| 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 |
| $a_{2}$ |
$a_{3}$ |
$a_{5}$ |
$a_{7}$ |
| 308.1.g.a |
$308$ |
$1$ |
308.g |
308.g |
$2$ |
$1$ |
$1$ |
$0.154$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-77}) \) |
\(\Q(\sqrt{11}) \) |
✓ |
$4$ |
$0$ |
\(-1\) |
\(0\) |
\(0\) |
\(1\) |
$1$ |
|
\(q-q^{2}+q^{4}+q^{7}-q^{8}-q^{9}+q^{11}+\cdots\) |
| 308.1.g.b |
$308$ |
$1$ |
308.g |
308.g |
$2$ |
$1$ |
$1$ |
$0.154$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-77}) \) |
\(\Q(\sqrt{11}) \) |
✓ |
$4$ |
$0$ |
\(1\) |
\(0\) |
\(0\) |
\(-1\) |
$1$ |
|
\(q+q^{2}+q^{4}-q^{7}+q^{8}-q^{9}-q^{11}+\cdots\) |
| 396.1.d.a |
$396$ |
$1$ |
396.d |
132.d |
$2$ |
$4$ |
$4$ |
$0.198$ |
\(\Q(\zeta_{8})\) |
$D_{4}$ |
None |
\(\Q(\sqrt{11}) \) |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2$ |
|
\(q+\zeta_{8}^{2}q^{2}-q^{4}+(-\zeta_{8}-\zeta_{8}^{3})q^{5}+\cdots\) |
| 1408.1.b.a |
$1408$ |
$1$ |
1408.b |
88.b |
$2$ |
$1$ |
$1$ |
$0.703$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-22}) \) |
\(\Q(\sqrt{11}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+q^{9}-q^{11}+2q^{19}+q^{25}-2q^{43}+\cdots\) |
| 1408.1.b.b |
$1408$ |
$1$ |
1408.b |
88.b |
$2$ |
$1$ |
$1$ |
$0.703$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-22}) \) |
\(\Q(\sqrt{11}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+q^{9}+q^{11}-2q^{19}+q^{25}+2q^{43}+\cdots\) |
| 1936.1.d.a |
$1936$ |
$1$ |
1936.d |
4.b |
$2$ |
$1$ |
$1$ |
$0.966$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-11}) \) |
\(\Q(\sqrt{11}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(-2\) |
\(0\) |
$1$ |
|
\(q-2q^{5}+q^{9}+3q^{25}+2q^{37}-2q^{45}+\cdots\) |
| 1936.1.r.a |
$1936$ |
$1$ |
1936.r |
44.h |
$10$ |
$4$ |
$1$ |
$0.966$ |
\(\Q(\zeta_{10})\) |
$D_{2}$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-11}) \) |
\(\Q(\sqrt{11}) \) |
|
$16$ |
$0$ |
\(0\) |
\(0\) |
\(2\) |
\(0\) |
$1$ |
|
\(q-\zeta_{10}^{2}q^{5}-\zeta_{10}^{3}q^{9}+3\zeta_{10}^{4}q^{25}+\cdots\) |
| 2156.1.m.a |
$2156$ |
$1$ |
2156.m |
308.m |
$6$ |
$2$ |
$1$ |
$1.076$ |
\(\Q(\sqrt{-3}) \) |
$D_{2}$ |
\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-77}) \) |
\(\Q(\sqrt{11}) \) |
|
$8$ |
$0$ |
\(-1\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+q^{8}-\zeta_{6}^{2}q^{9}+\cdots\) |
| 2156.1.m.b |
$2156$ |
$1$ |
2156.m |
308.m |
$6$ |
$2$ |
$1$ |
$1.076$ |
\(\Q(\sqrt{-3}) \) |
$D_{2}$ |
\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-77}) \) |
\(\Q(\sqrt{11}) \) |
|
$8$ |
$0$ |
\(1\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-q^{8}-\zeta_{6}^{2}q^{9}+\cdots\) |
| 2420.1.h.b |
$2420$ |
$1$ |
2420.h |
20.d |
$2$ |
$1$ |
