| 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 |
| $a_{2}$ |
$a_{3}$ |
$a_{5}$ |
$a_{7}$ |
| 180.1.f.a |
$180$ |
$1$ |
180.f |
20.d |
$2$ |
$2$ |
$2$ |
$0.090$ |
\(\Q(\sqrt{-1}) \) |
$D_{2}$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-15}) \) |
\(\Q(\sqrt{15}) \) |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-iq^{2}-q^{4}-iq^{5}+iq^{8}-q^{10}+\cdots\) |
| 900.1.c.a |
$900$ |
$1$ |
900.c |
4.b |
$2$ |
$1$ |
$1$ |
$0.449$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-15}) \) |
\(\Q(\sqrt{15}) \) |
✓ |
$4$ |
$0$ |
\(-1\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-q^{2}+q^{4}-q^{8}+q^{16}+2q^{17}-q^{32}+\cdots\) |
| 900.1.c.b |
$900$ |
$1$ |
900.c |
4.b |
$2$ |
$1$ |
$1$ |
$0.449$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-15}) \) |
\(\Q(\sqrt{15}) \) |
✓ |
$4$ |
$0$ |
\(1\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+q^{2}+q^{4}+q^{8}+q^{16}-2q^{17}+q^{32}+\cdots\) |
| 1200.1.bj.a |
$1200$ |
$1$ |
1200.bj |
60.l |
$4$ |
$4$ |
$2$ |
$0.599$ |
\(\Q(\zeta_{8})\) |
$D_{2}$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-5}) \) |
\(\Q(\sqrt{15}) \) |
|
$16$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{8}q^{3}-\zeta_{8}^{3}q^{7}+\zeta_{8}^{2}q^{9}-2q^{21}+\cdots\) |
| 1620.1.p.b |
$1620$ |
$1$ |
1620.p |
180.p |
$6$ |
$4$ |
$2$ |
$0.808$ |
\(\Q(\zeta_{12})\) |
$D_{2}$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-15}) \) |
\(\Q(\sqrt{15}) \) |
|
$16$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{5}q^{5}+\zeta_{12}^{3}q^{8}+\cdots\) |
| 1680.1.bb.e |
$1680$ |
$1$ |
1680.bb |
420.o |
$2$ |
$2$ |
$2$ |
$0.838$ |
\(\Q(\sqrt{-1}) \) |
$D_{2}$ |
\(\Q(\sqrt{-35}) \), \(\Q(\sqrt{-21}) \) |
\(\Q(\sqrt{15}) \) |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+iq^{3}-iq^{5}-iq^{7}-q^{9}-q^{11}+\cdots\) |
| 1680.1.bb.f |
$1680$ |
$1$ |
1680.bb |
420.o |
$2$ |
$2$ |
$2$ |
$0.838$ |
\(\Q(\sqrt{-1}) \) |
$D_{2}$ |
\(\Q(\sqrt{-35}) \), \(\Q(\sqrt{-21}) \) |
\(\Q(\sqrt{15}) \) |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-iq^{3}-iq^{5}+iq^{7}-q^{9}+q^{11}+\cdots\) |
| 2580.1.g.e |
$2580$ |
$1$ |
2580.g |
2580.g |
$2$ |
$2$ |
$2$ |
$1.288$ |
\(\Q(\sqrt{-1}) \) |
$D_{2}$ |
\(\Q(\sqrt{-215}) \), \(\Q(\sqrt{-129}) \) |
\(\Q(\sqrt{15}) \) |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+iq^{2}+iq^{3}-q^{4}-iq^{5}-q^{6}+iq^{7}+\cdots\) |
| 2580.1.g.f |
$2580$ |
$1$ |
2580.g |
2580.g |
$2$ |
$2$ |
$2$ |
$1.288$ |
\(\Q(\sqrt{-1}) \) |
$D_{2}$ |
\(\Q(\sqrt{-215}) \), \(\Q(\sqrt{-129}) \) |
\(\Q(\sqrt{15}) \) |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+iq^{2}-iq^{3}-q^{4}-iq^{5}+q^{6}-iq^{7}+\cdots\) |
| 2580.1.bm.e |
$2580$ |
$1$ |
2580.bm |
2580.am |
$6$ |
$4$ |
$2$ |
$1.288$ |
\(\Q(\zeta_{12})\) |
$D_{6}$ |
None |
