Label |
Level |
Weight |
Char |
Prim |
Char order |
Dim |
Rel. Dim |
$A$ |
Field |
Image |
CM |
RM |
Self-dual |
Inner twists |
Rank* |
Traces |
Fricke sign |
Coefficient ring index |
Sato-Tate |
$q$-expansion |
$a_{2}$ |
$a_{3}$ |
$a_{5}$ |
$a_{7}$ |
1764.1.d.a |
$1764$ |
$1$ |
1764.d |
7.b |
$2$ |
$2$ |
$2$ |
$0.880$ |
\(\Q(\sqrt{-3}) \) |
$D_{6}$ |
\(\Q(\sqrt{-3}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$2$ |
|
\(q+(\zeta_{6}+\zeta_{6}^{2})q^{13}+(\zeta_{6}+\zeta_{6}^{2})q^{19}+\cdots\) |
1764.1.g.a |
$1764$ |
$1$ |
1764.g |
4.b |
$2$ |
$1$ |
$1$ |
$0.880$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-7}) \) |
\(\Q(\sqrt{7}) \) |
✓ |
$4$ |
$0$ |
\(1\) |
\(0\) |
\(0\) |
\(0\) |
|
$1$ |
|
\(q+q^{2}+q^{4}+q^{8}+q^{16}-q^{25}+2q^{29}+\cdots\) |
1764.1.g.b |
$1764$ |
$1$ |
1764.g |
4.b |
$2$ |
$2$ |
$2$ |
$0.880$ |
\(\Q(\sqrt{2}) \) |
$D_{4}$ |
\(\Q(\sqrt{-1}) \) |
None |
✓ |
$4$ |
$0$ |
\(-2\) |
\(0\) |
\(0\) |
\(0\) |
|
$1$ |
|
\(q-q^{2}+q^{4}-\beta q^{5}-q^{8}+\beta q^{10}-\beta q^{13}+\cdots\) |
1764.1.g.c |
$1764$ |
$1$ |
1764.g |
4.b |
$2$ |
$2$ |
$2$ |
$0.880$ |
\(\Q(\sqrt{-1}) \) |
$D_{2}$ |
\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-21}) \) |
\(\Q(\sqrt{3}) \) |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$1$ |
|
\(q-iq^{2}-q^{4}+iq^{8}+iq^{11}+q^{16}+\cdots\) |
1764.1.g.d |
$1764$ |
$1$ |
1764.g |
4.b |
$2$ |
$2$ |
$2$ |
$0.880$ |
\(\Q(\sqrt{2}) \) |
$D_{4}$ |
\(\Q(\sqrt{-1}) \) |
None |
✓ |
$4$ |
$0$ |
\(2\) |
\(0\) |
\(0\) |
\(0\) |
|
$1$ |
|
\(q+q^{2}+q^{4}-\beta q^{5}+q^{8}-\beta q^{10}+\beta q^{13}+\cdots\) |
1764.1.h.a |
$1764$ |
$1$ |
1764.h |
84.h |
$2$ |
$8$ |
$8$ |
$0.880$ |
\(\Q(\zeta_{16})\) |
$D_{8}$ |
\(\Q(\sqrt{-1}) \) |
None |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$2^{3}$ |
|
\(q-\zeta_{16}^{4}q^{2}-q^{4}+(\zeta_{16}^{3}-\zeta_{16}^{5})q^{5}+\cdots\) |
1764.1.q.a |
$1764$ |
$1$ |
1764.q |
84.j |
$6$ |
$8$ |
$4$ |
$0.880$ |
\(\Q(\zeta_{24})\) |
$D_{4}$ |
\(\Q(\sqrt{-7}) \) |
None |
|
$16$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$1$ |
|
\(q-\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+\zeta_{24}^{9}q^{8}+\cdots\) |
1764.1.q.b |
$1764$ |
$1$ |
1764.q |
84.j |
$6$ |
$16$ |
$8$ |
$0.880$ |
\(\Q(\zeta_{48})\) |
$D_{8}$ |
\(\Q(\sqrt{-1}) \) |
None |
|
$16$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$2^{6}$ |
|
\(q-\zeta_{48}^{20}q^{2}-\zeta_{48}^{16}q^{4}+(-\zeta_{48}^{5}+\cdots)q^{5}+\cdots\) |