$1$ |
$1.208$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-5}) \), \(\Q(\sqrt{-55}) \) |
\(\Q(\sqrt{11}) \) |
✓ |
$4$ |
$0$ |
\(-1\) |
\(0\) |
\(-1\) |
\(-2\) |
$1$ |
|
\(q-q^{2}+q^{4}-q^{5}-2q^{7}-q^{8}-q^{9}+\cdots\) |
| 2420.1.h.e |
$2420$ |
$1$ |
2420.h |
20.d |
$2$ |
$1$ |
$1$ |
$1.208$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-5}) \), \(\Q(\sqrt{-55}) \) |
\(\Q(\sqrt{11}) \) |
✓ |
$4$ |
$0$ |
\(1\) |
\(0\) |
\(-1\) |
\(2\) |
$1$ |
|
\(q+q^{2}+q^{4}-q^{5}+2q^{7}+q^{8}-q^{9}+\cdots\) |
| 2420.1.n.b |
$2420$ |
$1$ |
2420.n |
220.n |
$10$ |
$4$ |
$1$ |
$1.208$ |
\(\Q(\zeta_{10})\) |
$D_{2}$ |
\(\Q(\sqrt{-5}) \), \(\Q(\sqrt{-55}) \) |
\(\Q(\sqrt{11}) \) |
|
$16$ |
$0$ |
\(-1\) |
\(0\) |
\(1\) |
\(-2\) |
$1$ |
|
\(q+\zeta_{10}^{4}q^{2}-\zeta_{10}^{3}q^{4}+\zeta_{10}q^{5}-\zeta_{10}^{3}q^{7}+\cdots\) |
| 2420.1.n.e |
$2420$ |
$1$ |
2420.n |
220.n |
$10$ |
$4$ |
$1$ |
$1.208$ |
\(\Q(\zeta_{10})\) |
$D_{2}$ |
\(\Q(\sqrt{-5}) \), \(\Q(\sqrt{-55}) \) |
\(\Q(\sqrt{11}) \) |
|
$16$ |
$0$ |
\(1\) |
\(0\) |
\(1\) |
\(2\) |
$1$ |
|
\(q-\zeta_{10}^{4}q^{2}-\zeta_{10}^{3}q^{4}+\zeta_{10}q^{5}+\zeta_{10}^{3}q^{7}+\cdots\) |
| 2772.1.h.a |
$2772$ |
$1$ |
2772.h |
308.g |
$2$ |
$1$ |
$1$ |
$1.383$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-77}) \) |
\(\Q(\sqrt{11}) \) |
✓ |
$4$ |
$0$ |
\(-1\) |
\(0\) |
\(0\) |
\(-1\) |
$1$ |
|
\(q-q^{2}+q^{4}-q^{7}-q^{8}+q^{11}+q^{14}+\cdots\) |
| 2772.1.h.b |
$2772$ |
$1$ |
2772.h |
308.g |
$2$ |
$1$ |
$1$ |
$1.383$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-77}) \) |
\(\Q(\sqrt{11}) \) |
✓ |
$4$ |
$0$ |
\(1\) |
\(0\) |
\(0\) |
\(1\) |
$1$ |
|
\(q+q^{2}+q^{4}+q^{7}+q^{8}-q^{11}+q^{14}+\cdots\) |
| 2772.1.h.c |
$2772$ |
$1$ |
2772.h |
308.g |
$2$ |
$2$ |
$2$ |
$1.383$ |
\(\Q(\sqrt{-1}) \) |
$D_{2}$ |
\(\Q(\sqrt{-21}) \), \(\Q(\sqrt{-231}) \) |
\(\Q(\sqrt{11}) \) |
|
$8$ |
$0$ |
\(-2\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-q^{2}+q^{4}-iq^{5}+iq^{7}-q^{8}+2iq^{10}+\cdots\) |
| 2772.1.h.f |
$2772$ |
$1$ |
2772.h |
308.g |
$2$ |
$2$ |
$2$ |
$1.383$ |
\(\Q(\sqrt{-1}) \) |
$D_{2}$ |
\(\Q(\sqrt{-21}) \), \(\Q(\sqrt{-231}) \) |
\(\Q(\sqrt{11}) \) |
|
$8$ |
$0$ |
\(2\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+q^{2}+q^{4}-iq^{5}-iq^{7}+q^{8}-2iq^{10}+\cdots\) |
| 2816.1.h.d |
$2816$ |
$1$ |
2816.h |
11.b |
$2$ |
$2$ |
$2$ |
$1.405$ |
\(\Q(\sqrt{-1}) \) |
$D_{2}$ |
\(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-22}) \) |
\(\Q(\sqrt{11}) \) |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-q^{9}-iq^{11}-iq^{19}-q^{25}-iq^{43}+\cdots\) |
| 3344.1.p.a |
$3344$ |
$1$ |
3344.p |
836.h |
$2$ |
$1$ |
$1$ |
