| Label |
Level |
Weight |
Char |
Prim |
Char order |
Dim |
Rel. Dim |
$A$ |
Field |
Image |
CM |
RM |
Self-dual |
Inner twists |
Rank* |
Traces |
Coefficient ring index |
Sato-Tate |
$q$-expansion |
| $a_{2}$ |
$a_{3}$ |
$a_{5}$ |
$a_{7}$ |
| 255.1.h.e |
$255$ |
$1$ |
255.h |
255.h |
$2$ |
$2$ |
$2$ |
$0.127$ |
\(\Q(\sqrt{-1}) \) |
$D_{2}$ |
\(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-51}) \) |
\(\Q(\sqrt{85}) \) |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-iq^{3}-q^{4}-iq^{5}-q^{9}+iq^{12}+\cdots\) |
| 595.1.b.a |
$595$ |
$1$ |
595.b |
595.b |
$2$ |
$2$ |
$2$ |
$0.297$ |
\(\Q(\sqrt{-1}) \) |
$D_{2}$ |
\(\Q(\sqrt{-35}) \), \(\Q(\sqrt{-119}) \) |
\(\Q(\sqrt{85}) \) |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-iq^{3}+q^{4}+iq^{5}-iq^{7}-3q^{9}+\cdots\) |
| 765.1.v.a |
$765$ |
$1$ |
765.v |
765.v |
$6$ |
$4$ |
$2$ |
$0.382$ |
\(\Q(\zeta_{12})\) |
$D_{6}$ |
None |
\(\Q(\sqrt{85}) \) |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+\zeta_{12}^{5}q^{3}-\zeta_{12}^{4}q^{4}+\zeta_{12}q^{5}+(-\zeta_{12}+\cdots)q^{7}+\cdots\) |
| 1275.1.c.a |
$1275$ |
$1$ |
1275.c |
51.c |
$2$ |
$1$ |
$1$ |
$0.636$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-51}) \) |
\(\Q(\sqrt{85}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(-1\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-q^{3}+q^{4}+q^{9}-q^{12}+q^{16}+q^{17}+\cdots\) |
| 1275.1.c.b |
$1275$ |
$1$ |
1275.c |
51.c |
$2$ |
$1$ |
$1$ |
$0.636$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-51}) \) |
\(\Q(\sqrt{85}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(1\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+q^{3}+q^{4}+q^{9}+q^{12}+q^{16}-q^{17}+\cdots\) |
| 1360.1.d.a |
$1360$ |
$1$ |
1360.d |
340.d |
$2$ |
$1$ |
$1$ |
$0.679$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-85}) \) |
\(\Q(\sqrt{85}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(-1\) |
\(0\) |
$1$ |
|
\(q-q^{5}+q^{9}+q^{17}+q^{25}+2q^{37}+\cdots\) |
| 1360.1.d.b |
$1360$ |
$1$ |
1360.d |
340.d |
$2$ |
$1$ |
$1$ |
$0.679$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-85}) \) |
\(\Q(\sqrt{85}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(1\) |
\(0\) |
$1$ |
|
\(q+q^{5}+q^{9}-q^{17}+q^{25}-2q^{37}+\cdots\) |
| 1615.1.g.c |
$1615$ |
$1$ |
1615.g |
1615.g |
$2$ |
$1$ |
$1$ |
$0.806$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-19}) \), \(\Q(\sqrt{-1615}) \) |
\(\Q(\sqrt{85}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(-1\) |
\(-2\) |
$1$ |
|
\(q-q^{4}-q^{5}-2q^{7}+q^{9}+q^{16}+q^{17}+\cdots\) |
| 1615.1.g.d |
