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 |
$a_{2}$ |
$a_{3}$ |
$a_{5}$ |
$a_{7}$ |
1536.1.e.a |
$1536$ |
$1$ |
1536.e |
3.b |
$2$ |
$4$ |
$4$ |
$0.767$ |
\(\Q(\zeta_{8})\) |
$D_{4}$ |
\(\Q(\sqrt{-6}) \) |
None |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$2$ |
|
\(q-\zeta_{8}^{2}q^{3}+(-\zeta_{8}-\zeta_{8}^{3})q^{5}+(-\zeta_{8}+\cdots)q^{7}+\cdots\) |
1536.1.e.b |
$1536$ |
$1$ |
1536.e |
3.b |
$2$ |
$4$ |
$4$ |
$0.767$ |
\(\Q(\zeta_{8})\) |
$D_{4}$ |
\(\Q(\sqrt{-2}) \) |
None |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$1$ |
|
\(q-\zeta_{8}q^{3}+\zeta_{8}^{2}q^{9}+(\zeta_{8}+\zeta_{8}^{3})q^{11}+\cdots\) |
1536.1.h.a |
$1536$ |
$1$ |
1536.h |
24.h |
$2$ |
$2$ |
$2$ |
$0.767$ |
\(\Q(\sqrt{2}) \) |
$D_{4}$ |
\(\Q(\sqrt{-6}) \) |
None |
✓ |
$4$ |
$0$ |
\(0\) |
\(-2\) |
\(0\) |
\(0\) |
|
$1$ |
|
\(q-q^{3}-\beta q^{5}-\beta q^{7}+q^{9}+\beta q^{15}+\cdots\) |
1536.1.h.b |
$1536$ |
$1$ |
1536.h |
24.h |
$2$ |
$2$ |
$2$ |
$0.767$ |
\(\Q(\sqrt{2}) \) |
$D_{4}$ |
\(\Q(\sqrt{-6}) \) |
None |
✓ |
$4$ |
$0$ |
\(0\) |
\(2\) |
\(0\) |
\(0\) |
|
$1$ |
|
\(q+q^{3}-\beta q^{5}+\beta q^{7}+q^{9}-\beta q^{15}+\cdots\) |
1536.1.h.c |
$1536$ |
$1$ |
1536.h |
24.h |
$2$ |
$4$ |
$4$ |
$0.767$ |
\(\Q(\zeta_{8})\) |
$D_{4}$ |
\(\Q(\sqrt{-2}) \) |
None |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$1$ |
|
\(q-\zeta_{8}q^{3}+\zeta_{8}^{2}q^{9}+(-\zeta_{8}+\zeta_{8}^{3})q^{11}+\cdots\) |
1536.2.a.a |
$1536$ |
$2$ |
1536.a |
1.a |
$1$ |
$2$ |
$2$ |
$12.265$ |
\(\Q(\sqrt{2}) \) |
$_{}$ |
None |
None |
✓ |
$1$ |
$1$ |
\(0\) |
\(-2\) |
\(-4\) |
\(0\) |
$+$ |
$1$ |
$\mathrm{SU}(2)$ |
\(q-q^{3}+(-2+\beta )q^{5}+\beta q^{7}+q^{9}+(2+\cdots)q^{11}+\cdots\) |
1536.2.a.b |
$1536$ |
$2$ |
1536.a |
1.a |
$1$ |
$2$ |
$2$ |
$12.265$ |
\(\Q(\sqrt{2}) \) |
$_{}$ |
None |
None |
✓ |
$1$ |
$0$ |
\(0\) |
\(-2\) |
\(-4\) |
\(4\) |
$-$ |
$1$ |
$\mathrm{SU}(2)$ |
\(q-q^{3}+(-2+\beta )q^{5}+(2+\beta )q^{7}+q^{9}+\cdots\) |
1536.2.a.c |
$1536$ |
$2$ |
1536.a |
1.a |
$1$ |
$2$ |
$2$ |
$12.265$ |
\(\Q(\sqrt{2}) \) |
$_{}$ |
None |
None |
✓ |
$2$ |
$1$ |
\(0\) |
\(-2\) |
\(0\) |
\(0\) |
$+$ |
$1$ |
$\mathrm{SU}(2)$ |
\(q-q^{3}+\beta q^{5}-\beta q^{7}+q^{9}-2q^{11}+\cdots\) |
1536.2.a.d |
$1536$ |
$2$ |
1536.a |
1.a |
$1$ |
$2$ |
$2$ |
$12.265$ |
\(\Q(\sqrt{2}) \) |
$_{}$ |
None |
None |
✓ |
$2$ |
$0$ |
\(0\) |
\(-2\) |
\(0\) |
\(0\) |
$-$ |
$1$ |
$\mathrm{SU}(2)$ |
\(q-q^{3}+\beta q^{5}+3\beta q^{7}+q^{9}+6q^{11}+\cdots\) |
1536.2.a.e |
