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 |
$a_{2}$ |
$a_{3}$ |
$a_{5}$ |
$a_{7}$ |
183.1.d.a |
$183$ |
$1$ |
183.d |
183.d |
$2$ |
$1$ |
$1$ |
$0.091$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-183}) \) |
\(\Q(\sqrt{61}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(1\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+q^{3}-q^{4}+q^{9}-q^{12}-2q^{13}+q^{16}+\cdots\) |
793.1.m.a |
$793$ |
$1$ |
793.m |
793.m |
$4$ |
$2$ |
$1$ |
$0.396$ |
\(\Q(\sqrt{-1}) \) |
$D_{4}$ |
None |
\(\Q(\sqrt{61}) \) |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(2\) |
\(0\) |
$1$ |
|
\(q+iq^{4}+(1+i)q^{5}-q^{9}+q^{13}-q^{16}+\cdots\) |
793.1.bn.a |
$793$ |
$1$ |
793.bn |
793.an |
$12$ |
$4$ |
$1$ |
$0.396$ |
\(\Q(\zeta_{12})\) |
$D_{12}$ |
None |
\(\Q(\sqrt{61}) \) |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(-2\) |
\(0\) |
$1$ |
|
\(q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+\zeta_{12}q^{4}+(\zeta_{12}^{4}+\cdots)q^{5}+\cdots\) |
915.1.e.a |
$915$ |
$1$ |
915.e |
915.e |
$2$ |
$1$ |
$1$ |
$0.457$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-915}) \) |
\(\Q(\sqrt{61}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(-1\) |
\(1\) |
\(0\) |
$1$ |
|
\(q-q^{3}+q^{4}+q^{5}+q^{9}-q^{12}-q^{15}+\cdots\) |
915.1.e.b |
$915$ |
$1$ |
915.e |
915.e |
$2$ |
$1$ |
$1$ |
$0.457$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-915}) \) |
\(\Q(\sqrt{61}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(1\) |
\(-1\) |
\(0\) |
$1$ |
|
\(q+q^{3}+q^{4}-q^{5}+q^{9}+q^{12}-q^{15}+\cdots\) |
976.1.e.a |
$976$ |
$1$ |
976.e |
244.c |
$2$ |
$1$ |
$1$ |
$0.487$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-61}) \) |
\(\Q(\sqrt{61}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(-2\) |
\(0\) |
$1$ |
|
\(q-2q^{5}+q^{9}+2q^{13}+3q^{25}+2q^{41}+\cdots\) |
1159.1.d.a |
$1159$ |
$1$ |
1159.d |
1159.d |
$2$ |
$1$ |
$1$ |
$0.578$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-19}) \), \(\Q(\sqrt{-1159}) \) |
\(\Q(\sqrt{61}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(-2\) |
\(0\) |
$1$ |
|
\(q-q^{4}-2q^{5}+q^{9}+q^{16}+q^{19}+2q^{20}+\cdots\) |
2196.1.bl.a |
$2196$ |
$1$ |
2196.bl |
549.o |
$6$ |
$2$ |
$1$ |
$1.096$ |
\(\Q(\sqrt{-3}) \) |
$D_{6}$ |
None |
\(\Q(\sqrt{61}) \) |
|
$4$ |
$0$ |
\(0\) |
\(-1\) |
\(3\) |
\(0\) |
$1$ |
|
\(q+\zeta_{6}^{2}q^{3}+(1-\zeta_{6}^{2})q^{5}-\zeta_{6}q^{9}-\zeta_{6}q^{13}+\cdots\) |
2379.1.e.a |
$2379$ |
$1$ |
2379.e |
2379.e |
$2$ |
$1$ |
$1$ |
$1.187$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-39}) \), \(\Q(\sqrt{-2379}) \) |
\(\Q(\sqrt{61}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(-1\) |
\(-2\) |
\(0\) |
$1$ |
|
\(q-q^{3}+q^{4}-2q^{5}+q^{9}-q^{12}-q^{13}+\cdots\) |
2379.1.e.d |
$2379$ |
$1$ |
2379.e |
2379.e |
$2$ |
$1$ |
$1$ |
$1.187$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-39}) \), \(\Q(\sqrt{-2379}) \) |
\(\Q(\sqrt{61}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(-1\) |
\(2\) |
\(0\) |
$1$ |
|
\(q-q^{3}+q^{4}+2q^{5}+q^{9}-q^{12}-q^{13}+\cdots\) |
2379.1.be.b |
$2379$ |
$1$ |
2379.be |
2379.ae |
$6$ |
$2$ |
$1$ |
$1.187$ |
\(\Q(\sqrt{-3}) \) |
$D_{6}$ |
None |
\(\Q(\sqrt{61}) \) |
|
$4$ |
$0$ |
\(0\) |
