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 |
$a_{2}$ |
$a_{3}$ |
$a_{5}$ |
$a_{7}$ |
171.1.c.a |
$171$ |
$1$ |
171.c |
19.b |
$2$ |
$1$ |
$1$ |
$0.085$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-19}) \) |
\(\Q(\sqrt{57}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(-2\) |
$1$ |
|
\(q+q^{4}-2q^{7}+q^{16}-q^{19}-q^{25}+\cdots\) |
456.1.l.a |
$456$ |
$1$ |
456.l |
456.l |
$2$ |
$1$ |
$1$ |
$0.228$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-114}) \) |
\(\Q(\sqrt{57}) \) |
✓ |
$4$ |
$0$ |
\(-1\) |
\(1\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots\) |
456.1.l.b |
$456$ |
$1$ |
456.l |
456.l |
$2$ |
$1$ |
$1$ |
$0.228$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-114}) \) |
\(\Q(\sqrt{57}) \) |
✓ |
$4$ |
$0$ |
\(1\) |
\(-1\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots\) |
1425.1.j.f |
$1425$ |
$1$ |
1425.j |
285.j |
$4$ |
$4$ |
$2$ |
$0.711$ |
\(\Q(\zeta_{8})\) |
$D_{2}$ |
\(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-95}) \) |
\(\Q(\sqrt{57}) \) |
|
$16$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{8}^{3}q^{2}+\zeta_{8}q^{3}-3\zeta_{8}^{2}q^{4}+2q^{6}+\cdots\) |
1425.1.j.g |
$1425$ |
$1$ |
1425.j |
285.j |
$4$ |
$8$ |
$4$ |
$0.711$ |
\(\Q(\zeta_{24})\) |
$D_{6}$ |
None |
\(\Q(\sqrt{57}) \) |
|
$16$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2^{4}$ |
|
\(q-\zeta_{24}^{9}q^{2}-\zeta_{24}^{3}q^{3}-q^{6}+(-\zeta_{24}^{7}+\cdots)q^{7}+\cdots\) |
1539.1.o.b |
$1539$ |
$1$ |
1539.o |
171.o |
$6$ |
$2$ |
$1$ |
$0.768$ |
\(\Q(\sqrt{-3}) \) |
$D_{2}$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-19}) \) |
\(\Q(\sqrt{57}) \) |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(2\) |
$1$ |
|
\(q+\zeta_{6}^{2}q^{4}+\zeta_{6}q^{7}-\zeta_{6}q^{16}-q^{19}+\cdots\) |
1824.1.l.a |
$1824$ |
$1$ |
1824.l |
456.l |
$2$ |
$1$ |
$1$ |
$0.910$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-114}) \) |
\(\Q(\sqrt{57}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(-1\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-q^{3}+q^{9}+q^{19}-q^{25}-q^{27}+2q^{41}+\cdots\) |
1824.1.l.b |
$1824$ |
$1$ |
1824.l |
456.l |
$2$ |
$1$ |
$1$ |
$0.910$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-114}) \) |
\(\Q(\sqrt{57}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(1\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+q^{3}+q^{9}+q^{19}-q^{25}+q^{27}-2q^{41}+\cdots\) |
2736.1.o.a |
$2736$ |
$1$ |
2736.o |
19.b |
$2$ |
$1$ |
$1$ |
$1.365$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-19}) \) |
\(\Q(\sqrt{57}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(2\) |
$1$ |
|
\(q+2q^{7}+q^{19}-q^{25}-2q^{43}+3q^{49}+\cdots\) |
3192.1.m.a |
$3192$ |
$1$ |
3192.m |
3192.m |
$2$ |
$1$ |
$1$ |
$1.593$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-14}) \), \(\Q(\sqrt{-798}) \) |
\(\Q(\sqrt{57}) \) |
✓ |
$4$ |
$0$ |
\(-1\) |
\(-1\) |
\(0\) |
\(-1\) |
$1$ |
|
\(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{7}-q^{8}+\cdots\) |
3192.1.m.b |
$3192$ |
$1$ |
3192.m |
3192.m |
$2$ |
$1$ |
$1$ |