1764.1.y.a |
$1764$ |
$1$ |
1764.y |
28.g |
$6$ |
$2$ |
$1$ |
$0.880$ |
\(\Q(\sqrt{-3}) \) |
$D_{2}$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-7}) \) |
\(\Q(\sqrt{7}) \) |
|
$8$ |
$0$ |
\(-1\) |
\(0\) |
\(0\) |
\(0\) |
|
$1$ |
|
\(q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+q^{8}-\zeta_{6}q^{16}+\cdots\) |
1764.1.y.b |
$1764$ |
$1$ |
1764.y |
28.g |
$6$ |
$4$ |
$2$ |
$0.880$ |
\(\Q(\sqrt{2}, \sqrt{-3})\) |
$D_{4}$ |
\(\Q(\sqrt{-1}) \) |
None |
|
$8$ |
$0$ |
\(-2\) |
\(0\) |
\(0\) |
\(0\) |
|
$1$ |
|
\(q+\beta _{2}q^{2}+(-1-\beta _{2})q^{4}+(-\beta _{1}-\beta _{3})q^{5}+\cdots\) |
1764.1.y.c |
$1764$ |
$1$ |
1764.y |
28.g |
$6$ |
$4$ |
$2$ |
$0.880$ |
\(\Q(\zeta_{12})\) |
$D_{2}$ |
\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-21}) \) |
\(\Q(\sqrt{3}) \) |
|
$16$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$1$ |
|
\(q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{3}q^{8}+\zeta_{12}^{5}q^{11}+\cdots\) |
1764.1.y.d |
$1764$ |
$1$ |
1764.y |
28.g |
$6$ |
$4$ |
$2$ |
$0.880$ |
\(\Q(\sqrt{2}, \sqrt{-3})\) |
$D_{4}$ |
\(\Q(\sqrt{-1}) \) |
None |
|
$8$ |
$0$ |
\(2\) |
\(0\) |
\(0\) |
\(0\) |
|
$1$ |
|
\(q-\beta _{2}q^{2}+(-1-\beta _{2})q^{4}+(-\beta _{1}-\beta _{3})q^{5}+\cdots\) |
1764.1.z.a |
$1764$ |
$1$ |
1764.z |
7.d |
$6$ |
$2$ |
$1$ |
$0.880$ |
\(\Q(\sqrt{-3}) \) |
$D_{6}$ |
\(\Q(\sqrt{-3}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$1$ |
|
\(q+(-\zeta_{6}-\zeta_{6}^{2})q^{13}+(1+\zeta_{6})q^{19}+\cdots\) |
1764.1.co.a |
$1764$ |
$1$ |
1764.co |
49.h |
$42$ |
$12$ |
$1$ |
$0.880$ |
\(\Q(\zeta_{21})\) |
$D_{42}$ |
\(\Q(\sqrt{-3}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(-1\) |
|
$1$ |
|
\(q-\zeta_{42}^{16}q^{7}+(-\zeta_{42}^{8}+\zeta_{42}^{10})q^{13}+\cdots\) |
1764.2.a.a |
$1764$ |
$2$ |
1764.a |
1.a |
$1$ |
$1$ |
$1$ |
$14.086$ |
\(\Q\) |
$_{}$ |
None |
None |
✓ |
$1$ |
$1$ |
\(0\) |
\(0\) |
\(-3\) |
\(0\) |
$+$ |
$1$ |
$\mathrm{SU}(2)$ |
\(q-3q^{5}+3q^{11}+2q^{13}-3q^{17}-q^{19}+\cdots\) |
1764.2.a.b |
$1764$ |
$2$ |
1764.a |
1.a |
$1$ |
$1$ |
$1$ |
$14.086$ |
\(\Q\) |
$_{}$ |
None |
None |
✓ |
$1$ |
$0$ |
\(0\) |
\(0\) |
\(-2\) |
\(0\) |
$-$ |
$1$ |
$\mathrm{SU}(2)$ |
\(q-2q^{5}-2q^{11}-4q^{13}-6q^{17}+8q^{19}+\cdots\) |
1764.2.a.c |
$1764$ |
$2$ |
1764.a |
1.a |
$1$ |
$1$ |
$1$ |
$14.086$ |
\(\Q\) |
$_{}$ |
None |
None |
✓ |
$1$ |
$0$ |
\(0\) |
\(0\) |
\(-2\) |
\(0\) |
$-$ |
$1$ |
$\mathrm{SU}(2)$ |
\(q-2q^{5}-2q^{11}+3q^{13}+8q^{17}+q^{19}+\cdots\) |