$1536$ |
$2$ |
1536.a |
1.a |
$1$ |
$2$ |
$2$ |
$12.265$ |
\(\Q(\sqrt{2}) \) |
$_{}$ |
None |
None |
✓ |
$1$ |
$1$ |
\(0\) |
\(-2\) |
\(4\) |
\(-4\) |
$+$ |
$1$ |
$\mathrm{SU}(2)$ |
\(q-q^{3}+(2+\beta )q^{5}+(-2+\beta )q^{7}+q^{9}+\cdots\) |
1536.2.a.f |
$1536$ |
$2$ |
1536.a |
1.a |
$1$ |
$2$ |
$2$ |
$12.265$ |
\(\Q(\sqrt{2}) \) |
$_{}$ |
None |
None |
✓ |
$1$ |
$0$ |
\(0\) |
\(-2\) |
\(4\) |
\(0\) |
$-$ |
$1$ |
$\mathrm{SU}(2)$ |
\(q-q^{3}+(2+\beta )q^{5}+\beta q^{7}+q^{9}+(2+2\beta )q^{11}+\cdots\) |
1536.2.a.g |
$1536$ |
$2$ |
1536.a |
1.a |
$1$ |
$2$ |
$2$ |
$12.265$ |
\(\Q(\sqrt{2}) \) |
$_{}$ |
None |
None |
✓ |
$1$ |
$1$ |
\(0\) |
\(2\) |
\(-4\) |
\(-4\) |
$+$ |
$1$ |
$\mathrm{SU}(2)$ |
\(q+q^{3}+(-2+\beta )q^{5}+(-2-\beta )q^{7}+\cdots\) |
1536.2.a.h |
$1536$ |
$2$ |
1536.a |
1.a |
$1$ |
$2$ |
$2$ |
$12.265$ |
\(\Q(\sqrt{2}) \) |
$_{}$ |
None |
None |
✓ |
$1$ |
$1$ |
\(0\) |
\(2\) |
\(-4\) |
\(0\) |
$+$ |
$1$ |
$\mathrm{SU}(2)$ |
\(q+q^{3}+(-2+\beta )q^{5}-\beta q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots\) |
1536.2.a.i |
$1536$ |
$2$ |
1536.a |
1.a |
$1$ |
$2$ |
$2$ |
$12.265$ |
\(\Q(\sqrt{2}) \) |
$_{}$ |
None |
None |
✓ |
$2$ |
$1$ |
\(0\) |
\(2\) |
\(0\) |
\(0\) |
$+$ |
$1$ |
$\mathrm{SU}(2)$ |
\(q+q^{3}+\beta q^{5}-3\beta q^{7}+q^{9}-6q^{11}+\cdots\) |
1536.2.a.j |
$1536$ |
$2$ |
1536.a |
1.a |
$1$ |
$2$ |
$2$ |
$12.265$ |
\(\Q(\sqrt{2}) \) |
$_{}$ |
None |
None |
✓ |
$2$ |
$0$ |
\(0\) |
\(2\) |
\(0\) |
\(0\) |
$-$ |
$1$ |
$\mathrm{SU}(2)$ |
\(q+q^{3}+\beta q^{5}+\beta q^{7}+q^{9}+2q^{11}+\cdots\) |
1536.2.a.k |
$1536$ |
$2$ |
1536.a |
1.a |
$1$ |
$2$ |
$2$ |
$12.265$ |
\(\Q(\sqrt{2}) \) |
$_{}$ |
None |
None |
✓ |
$1$ |
$0$ |
\(0\) |
\(2\) |
\(4\) |
\(0\) |
$-$ |
$1$ |
$\mathrm{SU}(2)$ |
\(q+q^{3}+(2+\beta )q^{5}-\beta q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots\) |
1536.2.a.l |
$1536$ |
$2$ |
1536.a |
1.a |
$1$ |
$2$ |
$2$ |
$12.265$ |
\(\Q(\sqrt{2}) \) |
$_{}$ |
None |
None |
✓ |
$1$ |
$0$ |
\(0\) |
\(2\) |
\(4\) |
\(4\) |
$-$ |
$1$ |
$\mathrm{SU}(2)$ |
\(q+q^{3}+(2+\beta )q^{5}+(2-\beta )q^{7}+q^{9}+\cdots\) |
1536.2.a.m |
$1536$ |
$2$ |
1536.a |
1.a |
$1$ |
$4$ |
$4$ |
$12.265$ |
4.4.4352.1 |
$_{}$ |
None |
None |
✓ |
$2$ |
$0$ |
\(0\) |
\(-4\) |
\(0\) |
\(0\) |
$-$ |
$2^{3}$ |
$\mathrm{SU}(2)$ |
\(q-q^{3}+\beta _{1}q^{5}-\beta _{3}q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots\) |
1536.2.a.n |
$1536$ |
$2$ |
1536.a |
1.a |
$1$ |
$4$ |
$4$ |
$12.265$ |
