)$
\(q-q^{3}-q^{5}-q^{7}-2q^{9}-2q^{11}+q^{13}+\cdots\)
3328.2.a.e
$3328$
$2$
3328.a
1.a
$1$
$1$
$1$
$26.574$
\(\Q\)
$_{}$
None
None
✓
1664.2.b.b
$1$
$1$
\(0\)
\(-1\)
\(1\)
\(1\)
$+$
$1$
$\mathrm{SU}(2)$
\(q-q^{3}+q^{5}+q^{7}-2q^{9}-2q^{11}-q^{13}+\cdots\)
3328.2.a.f
$3328$
$2$
3328.a
1.a
$1$
$1$
$1$
$26.574$
\(\Q\)
$_{}$
None
None
✓
104.2.b.a
$1$
$0$
\(0\)
\(-1\)
\(3\)
\(3\)
$-$
$1$
$\mathrm{SU}(2)$
\(q-q^{3}+3q^{5}+3q^{7}-2q^{9}-q^{13}+\cdots\)
3328.2.a.g
$3328$
$2$
3328.a
1.a
$1$
$1$
$1$
$26.574$
\(\Q\)
$_{}$
None
None
✓
104.2.b.a
$1$
$1$
\(0\)
\(1\)
\(-3\)
\(3\)
$+$
$1$
$\mathrm{SU}(2)$
\(q+q^{3}-3q^{5}+3q^{7}-2q^{9}+q^{13}+\cdots\)
3328.2.a.h
$3328$
$2$
3328.a
1.a
$1$
$1$
$1$
$26.574$
\(\Q\)
$_{}$
None
None
✓
1664.2.b.b
$1$
$1$
\(0\)
\(1\)
\(-1\)
\(1\)
$+$
$1$
$\mathrm{SU}(2)$
\(q+q^{3}-q^{5}+q^{7}-2q^{9}+2q^{11}+q^{13}+\cdots\)
3328.2.a.i
$3328$
$2$
3328.a
1.a
$1$
$1$
$1$
$26.574$
\(\Q\)
$_{}$
None
None
✓
1664.2.b.b
$1$
$1$
\(0\)
\(1\)
\(1\)
\(-1\)
$+$
$1$
$\mathrm{SU}(2)$
\(q+q^{3}+q^{5}-q^{7}-2q^{9}+2q^{11}-q^{13}+\cdots\)
3328.2.a.j
$3328$
$2$
3328.a
1.a
$1$
$1$
$1$
$26.574$
\(\Q\)
$_{}$
None
None
✓
104.2.b.a
$1$
$1$
\(0\)
\(1\)
\(3\)
\(-3\)
$+$
$1$
$\mathrm{SU}(2)$
\(q+q^{3}+3q^{5}-3q^{7}-2q^{9}-q^{13}+\cdots\)
3328.2.a.k
$3328$
$2$
3328.a
1.a
$1$
$1$
$1$
$26.574$
\(\Q\)
$_{}$
None
None
✓
1664.2.b.a
$1$
$0$
\(0\)
\(3\)
\(-1\)
\(3\)
$-$
$1$
$\mathrm{SU}(2)$
\(q+3q^{3}-q^{5}+3q^{7}+6q^{9}+6q^{11}+\cdots\)
3328.2.a.l
$3328$
$2$
3328.a
1.a
$1$
$1$
$1$
$26.574$
\(\Q\)
$_{}$
None
None
✓
1664.2.b.a
$1$
$0$
\(0\)
\(3\)
\(1\)
\(-3\)
$-$
$1$
$\mathrm{SU}(2)$
\(q+3q^{3}+q^{5}-3q^{7}+6q^{9}+6q^{11}+\cdots\)
3328.2.a.m
$3328$
$2$
3328.a
1.a
$1$
$2$
$2$
$26.574$
\(\Q(\sqrt{3}) \)
$_{}$
None
None
✓
104.2.b.b
$1$
$1$
\(0\)
\(-4\)
\(0\)
\(-6\)
$+$
$1$
$\mathrm{SU}(2)$
\(q-2q^{3}-2\beta q^{5}+(-3+\beta )q^{7}+q^{9}+\cdots\)
3328.2.a.n
$3328$
$2$
3328.a
1.a
$1$
$2$
$2$
$26.574$
\(\Q(\sqrt{3}) \)
$_{}$
None
None
✓
104.2.b.b
$1$
$1$
\(0\)
\(-4\)
\(0\)
\(6\)
$+$
$1$
$\mathrm{SU}(2)$
\(q-2q^{3}+2\beta q^{5}+(3-\beta )q^{7}+q^{9}+(-3+\cdots)q^{11}+\cdots\)
3328.2.a.o
$3328$
$2$
3328.a
1.a
$1$
$2$
$2$
$26.574$
\(\Q(\sqrt{2}) \)
$_{}$
None
None
✓
1664.2.b.e
$1$
$1$
\(0\)
\(-2\)
\(-2\)
\(-2\)
$+$
$2$
$\mathrm{SU}(2)$
\(q-q^{3}+(-1+\beta )q^{5}+(-1+\beta )q^{7}+\cdots\)
3328.2.a.p
$3328$
$2$
3328.a
1.a
$1$
$2$
$2$
$26.574$
\(\Q(\sqrt{2}) \)
$_{}$
None
None
✓
832.2.b.a
$1$
$0$
\(0\)
\(-2\)
\(-2\)
\(6\)
$-$
$1$
$\mathrm{SU}(2)$
\(q+(-1+\beta )q^{3}+(-1-2\beta )q^{5}+(3-\beta )q^{7}+\cdots\)
3328.2.a.q
$3328$
$2$
3328.a
1.a
$1$
$2$
$2$
$26.574$
\(\Q(\sqrt{2}) \)
$_{}$
None
None
✓
832.2.b.a
$1$
$1$
\(0\)
\(-2\)
\(2\)
\(-6\)
$+$
$1$
$\mathrm{SU}(2)$
\(q+(-1+\beta )q^{3}+(1+2\beta )q^{5}+(-3+\beta )q^{7}+\cdots\)
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