1764.2.a.d |
$1764$ |
$2$ |
1764.a |
1.a |
$1$ |
$1$ |
$1$ |
$14.086$ |
\(\Q\) |
$_{}$ |
\(\Q(\sqrt{-3}) \) |
None |
✓ |
$2$ |
$1$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$+$ |
$1$ |
$N(\mathrm{U}(1))$ |
\(q-5q^{13}+q^{19}-5q^{25}-11q^{31}+\cdots\) |
1764.2.a.e |
$1764$ |
$2$ |
1764.a |
1.a |
$1$ |
$1$ |
$1$ |
$14.086$ |
\(\Q\) |
$_{}$ |
\(\Q(\sqrt{-3}) \) |
None |
✓ |
$2$ |
$1$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$+$ |
$1$ |
$N(\mathrm{U}(1))$ |
\(q-2q^{13}-8q^{19}-5q^{25}+4q^{31}+\cdots\) |
1764.2.a.f |
$1764$ |
$2$ |
1764.a |
1.a |
$1$ |
$1$ |
$1$ |
$14.086$ |
\(\Q\) |
$_{}$ |
\(\Q(\sqrt{-3}) \) |
None |
✓ |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$-$ |
$1$ |
$N(\mathrm{U}(1))$ |
\(q+5q^{13}-q^{19}-5q^{25}+11q^{31}+\cdots\) |
1764.2.a.g |
$1764$ |
$2$ |
1764.a |
1.a |
$1$ |
$1$ |
$1$ |
$14.086$ |
\(\Q\) |
$_{}$ |
None |
None |
✓ |
$1$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$-$ |
$1$ |
$\mathrm{SU}(2)$ |
\(q+6q^{11}-2q^{13}+4q^{19}+6q^{23}+\cdots\) |
1764.2.a.h |
$1764$ |
$2$ |
1764.a |
1.a |
$1$ |
$1$ |
$1$ |
$14.086$ |
\(\Q\) |
$_{}$ |
None |
None |
✓ |
$1$ |
$1$ |
\(0\) |
\(0\) |
\(2\) |
\(0\) |
$+$ |
$1$ |
$\mathrm{SU}(2)$ |
\(q+2q^{5}-2q^{11}-3q^{13}-8q^{17}-q^{19}+\cdots\) |
1764.2.a.i |
$1764$ |
$2$ |
1764.a |
1.a |
$1$ |
$1$ |
$1$ |
$14.086$ |
\(\Q\) |
$_{}$ |
None |
None |
✓ |
$1$ |
$0$ |
\(0\) |
\(0\) |
\(2\) |
\(0\) |
$-$ |
$1$ |
$\mathrm{SU}(2)$ |
\(q+2q^{5}-2q^{11}+4q^{13}+6q^{17}-8q^{19}+\cdots\) |
1764.2.a.j |
$1764$ |
$2$ |
1764.a |
1.a |
$1$ |
$1$ |
$1$ |
$14.086$ |
\(\Q\) |
$_{}$ |
None |
None |
✓ |
$1$ |
$0$ |
\(0\) |
\(0\) |
\(3\) |
\(0\) |
$-$ |
$1$ |
$\mathrm{SU}(2)$ |
\(q+3q^{5}+3q^{11}-2q^{13}+3q^{17}+q^{19}+\cdots\) |
1764.2.a.k |
$1764$ |
$2$ |
1764.a |
1.a |
$1$ |
$1$ |
$1$ |
$14.086$ |
\(\Q\) |
$_{}$ |
None |
None |
✓ |
$1$ |
$0$ |
\(0\) |
\(0\) |
\(4\) |
\(0\) |
$-$ |
$1$ |
$\mathrm{SU}(2)$ |
\(q+4q^{5}-2q^{11}+6q^{13}-4q^{17}+4q^{19}+\cdots\) |
1764.2.a.l |
$1764$ |
$2$ |
1764.a |
1.a |
$1$ |
$2$ |
$2$ |
$14.086$ |
\(\Q(\sqrt{2}) \) |
$_{}$ |
None |
None |
✓ |
$2$ |
$1$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$+$ |
$1$ |
$\mathrm{SU}(2)$ |
\(q+\beta q^{5}-4q^{11}-3\beta q^{13}+\beta q^{17}+\cdots\) |
1764.2.a.m |
$1764$ |
$2$ |
1764.a |
1.a |
$1$ |
$4$ |
$4$ |
$14.086$ |
\(\Q(\sqrt{2}, \sqrt{7})\) |
$_{}$ |
None |
None |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$-$ |