$1615$ |
$1$ |
1615.g |
1615.g |
$2$ |
$1$ |
$1$ |
$0.806$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-19}) \), \(\Q(\sqrt{-1615}) \) |
\(\Q(\sqrt{85}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(1\) |
\(2\) |
$1$ |
|
\(q-q^{4}+q^{5}+2q^{7}+q^{9}+q^{16}-q^{17}+\cdots\) |
| 1955.1.d.e |
$1955$ |
$1$ |
1955.d |
1955.d |
$2$ |
$2$ |
$2$ |
$0.976$ |
\(\Q(\sqrt{-1}) \) |
$D_{2}$ |
\(\Q(\sqrt{-115}) \), \(\Q(\sqrt{-391}) \) |
\(\Q(\sqrt{85}) \) |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+q^{4}-iq^{5}-iq^{7}-q^{9}+q^{16}+iq^{17}+\cdots\) |
| 2295.1.v.a |
$2295$ |
$1$ |
2295.v |
765.v |
$6$ |
$4$ |
$2$ |
$1.145$ |
\(\Q(\zeta_{12})\) |
$D_{6}$ |
None |
\(\Q(\sqrt{85}) \) |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{12}^{4}q^{4}+\zeta_{12}q^{5}+(\zeta_{12}+\zeta_{12}^{3}+\cdots)q^{7}+\cdots\) |
| 2380.1.cc.a |
$2380$ |
$1$ |
2380.cc |
595.ab |
$6$ |
$4$ |
$2$ |
$1.188$ |
\(\Q(\zeta_{12})\) |
$D_{6}$ |
None |
\(\Q(\sqrt{85}) \) |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{12}q^{3}-\zeta_{12}^{5}q^{5}+\zeta_{12}^{5}q^{7}-q^{15}+\cdots\) |
| 2975.1.h.a |
$2975$ |
$1$ |
2975.h |
119.d |
$2$ |
$1$ |
$1$ |
$1.485$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-35}) \), \(\Q(\sqrt{-119}) \) |
\(\Q(\sqrt{85}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(-2\) |
\(0\) |
\(1\) |
$1$ |
|
\(q-2q^{3}-q^{4}+q^{7}+3q^{9}+2q^{12}+\cdots\) |
| 2975.1.h.b |
$2975$ |
$1$ |
2975.h |
119.d |
$2$ |
$1$ |
$1$ |
$1.485$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-35}) \), \(\Q(\sqrt{-119}) \) |
\(\Q(\sqrt{85}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(2\) |
\(0\) |
\(-1\) |
$1$ |
|
\(q+2q^{3}-q^{4}-q^{7}+3q^{9}-2q^{12}+\cdots\) |
| 3145.1.s.a |
$3145$ |
$1$ |
3145.s |
3145.s |
$4$ |
$4$ |
$2$ |
$1.570$ |
\(\Q(\zeta_{8})\) |
$D_{4}$ |
None |
\(\Q(\sqrt{85}) \) |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+(-\zeta_{8}-\zeta_{8}^{3})q^{3}-\zeta_{8}^{2}q^{4}+\zeta_{8}q^{5}+\cdots\) |
| 3825.1.bb.a |
$3825$ |
$1$ |
3825.bb |
153.i |
$6$ |
$2$ |
$1$ |
$1.909$ |
\(\Q(\sqrt{-3}) \) |
$D_{6}$ |
None |
\(\Q(\sqrt{85}) \) |
|
$4$ |
$0$ |
\(0\) |
\(-1\) |
\(0\) |
\(-3\) |
$1$ |
|
\(q-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}+(-1+\zeta_{6}^{2})q^{7}+\cdots\) |
| 3825.1.bb.b |
$3825$ |
$1$ |
3825.bb |
153.i |
$6$ |
$2$ |
$1$ |
$1.909$ |
\(\Q(\sqrt{-3}) \) |
$D_{6}$ |
None |
\(\Q(\sqrt{85}) \) |
|
$4$ |
$0$ |
\(0\) |
\(1\) |
\(0\) |
\(3\) |
$1$ |
|
\(q+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}+(1-\zeta_{6}^{2})q^{7}+\zeta_{6}^{2}q^{9}+\cdots\) |