$1.669$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-19}) \), \(\Q(\sqrt{-209}) \) |
\(\Q(\sqrt{11}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(-2\) |
\(-2\) |
$1$ |
|
\(q-2q^{5}-2q^{7}-q^{9}-q^{11}+q^{19}+\cdots\) |
| 3344.1.p.b |
$3344$ |
$1$ |
3344.p |
836.h |
$2$ |
$1$ |
$1$ |
$1.669$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-19}) \), \(\Q(\sqrt{-209}) \) |
\(\Q(\sqrt{11}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(-2\) |
\(2\) |
$1$ |
|
\(q-2q^{5}+2q^{7}-q^{9}+q^{11}-q^{19}+\cdots\) |
| 3344.1.bc.a |
$3344$ |
$1$ |
3344.bc |
836.m |
$6$ |
$2$ |
$1$ |
$1.669$ |
\(\Q(\sqrt{-3}) \) |
$D_{6}$ |
None |
\(\Q(\sqrt{11}) \) |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(-1\) |
\(-2\) |
$1$ |
|
\(q+\zeta_{6}^{2}q^{5}-q^{7}+\zeta_{6}q^{9}+q^{11}-\zeta_{6}^{2}q^{19}+\cdots\) |
| 3344.1.bc.b |
$3344$ |
$1$ |
3344.bc |
836.m |
$6$ |
$2$ |
$1$ |
$1.669$ |
\(\Q(\sqrt{-3}) \) |
$D_{6}$ |
None |
\(\Q(\sqrt{11}) \) |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(-1\) |
\(2\) |
$1$ |
|
\(q+\zeta_{6}^{2}q^{5}+q^{7}+\zeta_{6}q^{9}-q^{11}+\zeta_{6}^{2}q^{19}+\cdots\) |
| 3388.1.s.c |
$3388$ |
$1$ |
3388.s |
308.s |
$10$ |
$4$ |
$1$ |
$1.691$ |
\(\Q(\zeta_{10})\) |
$D_{2}$ |
\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-77}) \) |
\(\Q(\sqrt{11}) \) |
|
$16$ |
$0$ |
\(-1\) |
\(0\) |
\(0\) |
\(1\) |
$1$ |
|
\(q+\zeta_{10}^{4}q^{2}-\zeta_{10}^{3}q^{4}+\zeta_{10}^{3}q^{7}+\cdots\) |
| 3388.1.s.f |
$3388$ |
$1$ |
3388.s |
308.s |
$10$ |
$4$ |
$1$ |
$1.691$ |
\(\Q(\zeta_{10})\) |
$D_{2}$ |
\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-77}) \) |
\(\Q(\sqrt{11}) \) |
|
$16$ |
$0$ |
\(1\) |
\(0\) |
\(0\) |
\(-1\) |
$1$ |
|
\(q-\zeta_{10}^{4}q^{2}-\zeta_{10}^{3}q^{4}-\zeta_{10}^{3}q^{7}+\cdots\) |
| 3476.1.g.a |
$3476$ |
$1$ |
3476.g |
3476.g |
$2$ |
$1$ |
$1$ |
$1.735$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-79}) \), \(\Q(\sqrt{-869}) \) |
\(\Q(\sqrt{11}) \) |
✓ |
$4$ |
$0$ |
\(-1\) |
\(0\) |
\(-2\) |
\(0\) |
$1$ |
|
\(q-q^{2}+q^{4}-2q^{5}-q^{8}-q^{9}+2q^{10}+\cdots\) |
| 3476.1.g.b |
$3476$ |
$1$ |
3476.g |
3476.g |
$2$ |
$1$ |
$1$ |
$1.735$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-79}) \), \(\Q(\sqrt{-869}) \) |
\(\Q(\sqrt{11}) \) |
✓ |
$4$ |
$0$ |
\(1\) |
\(0\) |
\(-2\) |
\(0\) |
$1$ |
|
\(q+q^{2}+q^{4}-2q^{5}+q^{8}-q^{9}-2q^{10}+\cdots\) |
| 3564.1.o.e |
$3564$ |
$1$ |
3564.o |
396.o |
$6$ |
$8$ |
$4$ |
$1.779$ |
\(\Q(\zeta_{24})\) |
$D_{4}$ |
None |
\(\Q(\sqrt{11}) \) |
|
$16$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2^{2}$ |
|
\(q-\zeta_{24}^{2}q^{2}+\zeta_{24}^{4}q^{4}+(-\zeta_{24}+\zeta_{24}^{7}+\cdots)q^{5}+\cdots\) |