$2^{2}$ |
$\mathrm{SU}(2)$ |
\(q+\beta _{2}q^{5}-\beta _{3}q^{11}-3\beta _{1}q^{13}+\beta _{2}q^{17}+\cdots\) |
1764.2.b.a |
$1764$ |
$2$ |
1764.b |
28.d |
$2$ |
$4$ |
$4$ |
$14.086$ |
\(\Q(\zeta_{12})\) |
$_{}$ |
None |
None |
|
$4$ |
$0$ |
\(-4\) |
\(0\) |
\(0\) |
\(0\) |
|
$2^{2}$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+(-1+\zeta_{12})q^{2}-2\zeta_{12}q^{4}-\zeta_{12}^{2}q^{5}+\cdots\) |
1764.2.b.b |
$1764$ |
$2$ |
1764.b |
28.d |
$2$ |
$4$ |
$4$ |
$14.086$ |
\(\Q(\sqrt{-3}, \sqrt{-7})\) |
$_{}$ |
None |
None |
|
$4$ |
$0$ |
\(-2\) |
\(0\) |
\(0\) |
\(0\) |
|
$2^{2}$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+\beta _{2}q^{2}+(-2-\beta _{2})q^{4}+\beta _{3}q^{5}+(2+\cdots)q^{8}+\cdots\) |
1764.2.b.c |
$1764$ |
$2$ |
1764.b |
28.d |
$2$ |
$4$ |
$4$ |
$14.086$ |
\(\Q(\sqrt{-2}, \sqrt{-3})\) |
$_{}$ |
None |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$2^{2}$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q-\beta _{3}q^{2}+(1-\beta _{2})q^{4}+(\beta _{1}-\beta _{3})q^{5}+\cdots\) |
1764.2.b.d |
$1764$ |
$2$ |
1764.b |
28.d |
$2$ |
$4$ |
$4$ |
$14.086$ |
\(\Q(\sqrt{-2}, \sqrt{-3})\) |
$_{}$ |
None |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$2^{2}$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+\beta _{3}q^{2}+(1-\beta _{2})q^{4}+(\beta _{1}-\beta _{3})q^{5}+\cdots\) |
1764.2.b.e |
$1764$ |
$2$ |
1764.b |
28.d |
$2$ |
$4$ |
$4$ |
$14.086$ |
4.0.2048.2 |
$_{}$ |
\(\Q(\sqrt{-1}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$1$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q+\beta _{2}q^{2}+2q^{4}+(\beta _{1}+2\beta _{3})q^{5}+2\beta _{2}q^{8}+\cdots\) |
1764.2.b.f |
$1764$ |
$2$ |
1764.b |
28.d |
$2$ |
$4$ |
$4$ |
$14.086$ |
4.0.2048.2 |
$_{}$ |
\(\Q(\sqrt{-1}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$7$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q+\beta _{2}q^{2}+2q^{4}+\beta _{1}q^{5}+2\beta _{2}q^{8}+\cdots\) |
1764.2.b.g |
$1764$ |
$2$ |
1764.b |
28.d |
$2$ |
$4$ |
$4$ |
$14.086$ |
4.0.2048.2 |
$_{}$ |
\(\Q(\sqrt{-1}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$1$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q-\beta _{2}q^{2}+2q^{4}+(\beta _{1}+2\beta _{3})q^{5}-2\beta _{2}q^{8}+\cdots\) |
1764.2.b.h |
$1764$ |
$2$ |
1764.b |
28.d |
$2$ |
$4$ |
$4$ |
$14.086$ |
\(\Q(\sqrt{-3}, \sqrt{-7})\) |
$_{}$ |
None |
None |
|
$4$ |
$0$ |
\(2\) |
\(0\) |
\(0\) |
\(0\) |
|