4.4.4352.1 |
$_{}$ |
None |
None |
✓ |
$2$ |
$0$ |
\(0\) |
\(4\) |
\(0\) |
\(0\) |
$-$ |
$2^{3}$ |
$\mathrm{SU}(2)$ |
\(q+q^{3}+\beta _{1}q^{5}+\beta _{3}q^{7}+q^{9}+(2+\beta _{2}+\cdots)q^{11}+\cdots\) |
1536.2.c.a |
$1536$ |
$2$ |
1536.c |
12.b |
$2$ |
$2$ |
$2$ |
$12.265$ |
\(\Q(\sqrt{-2}) \) |
$_{}$ |
None |
None |
|
$2$ |
$0$ |
\(0\) |
\(-2\) |
\(0\) |
\(0\) |
|
$1$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+(-1+\beta )q^{3}+\beta q^{5}-3\beta q^{7}+(-1+\cdots)q^{9}+\cdots\) |
1536.2.c.b |
$1536$ |
$2$ |
1536.c |
12.b |
$2$ |
$2$ |
$2$ |
$12.265$ |
\(\Q(\sqrt{-2}) \) |
$_{}$ |
None |
None |
|
$2$ |
$1$ |
\(0\) |
\(-2\) |
\(0\) |
\(0\) |
|
$1$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+(-1-\beta )q^{3}+\beta q^{5}-3\beta q^{7}+(-1+\cdots)q^{9}+\cdots\) |
1536.2.c.c |
$1536$ |
$2$ |
1536.c |
12.b |
$2$ |
$2$ |
$2$ |
$12.265$ |
\(\Q(\sqrt{-2}) \) |
$_{}$ |
None |
None |
|
$2$ |
$0$ |
\(0\) |
\(2\) |
\(0\) |
\(0\) |
|
$1$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+(1-\beta )q^{3}+\beta q^{5}+3\beta q^{7}+(-1-2\beta )q^{9}+\cdots\) |
1536.2.c.d |
$1536$ |
$2$ |
1536.c |
12.b |
$2$ |
$2$ |
$2$ |
$12.265$ |
\(\Q(\sqrt{-2}) \) |
$_{}$ |
None |
None |
|
$2$ |
$0$ |
\(0\) |
\(2\) |
\(0\) |
\(0\) |
|
$1$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+(1+\beta )q^{3}+\beta q^{5}+3\beta q^{7}+(-1+2\beta )q^{9}+\cdots\) |
1536.2.c.e |
$1536$ |
$2$ |
1536.c |
12.b |
$2$ |
$4$ |
$4$ |
$12.265$ |
\(\Q(\sqrt{-2}, \sqrt{7})\) |
$_{}$ |
None |
None |
|
$4$ |
$0$ |
\(0\) |
\(-4\) |
\(0\) |
\(0\) |
|
$2^{2}$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+(-1-\beta _{1})q^{3}+\beta _{2}q^{5}+\beta _{2}q^{7}+(-1+\cdots)q^{9}+\cdots\) |
1536.2.c.f |
$1536$ |
$2$ |
1536.c |
12.b |
$2$ |
$4$ |
$4$ |
$12.265$ |
\(\Q(\zeta_{8})\) |
$_{}$ |
\(\Q(\sqrt{-2}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(-4\) |
\(0\) |
\(0\) |
|
$3$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q+(-1-\zeta_{8}^{2})q^{3}+(-\zeta_{8}+2\zeta_{8}^{2}+\zeta_{8}^{3})q^{9}+\cdots\) |
1536.2.c.g |
$1536$ |
$2$ |
1536.c |
12.b |
$2$ |
$4$ |
$4$ |
$12.265$ |
\(\Q(\sqrt{-2}, \sqrt{-5})\) |
$_{}$ |
None |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$1$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q-\beta _{1}q^{3}-2\beta _{2}q^{5}+(2+\beta _{3})q^{9}+(2\beta _{1}+\cdots)q^{11}+\cdots\) |
1536.2.c.h |
$1536$ |
$2$ |
1536.c |
12.b |
$2$ |
$4$ |
$4$ |
$12.265$ |
\(\Q(\sqrt{-2}, \sqrt{-5})\) |
$_{}$ |