\(\Q(\sqrt{15}) \) |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{12}^{3}q^{2}-\zeta_{12}^{5}q^{3}-q^{4}-\zeta_{12}^{5}q^{5}+\cdots\) |
| 2580.1.bm.f |
$2580$ |
$1$ |
2580.bm |
2580.am |
$6$ |
$4$ |
$2$ |
$1.288$ |
\(\Q(\zeta_{12})\) |
$D_{6}$ |
None |
\(\Q(\sqrt{15}) \) |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{12}^{3}q^{2}+\zeta_{12}^{5}q^{3}-q^{4}-\zeta_{12}^{5}q^{5}+\cdots\) |
| 2640.1.l.a |
$2640$ |
$1$ |
2640.l |
660.g |
$2$ |
$1$ |
$1$ |
$1.318$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-165}) \) |
\(\Q(\sqrt{15}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(-1\) |
\(-1\) |
\(0\) |
$1$ |
|
\(q-q^{3}-q^{5}+q^{9}-q^{11}+q^{15}+q^{25}+\cdots\) |
| 2640.1.l.b |
$2640$ |
$1$ |
2640.l |
660.g |
$2$ |
$1$ |
$1$ |
$1.318$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-165}) \) |
\(\Q(\sqrt{15}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(-1\) |
\(1\) |
\(0\) |
$1$ |
|
\(q-q^{3}+q^{5}+q^{9}+q^{11}-q^{15}+q^{25}+\cdots\) |
| 2640.1.l.c |
$2640$ |
$1$ |
2640.l |
660.g |
$2$ |
$1$ |
$1$ |
$1.318$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-165}) \) |
\(\Q(\sqrt{15}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(1\) |
\(-1\) |
\(0\) |
$1$ |
|
\(q+q^{3}-q^{5}+q^{9}+q^{11}-q^{15}+q^{25}+\cdots\) |
| 2640.1.l.d |
$2640$ |
$1$ |
2640.l |
660.g |
$2$ |
$1$ |
$1$ |
$1.318$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-165}) \) |
\(\Q(\sqrt{15}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(1\) |
\(1\) |
\(0\) |
$1$ |
|
\(q+q^{3}+q^{5}+q^{9}-q^{11}+q^{15}+q^{25}+\cdots\) |
| 2880.1.j.b |
$2880$ |
$1$ |
2880.j |
20.d |
$2$ |
$2$ |
$2$ |
$1.437$ |
\(\Q(\sqrt{-1}) \) |
$D_{2}$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-15}) \) |
\(\Q(\sqrt{15}) \) |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-iq^{5}-iq^{17}-q^{25}-q^{49}-iq^{53}+\cdots\) |
| 3180.1.q.c |
$3180$ |
$1$ |
3180.q |
3180.q |
$4$ |
$4$ |
$2$ |
$1.587$ |
\(\Q(\zeta_{8})\) |
$D_{4}$ |
None |
\(\Q(\sqrt{15}) \) |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{3}q^{3}-\zeta_{8}^{2}q^{4}+\zeta_{8}q^{5}+\cdots\) |
| 3180.1.q.d |
$3180$ |
$1$ |
3180.q |
3180.q |
$4$ |
$4$ |
$2$ |
$1.587$ |
\(\Q(\zeta_{8})\) |
$D_{4}$ |
None |
\(\Q(\sqrt{15}) \) |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+\zeta_{8}^{3}q^{2}-\zeta_{8}^{3}q^{3}-\zeta_{8}^{2}q^{4}-\zeta_{8}q^{5}+\cdots\) |
| 3780.1.ci.a |
$3780$ |
$1$ |
3780.ci |
140.p |
$6$ |
$4$ |
$2$ |
$1.886$ |
\(\Q(\zeta_{12})\) |
$D_{6}$ |
None |
\(\Q(\sqrt{15}) \) |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+\zeta_{12}q^{5}-\zeta_{12}^{5}q^{7}+\cdots\) |
| 3780.1.ci.b |
$3780$ |
$1$ |
3780.ci |
140.p |
$6$ |
$4$ |
$2$ |
$1.886$ |
\(\Q(\zeta_{12})\) |
$D_{6}$ |
None |
\(\Q(\sqrt{15}) \) |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}-\zeta_{12}q^{5}-\zeta_{12}^{5}q^{7}+\cdots\) |