$2^{2}$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q-\beta _{2}q^{2}+(-2-\beta _{2})q^{4}+\beta _{3}q^{5}+(-2+\cdots)q^{8}+\cdots\) |
1764.2.b.i |
$1764$ |
$2$ |
1764.b |
28.d |
$2$ |
$8$ |
$8$ |
$14.086$ |
8.0.562828176.1 |
$_{}$ |
None |
None |
|
$2$ |
$0$ |
\(2\) |
\(0\) |
\(0\) |
\(0\) |
|
$2^{4}$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{2}-\beta _{5})q^{5}+(\beta _{3}+\cdots)q^{8}+\cdots\) |
1764.2.b.j |
$1764$ |
$2$ |
1764.b |
28.d |
$2$ |
$8$ |
$8$ |
$14.086$ |
8.0.562828176.1 |
$_{}$ |
None |
None |
|
$2$ |
$0$ |
\(2\) |
\(0\) |
\(0\) |
\(0\) |
|
$2^{4}$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q-\beta _{4}q^{2}+\beta _{6}q^{4}+(\beta _{2}-\beta _{6})q^{5}+(-1+\cdots)q^{8}+\cdots\) |
1764.2.b.k |
$1764$ |
$2$ |
1764.b |
28.d |
$2$ |
$8$ |
$8$ |
$14.086$ |
8.0.\(\cdots\).10 |
$_{}$ |
None |
None |
|
$4$ |
$0$ |
\(4\) |
\(0\) |
\(0\) |
\(0\) |
|
$1$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+(1+\beta _{3})q^{2}+(1+\beta _{3}+\beta _{5}-\beta _{6})q^{4}+\cdots\) |
1764.2.b.l |
$1764$ |
$2$ |
1764.b |
28.d |
$2$ |
$12$ |
$12$ |
$14.086$ |
12.0.\(\cdots\).1 |
$_{}$ |
None |
None |
|
$2$ |
$0$ |
\(-4\) |
\(0\) |
\(0\) |
\(0\) |
|
$2^{2}$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q-\beta _{1}q^{2}+(\beta _{5}+\beta _{6})q^{4}+(1-\beta _{1}+\beta _{6}+\cdots)q^{5}+\cdots\) |
1764.2.b.m |
$1764$ |
$2$ |
1764.b |
28.d |
$2$ |
$12$ |
$12$ |
$14.086$ |
12.0.\(\cdots\).1 |
$_{}$ |
None |
None |
|
$2$ |
$0$ |
\(-4\) |
\(0\) |
\(0\) |
\(0\) |
|
$2^{2}$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+\beta _{4}q^{2}+(-\beta _{2}-\beta _{11})q^{4}+(-1+\beta _{3}+\cdots)q^{5}+\cdots\) |
1764.2.b.n |
$1764$ |
$2$ |
1764.b |
28.d |
$2$ |
$16$ |
$16$ |
$14.086$ |
\(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
$_{}$ |
None |
None |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$2^{5}\cdot 7^{2}$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+\beta _{7}q^{2}+(-1+\beta _{1}-\beta _{10})q^{4}+\beta _{12}q^{5}+\cdots\) |
1764.2.e.a |
$1764$ |
$2$ |
1764.e |
12.b |
$2$ |
$2$ |
$2$ |
$14.086$ |
\(\Q(\sqrt{-2}) \) |
$_{}$ |
\(\Q(\sqrt{-1}) \) |
None |
|
$4$ |
$1$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$1$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q+\beta q^{2}-2q^{4}+3\beta q^{5}-2\beta q^{8}-6q^{10}+\cdots\) |
1764.2.e.b |
$1764$ |
$2$ |
1764.e |
12.b |
$2$ |
$2$ |
$2$ |
$14.086$ |
\(\Q(\sqrt{-2}) \) |
$_{}$ |