$1.593$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-14}) \), \(\Q(\sqrt{-798}) \) |
\(\Q(\sqrt{57}) \) |
✓ |
$4$ |
$0$ |
\(-1\) |
\(1\) |
\(0\) |
\(-1\) |
$1$ |
|
\(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\) |
3192.1.m.c |
$3192$ |
$1$ |
3192.m |
3192.m |
$2$ |
$1$ |
$1$ |
$1.593$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-14}) \), \(\Q(\sqrt{-798}) \) |
\(\Q(\sqrt{57}) \) |
✓ |
$4$ |
$0$ |
\(1\) |
\(-1\) |
\(0\) |
\(-1\) |
$1$ |
|
\(q+q^{2}-q^{3}+q^{4}-q^{6}-q^{7}+q^{8}+\cdots\) |
3192.1.m.d |
$3192$ |
$1$ |
3192.m |
3192.m |
$2$ |
$1$ |
$1$ |
$1.593$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-14}) \), \(\Q(\sqrt{-798}) \) |
\(\Q(\sqrt{57}) \) |
✓ |
$4$ |
$0$ |
\(1\) |
\(1\) |
\(0\) |
\(-1\) |
$1$ |
|
\(q+q^{2}+q^{3}+q^{4}+q^{6}-q^{7}+q^{8}+\cdots\) |
3249.1.p.a |
$3249$ |
$1$ |
3249.p |
19.d |
$6$ |
$2$ |
$1$ |
$1.621$ |
\(\Q(\sqrt{-3}) \) |
$D_{2}$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-19}) \) |
\(\Q(\sqrt{57}) \) |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(-4\) |
$1$ |
|
\(q-\zeta_{6}q^{4}-q^{7}+\zeta_{6}^{2}q^{16}+\zeta_{6}q^{25}+\cdots\) |
3249.1.ba.c |
$3249$ |
$1$ |
3249.ba |
19.f |
$18$ |
$6$ |
$1$ |
$1.621$ |
\(\Q(\zeta_{18})\) |
$D_{2}$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-19}) \) |
\(\Q(\sqrt{57}) \) |
|
$24$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(6\) |
$1$ |
|
\(q-\zeta_{18}^{7}q^{4}+\zeta_{18}^{3}q^{7}-\zeta_{18}^{5}q^{16}+\cdots\) |
3363.1.c.a |
$3363$ |
$1$ |
3363.c |
3363.c |
$2$ |
$1$ |
$1$ |
$1.678$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-59}) \), \(\Q(\sqrt{-3363}) \) |
\(\Q(\sqrt{57}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(-1\) |
\(0\) |
\(-2\) |
$1$ |
|
\(q-q^{3}+q^{4}-2q^{7}+q^{9}-q^{12}+q^{16}+\cdots\) |
3363.1.c.b |
$3363$ |
$1$ |
3363.c |
3363.c |
$2$ |
$1$ |
$1$ |
$1.678$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-59}) \), \(\Q(\sqrt{-3363}) \) |
\(\Q(\sqrt{57}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(1\) |
\(0\) |
\(-2\) |
$1$ |
|
\(q+q^{3}+q^{4}-2q^{7}+q^{9}+q^{12}+q^{16}+\cdots\) |
3477.1.o.a |
$3477$ |
$1$ |
3477.o |
3477.o |
$4$ |
$2$ |
$1$ |
$1.735$ |
\(\Q(\sqrt{-1}) \) |
$D_{4}$ |
None |
\(\Q(\sqrt{57}) \) |
|
$4$ |
$0$ |
\(-2\) |
\(0\) |
\(0\) |
\(2\) |
$1$ |
|
\(q+(-1-i)q^{2}-iq^{3}+iq^{4}+(-1+\cdots)q^{6}+\cdots\) |
3477.1.o.d |
$3477$ |
$1$ |
3477.o |
3477.o |
$4$ |
$2$ |
$1$ |
$1.735$ |
\(\Q(\sqrt{-1}) \) |
$D_{4}$ |
None |
\(\Q(\sqrt{57}) \) |
|
$4$ |
$0$ |
\(2\) |
\(0\) |
\(0\) |
\(2\) |
$1$ |
|
\(q+(1+i)q^{2}+iq^{3}+iq^{4}+(-1+i+\cdots)q^{6}+\cdots\) |
3591.1.cz.a |
$3591$ |
$1$ |
3591.cz |
133.r |
$6$ |
$2$ |
$1$ |
$1.792$ |
\(\Q(\sqrt{-3}) \) |
$D_{6}$ |
None |
\(\Q(\sqrt{57}) \) |
|
$4$ |
$0$ |
\(-3\) |
\(0\) |
\(0\) |
\(1\) |
$1$ |
|
\(q+(-1+\zeta_{6}^{2})q^{2}+(1-\zeta_{6}-\zeta_{6}^{2})q^{4}+\cdots\) |
3591.1.cz.d |
$3591$ |
$1$ |
3591.cz |
133.r |
$6$ |
$2$ |
$1$ |
$1.792$ |
\(\Q(\sqrt{-3}) \) |
$D_{6}$ |
None |
\(\Q(\sqrt{57}) \) |
|
$4$ |
$0$ |
\(3\) |
\(0\) |
\(0\) |
\(1\) |
$1$ |
|
\(q+(1-\zeta_{6}^{2})q^{2}+(1-\zeta_{6}-\zeta_{6}^{2})q^{4}+\cdots\) |