None |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$1$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+(-\beta _{1}+\beta _{2})q^{3}-2\beta _{2}q^{5}+(2-\beta _{3})q^{9}+\cdots\) |
1536.2.c.i |
$1536$ |
$2$ |
1536.c |
12.b |
$2$ |
$4$ |
$4$ |
$12.265$ |
\(\Q(\sqrt{-2}, \sqrt{7})\) |
$_{}$ |
None |
None |
|
$4$ |
$0$ |
\(0\) |
\(4\) |
\(0\) |
\(0\) |
|
$2^{2}$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+(1-\beta _{1})q^{3}+\beta _{2}q^{5}-\beta _{2}q^{7}+(-1+\cdots)q^{9}+\cdots\) |
1536.2.c.j |
$1536$ |
$2$ |
1536.c |
12.b |
$2$ |
$4$ |
$4$ |
$12.265$ |
\(\Q(\zeta_{8})\) |
$_{}$ |
\(\Q(\sqrt{-2}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(4\) |
\(0\) |
\(0\) |
|
$3$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q+(1+\zeta_{8}^{2})q^{3}+(-\zeta_{8}+2\zeta_{8}^{2}+\zeta_{8}^{3})q^{9}+\cdots\) |
1536.2.c.k |
$1536$ |
$2$ |
1536.c |
12.b |
$2$ |
$8$ |
$8$ |
$12.265$ |
8.0.40960000.1 |
$_{}$ |
None |
None |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$2^{8}$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q-\beta _{4}q^{3}-\beta _{1}q^{5}+(-2+\beta _{2})q^{9}-\beta _{3}q^{11}+\cdots\) |
1536.2.c.l |
$1536$ |
$2$ |
1536.c |
12.b |
$2$ |
$8$ |
$8$ |
$12.265$ |
\(\Q(\zeta_{24})\) |
$_{}$ |
\(\Q(\sqrt{-6}) \) |
None |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$2^{16}$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q-\zeta_{24}q^{3}+\zeta_{24}^{3}q^{5}+\zeta_{24}^{2}q^{7}+3q^{9}+\cdots\) |
1536.2.c.m |
$1536$ |
$2$ |
1536.c |
12.b |
$2$ |
$16$ |
$16$ |
$12.265$ |
16.0.\(\cdots\).7 |
$_{}$ |
None |
None |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$2^{24}$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q-\beta _{7}q^{3}+\beta _{2}q^{5}-\beta _{6}q^{7}+\beta _{13}q^{9}+\cdots\) |
1536.2.d.a |
$1536$ |
$2$ |
1536.d |
8.b |
$2$ |
$4$ |
$4$ |
$12.265$ |
\(\Q(\zeta_{8})\) |
$_{}$ |
None |
None |
|
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(-8\) |
|
$2$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q-\zeta_{8}q^{3}+(2\zeta_{8}-\zeta_{8}^{2})q^{5}+(-2-\zeta_{8}^{3})q^{7}+\cdots\) |
1536.2.d.b |
$1536$ |
$2$ |
1536.d |
8.b |
$2$ |
$4$ |
$4$ |
$12.265$ |
\(\Q(\zeta_{8})\) |
$_{}$ |
None |
None |
|
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$2$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+\zeta_{8}q^{3}+(2\zeta_{8}-\zeta_{8}^{2})q^{5}+\zeta_{8}^{3}q^{7}+\cdots\) |
1536.2.d.c |
$1536$ |
$2$ |
1536.d |
8.b |
$2$ |
$4$ |
$4$ |
$12.265$ |