\(\Q(\sqrt{-1}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$1$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q+\beta q^{2}-2q^{4}+\beta q^{5}-2\beta q^{8}-2q^{10}+\cdots\) |
1764.2.e.c |
$1764$ |
$2$ |
1764.e |
12.b |
$2$ |
$2$ |
$2$ |
$14.086$ |
\(\Q(\sqrt{-2}) \) |
$_{}$ |
\(\Q(\sqrt{-1}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$1$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q-\beta q^{2}-2q^{4}+3\beta q^{5}+2\beta q^{8}+6q^{10}+\cdots\) |
1764.2.e.d |
$1764$ |
$2$ |
1764.e |
12.b |
$2$ |
$4$ |
$4$ |
$14.086$ |
\(\Q(\zeta_{8})\) |
$_{}$ |
\(\Q(\sqrt{-1}) \) |
None |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$2^{2}$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q-\zeta_{8}^{2}q^{2}-2q^{4}+2\zeta_{8}q^{5}+2\zeta_{8}^{2}q^{8}+\cdots\) |
1764.2.e.e |
$1764$ |
$2$ |
1764.e |
12.b |
$2$ |
$4$ |
$4$ |
$14.086$ |
\(\Q(\zeta_{8})\) |
$_{}$ |
\(\Q(\sqrt{-1}) \) |
None |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$2^{2}$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q+\zeta_{8}^{2}q^{2}-2q^{4}-\zeta_{8}q^{5}-2\zeta_{8}^{2}q^{8}+\cdots\) |
1764.2.e.f |
$1764$ |
$2$ |
1764.e |
12.b |
$2$ |
$8$ |
$8$ |
$14.086$ |
8.0.157351936.1 |
$_{}$ |
\(\Q(\sqrt{-7}) \) |
None |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$2^{2}\cdot 3^{4}$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q+\beta _{6}q^{2}-\beta _{1}q^{4}-\beta _{5}q^{8}+(\beta _{5}+\beta _{6}+\cdots)q^{11}+\cdots\) |
1764.2.e.g |
$1764$ |
$2$ |
1764.e |
12.b |
$2$ |
$12$ |
$12$ |
$14.086$ |
12.0.\(\cdots\).1 |
$_{}$ |
None |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$2^{9}$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+\beta _{6}q^{2}+(1+\beta _{10})q^{4}-\beta _{4}q^{5}+(\beta _{6}+\cdots)q^{8}+\cdots\) |
1764.2.e.h |
$1764$ |
$2$ |
1764.e |
12.b |
$2$ |
$16$ |
$16$ |
$14.086$ |
\(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
$_{}$ |
None |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$2^{10}$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q-\beta _{1}q^{2}+\beta _{2}q^{4}-\beta _{5}q^{5}+(\beta _{3}-\beta _{5}+\cdots)q^{8}+\cdots\) |
1764.2.e.i |
$1764$ |
$2$ |
1764.e |
12.b |
$2$ |
$16$ |
$16$ |
$14.086$ |
\(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
$_{}$ |
None |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$2^{10}$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+\beta _{1}q^{2}+\beta _{2}q^{4}-\beta _{5}q^{5}+(-\beta _{3}+\beta _{5}+\cdots)q^{8}+\cdots\) |