| 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 |
| $a_{2}$ |
$a_{3}$ |
$a_{5}$ |
$a_{7}$ |
| 420.1.o.a |
$420$ |
$1$ |
420.o |
420.o |
$2$ |
$2$ |
$2$ |
$0.210$ |
\(\Q(\sqrt{-1}) \) |
$D_{2}$ |
\(\Q(\sqrt{-5}) \), \(\Q(\sqrt{-21}) \) |
\(\Q(\sqrt{105}) \) |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(-2\) |
\(0\) |
$1$ |
|
\(q-iq^{2}-iq^{3}-q^{4}-q^{5}-q^{6}-iq^{7}+\cdots\) |
| 420.1.o.b |
$420$ |
$1$ |
420.o |
420.o |
$2$ |
$2$ |
$2$ |
$0.210$ |
\(\Q(\sqrt{-1}) \) |
$D_{2}$ |
\(\Q(\sqrt{-5}) \), \(\Q(\sqrt{-21}) \) |
\(\Q(\sqrt{105}) \) |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(2\) |
\(0\) |
$1$ |
|
\(q+iq^{2}-iq^{3}-q^{4}+q^{5}+q^{6}-iq^{7}+\cdots\) |
| 525.1.k.a |
$525$ |
$1$ |
525.k |
105.k |
$4$ |
$4$ |
$2$ |
$0.262$ |
\(\Q(\zeta_{8})\) |
$D_{2}$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-35}) \) |
\(\Q(\sqrt{105}) \) |
|
$16$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{8}q^{3}+\zeta_{8}^{2}q^{4}+\zeta_{8}^{3}q^{7}+\zeta_{8}^{2}q^{9}+\cdots\) |
| 2100.1.m.a |
$2100$ |
$1$ |
2100.m |
84.h |
$2$ |
$1$ |
$1$ |
$1.048$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-5}) \), \(\Q(\sqrt{-21}) \) |
\(\Q(\sqrt{105}) \) |
✓ |
$4$ |
$0$ |
\(-1\) |
\(-1\) |
\(0\) |
\(1\) |
$1$ |
|
\(q-q^{2}-q^{3}+q^{4}+q^{6}+q^{7}-q^{8}+\cdots\) |
| 2100.1.m.b |
$2100$ |
$1$ |
2100.m |
84.h |
$2$ |
$1$ |
$1$ |
$1.048$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-5}) \), \(\Q(\sqrt{-21}) \) |
\(\Q(\sqrt{105}) \) |
✓ |
$4$ |
$0$ |
\(-1\) |
\(1\) |
\(0\) |
\(-1\) |
$1$ |
|
\(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\) |
| 2100.1.m.c |
$2100$ |
$1$ |
2100.m |
84.h |
$2$ |
$1$ |
$1$ |
$1.048$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-5}) \), \(\Q(\sqrt{-21}) \) |
\(\Q(\sqrt{105}) \) |
✓ |
$4$ |
$0$ |
\(1\) |
\(-1\) |
\(0\) |
\(1\) |
$1$ |
|
\(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots\) |
| 2100.1.m.d |
$2100$ |
$1$ |
2100.m |
84.h |
$2$ |
$1$ |
$1$ |
$1.048$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-5}) \), \(\Q(\sqrt{-21}) \) |
\(\Q(\sqrt{105}) \) |
✓ |
$4$ |
$0$ |
\(1\) |
\(1\) |
\(0\) |
\(-1\) |
$1$ |
|
\(q+q^{2}+q^{3}+q^{4}+q^{6}-q^{7}+q^{8}+\cdots\) |
| 2520.1.h.a |
$2520$ |
$1$ |
2520.h |
280.c |
$2$ |
$1$ |
$1$ |
$1.258$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-6}) \), \(\Q(\sqrt{-70}) \) |
\(\Q(\sqrt{105}) \) |
✓ |
$4$ |
$0$ |
\(-1\) |
\(0\) |
\(-1\) |
\(-1\) |
$1$ |
|
\(q-q^{2}+q^{4}-q^{5}-q^{7}-q^{8}+q^{10}+\cdots\) |
| 2520.1.h.b |
$2520$ |
$1$ |
2520.h |
280.c |
$2$ |
$1$ |
$1$ |
$1.258$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-6}) \), \(\Q(\sqrt{-70}) \) |
\(\Q(\sqrt{105}) \) |
✓ |
$4$ |
$0$ |
\(-1\) |
\(0\) |
\(1\) |
\(1\) |
$1$ |
|
\(q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-q^{10}+\cdots\) |
| 2520.1.h.c |
$2520$ |
$1$ |
2520.h |
280.c |
$2$ |
$1$ |
$1$ |
$1.258$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-6}) \), \(\Q(\sqrt{-70}) \) |
\(\Q(\sqrt{105}) \) |
✓ |
$4$ |
$0$ |
\(1\) |
\(0\) |
\(-1\) |
\(1\) |
$1$ |
|
\(q+q^{2}+q^{4}-q^{5}+q^{7}+q^{8}-q^{10}+\cdots\) |
| 2520.1.h.d |
$2520$ |
$1$ |
2520.h |
280.c |
$2$ |
$1$ |
$1$ |
$1.258$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-6}) \), \(\Q(\sqrt{-70}) \) |
\(\Q(\sqrt{105}) \) |
✓ |
$4$ |
$0$ |
\(1\) |
\(0\) |
\(1\) |
\(-1\) |
$1$ |
|
\(q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots\) |
| 2940.1.be.b |
$2940$ |
$1$ |
2940.be |
420.ae |
$6$ |
$4$ |
$2$ |
$1.467$ |
\(\Q(\zeta_{12})\) |
$D_{2}$ |
\(\Q(\sqrt{-5}) \), \(\Q(\sqrt{-21}) \) |
\(\Q(\sqrt{105}) \) |
|
$16$ |
$0$ |
\(0\) |
\(0\) |
\(-2\) |
\(0\) |
$1$ |
|
\(q-\zeta_{12}^{5}q^{2}+\zeta_{12}q^{3}-\zeta_{12}^{4}q^{4}-\zeta_{12}^{2}q^{5}+\cdots\) |
| 2940.1.be.c |
$2940$ |
$1$ |
2940.be |
420.ae |
$6$ |
$4$ |
$2$ |
$1.467$ |
\(\Q(\zeta_{12})\) |
$D_{2}$ |
\(\Q(\sqrt{-5}) \), \(\Q(\sqrt{-21}) \) |
\(\Q(\sqrt{105}) \) |
|
$16$ |
$0$ |
\(0\) |
\(0\) |
\(2\) |
\(0\) |
$1$ |
|
\(q-\zeta_{12}^{5}q^{2}-\zeta_{12}q^{3}-\zeta_{12}^{4}q^{4}+\zeta_{12}^{2}q^{5}+\cdots\) |
| 3675.1.bf.a |
$3675$ |
$1$ |
3675.bf |
105.w |
$12$ |
$8$ |
$2$ |
$1.834$ |
\(\Q(\zeta_{24})\) |
$D_{2}$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-35}) \) |
\(\Q(\sqrt{105}) \) |
|
$32$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+\zeta_{24}^{7}q^{3}-\zeta_{24}^{10}q^{4}-\zeta_{24}^{2}q^{9}+\cdots\) |