\(\Q(\zeta_{8})\) |
$_{}$ |
None |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$2$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+\zeta_{8}q^{3}+\zeta_{8}^{2}q^{5}-3\zeta_{8}^{3}q^{7}-q^{9}+\cdots\) |
1536.2.d.d |
$1536$ |
$2$ |
1536.d |
8.b |
$2$ |
$4$ |
$4$ |
$12.265$ |
\(\Q(\zeta_{8})\) |
$_{}$ |
None |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$2$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q-\zeta_{8}q^{3}+\zeta_{8}^{2}q^{5}-\zeta_{8}^{3}q^{7}-q^{9}+\cdots\) |
1536.2.d.e |
$1536$ |
$2$ |
1536.d |
8.b |
$2$ |
$4$ |
$4$ |
$12.265$ |
\(\Q(\zeta_{8})\) |
$_{}$ |
None |
None |
|
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$2$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q-\zeta_{8}q^{3}+(2\zeta_{8}-\zeta_{8}^{2})q^{5}-\zeta_{8}^{3}q^{7}+\cdots\) |
1536.2.d.f |
$1536$ |
$2$ |
1536.d |
8.b |
$2$ |
$4$ |
$4$ |
$12.265$ |
\(\Q(\zeta_{8})\) |
$_{}$ |
None |
None |
|
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(8\) |
|
$2$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+\zeta_{8}q^{3}+(2\zeta_{8}-\zeta_{8}^{2})q^{5}+(2+\zeta_{8}^{3})q^{7}+\cdots\) |
1536.2.d.g |
$1536$ |
$2$ |
1536.d |
8.b |
$2$ |
$8$ |
$8$ |
$12.265$ |
8.0.18939904.2 |
$_{}$ |
None |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$2^{10}$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q-\beta _{4}q^{3}+\beta _{5}q^{5}-\beta _{2}q^{7}-q^{9}+(2\beta _{4}+\cdots)q^{11}+\cdots\) |
1536.2.f.a |
$1536$ |
$2$ |
1536.f |
24.f |
$2$ |
$4$ |
$4$ |
$12.265$ |
\(\Q(\zeta_{8})\) |
$_{}$ |
\(\Q(\sqrt{-2}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(-4\) |
\(0\) |
\(0\) |
|
$1$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q+(-1-\zeta_{8}+\zeta_{8}^{2})q^{3}+(2\zeta_{8}-\zeta_{8}^{2}+\cdots)q^{9}+\cdots\) |
1536.2.f.b |
$1536$ |
$2$ |
1536.f |
24.f |
$2$ |
$4$ |
$4$ |
$12.265$ |
\(\Q(\sqrt{-2}, \sqrt{-3})\) |
$_{}$ |
\(\Q(\sqrt{-6}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(-8\) |
\(0\) |
|
$2^{2}$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q-\beta _{2}q^{3}+(-2+\beta _{3})q^{5}+(-\beta _{1}-2\beta _{2}+\cdots)q^{7}+\cdots\) |
1536.2.f.c |
$1536$ |
$2$ |
1536.f |
24.f |
$2$ |
$4$ |
$4$ |
$12.265$ |
\(\Q(\sqrt{-2}, \sqrt{-5})\) |
$_{}$ |
None |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(-8\) |
\(0\) |
|
$1$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+\beta _{1}q^{3}-2q^{5}+(2+\beta _{3})q^{9}+\beta _{2}q^{11}+\cdots\) |
1536.2.f.d |
$1536$ |
$2$ |