\(-1\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{6}q^{3}+\zeta_{6}q^{4}+(\zeta_{6}+\zeta_{6}^{2})q^{5}+\zeta_{6}^{2}q^{9}+\cdots\) |
2379.1.be.c |
$2379$ |
$1$ |
2379.be |
2379.ae |
$6$ |
$2$ |
$1$ |
$1.187$ |
\(\Q(\sqrt{-3}) \) |
$D_{6}$ |
None |
\(\Q(\sqrt{61}) \) |
|
$4$ |
$0$ |
\(0\) |
\(2\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+q^{3}+\zeta_{6}q^{4}+(-\zeta_{6}-\zeta_{6}^{2})q^{5}+q^{9}+\cdots\) |
2379.1.bw.b |
$2379$ |
$1$ |
2379.bw |
2379.aw |
$6$ |
$2$ |
$1$ |
$1.187$ |
\(\Q(\sqrt{-3}) \) |
$D_{6}$ |
None |
\(\Q(\sqrt{61}) \) |
|
$4$ |
$0$ |
\(0\) |
\(-2\) |
\(-2\) |
\(0\) |
$1$ |
|
\(q-q^{3}+\zeta_{6}^{2}q^{4}-q^{5}+q^{9}-\zeta_{6}^{2}q^{12}+\cdots\) |
2379.1.bw.c |
$2379$ |
$1$ |
2379.bw |
2379.aw |
$6$ |
$2$ |
$1$ |
$1.187$ |
\(\Q(\sqrt{-3}) \) |
$D_{6}$ |
None |
\(\Q(\sqrt{61}) \) |
|
$4$ |
$0$ |
\(0\) |
\(1\) |
\(2\) |
\(0\) |
$1$ |
|
\(q-\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}+q^{5}-\zeta_{6}q^{9}+\cdots\) |
2501.1.v.a |
$2501$ |
$1$ |
2501.v |
2501.v |
$8$ |
$4$ |
$1$ |
$1.248$ |
\(\Q(\zeta_{8})\) |
$D_{8}$ |
None |
\(\Q(\sqrt{61}) \) |
|
$4$ |
$0$ |
\(0\) |
\(-4\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+(-1-\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{5}+\cdots\) |
2867.1.b.a |
$2867$ |
$1$ |
2867.b |
2867.b |
$2$ |
$1$ |
$1$ |
$1.431$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-47}) \), \(\Q(\sqrt{-2867}) \) |
\(\Q(\sqrt{61}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(-2\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-2q^{3}+q^{4}+3q^{9}-2q^{12}+q^{16}+\cdots\) |
2928.1.e.a |
$2928$ |
$1$ |
2928.e |
183.d |
$2$ |
$1$ |
$1$ |
$1.461$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-183}) \) |
\(\Q(\sqrt{61}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(-1\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-q^{3}+q^{9}-2q^{13}+2q^{19}+q^{25}+\cdots\) |
3904.1.e.c |
$3904$ |
$1$ |
3904.e |
244.c |
$2$ |
$1$ |
$1$ |
$1.948$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-61}) \) |
\(\Q(\sqrt{61}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(2\) |
\(0\) |
$1$ |
|
\(q+2q^{5}+q^{9}-2q^{13}+3q^{25}+2q^{41}+\cdots\) |
3965.1.u.a |
$3965$ |
$1$ |
3965.u |
3965.u |
$4$ |
$2$ |
$1$ |
$1.979$ |
\(\Q(\sqrt{-1}) \) |
$D_{4}$ |
None |
\(\Q(\sqrt{61}) \) |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+iq^{3}-iq^{4}+iq^{5}-3q^{9}+2q^{12}+\cdots\) |
3965.1.u.b |
$3965$ |
$1$ |
3965.u |
3965.u |
$4$ |
$2$ |
$1$ |
$1.979$ |
\(\Q(\sqrt{-1}) \) |
$D_{4}$ |
None |
\(\Q(\sqrt{61}) \) |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(2\) |
\(0\) |
$1$ |
|
\(q-iq^{3}-iq^{4}+q^{5}-3q^{9}-2q^{12}+\cdots\) |
3965.1.gd.a |
$3965$ |
$1$ |
3965.gd |
3965.fd |
$12$ |
$4$ |
$1$ |
$1.979$ |
\(\Q(\zeta_{12})\) |
$D_{12}$ |
None |
\(\Q(\sqrt{61}) \) |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(-2\) |
\(0\) |
$1$ |
|
\(q+\zeta_{12}^{5}q^{3}-\zeta_{12}q^{4}+\zeta_{12}^{4}q^{5}+q^{12}+\cdots\) |
3965.1.gd.b |
$3965$ |
$1$ |
3965.gd |
3965.fd |
$12$ |
$4$ |
$1$ |
$1.979$ |
\(\Q(\zeta_{12})\) |
$D_{12}$ |
None |
\(\Q(\sqrt{61}) \) |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{12}^{5}q^{3}-\zeta_{12}q^{4}+\zeta_{12}^{5}q^{5}-q^{12}+\cdots\) |