1536.f |
24.f |
$2$ |
$4$ |
$4$ |
$12.265$ |
\(\Q(\sqrt{2}, \sqrt{-5})\) |
$_{}$ |
None |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$1$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q-\beta _{1}q^{3}-2\beta _{2}q^{5}+(-2+\beta _{3})q^{9}+\cdots\) |
1536.2.f.e |
$1536$ |
$2$ |
1536.f |
24.f |
$2$ |
$4$ |
$4$ |
$12.265$ |
\(\Q(\sqrt{2}, \sqrt{-5})\) |
$_{}$ |
None |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$1$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+\beta _{1}q^{3}-2\beta _{2}q^{5}+(-2+\beta _{3})q^{9}+\cdots\) |
1536.2.f.f |
$1536$ |
$2$ |
1536.f |
24.f |
$2$ |
$4$ |
$4$ |
$12.265$ |
\(\Q(\zeta_{8})\) |
$_{}$ |
None |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$2$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+(\zeta_{8}+\zeta_{8}^{3})q^{3}-\zeta_{8}^{3}q^{5}+3\zeta_{8}^{2}q^{7}+\cdots\) |
1536.2.f.g |
$1536$ |
$2$ |
1536.f |
24.f |
$2$ |
$4$ |
$4$ |
$12.265$ |
\(\Q(\zeta_{8})\) |
$_{}$ |
None |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$2$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+(\zeta_{8}-\zeta_{8}^{3})q^{3}-\zeta_{8}^{3}q^{5}+3\zeta_{8}^{2}q^{7}+\cdots\) |
1536.2.f.h |
$1536$ |
$2$ |
1536.f |
24.f |
$2$ |
$4$ |
$4$ |
$12.265$ |
\(\Q(\sqrt{-2}, \sqrt{-3})\) |
$_{}$ |
\(\Q(\sqrt{-6}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(8\) |
\(0\) |
|
$2^{2}$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q+\beta _{2}q^{3}+(2+\beta _{3})q^{5}+(\beta _{1}-2\beta _{2})q^{7}+\cdots\) |
1536.2.f.i |
$1536$ |
$2$ |
1536.f |
24.f |
$2$ |
$4$ |
$4$ |
$12.265$ |
\(\Q(\sqrt{-2}, \sqrt{-5})\) |
$_{}$ |
None |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(8\) |
\(0\) |
|
$1$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+\beta _{1}q^{3}+2q^{5}+(2+\beta _{3})q^{9}+\beta _{2}q^{11}+\cdots\) |
1536.2.f.j |
$1536$ |
$2$ |
1536.f |
24.f |
$2$ |
$4$ |
$4$ |
$12.265$ |
\(\Q(\zeta_{8})\) |
$_{}$ |
\(\Q(\sqrt{-2}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(4\) |
\(0\) |
\(0\) |
|
$1$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q+(1+\zeta_{8}-\zeta_{8}^{2})q^{3}+(2\zeta_{8}-\zeta_{8}^{2}-2\zeta_{8}^{3})q^{9}+\cdots\) |
1536.2.f.k |
$1536$ |
$2$ |
1536.f |
24.f |
$2$ |
$8$ |
$8$ |
$12.265$ |
8.0.157351936.1 |
$_{}$ |
None |
None |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$2^{10}$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q-\beta _{2}q^{3}+\beta _{7}q^{5}-\beta _{6}q^{7}+(1-\beta _{4}+\cdots)q^{9}+\cdots\) |