| 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 |
| $a_{2}$ |
$a_{3}$ |
$a_{5}$ |
$a_{7}$ |
| 492.1.b.a |
$492$ |
$1$ |
492.b |
123.b |
$2$ |
$1$ |
$1$ |
$0.246$ |
\(\Q\) |
$D_{3}$ |
\(\Q(\sqrt{-123}) \) |
None |
✓ |
$2$ |
$0$ |
\(0\) |
\(-1\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-q^{3}+q^{9}+q^{11}+q^{17}+q^{25}-q^{27}+\cdots\) |
| 492.1.b.b |
$492$ |
$1$ |
492.b |
123.b |
$2$ |
$1$ |
$1$ |
$0.246$ |
\(\Q\) |
$D_{3}$ |
\(\Q(\sqrt{-123}) \) |
None |
✓ |
$2$ |
$0$ |
\(0\) |
\(1\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+q^{3}+q^{9}-q^{11}-q^{17}+q^{25}+q^{27}+\cdots\) |
| 1107.1.b.a |
$1107$ |
$1$ |
1107.b |
123.b |
$2$ |
$1$ |
$1$ |
$0.552$ |
\(\Q\) |
$D_{3}$ |
\(\Q(\sqrt{-123}) \) |
None |
✓ |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+q^{4}-q^{11}+q^{16}+2q^{17}+q^{25}+\cdots\) |
| 1107.1.b.b |
$1107$ |
$1$ |
1107.b |
123.b |
$2$ |
$1$ |
$1$ |
$0.552$ |
\(\Q\) |
$D_{3}$ |
\(\Q(\sqrt{-123}) \) |
None |
✓ |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+q^{4}+q^{11}+q^{16}-2q^{17}+q^{25}+\cdots\) |
| 1353.1.cf.a |
$1353$ |
$1$ |
1353.cf |
1353.bf |
$10$ |
$4$ |
$1$ |
$0.675$ |
\(\Q(\zeta_{10})\) |
$D_{5}$ |
\(\Q(\sqrt{-123}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(-1\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{10}^{3}q^{3}+\zeta_{10}^{2}q^{4}-\zeta_{10}q^{9}-\zeta_{10}^{3}q^{11}+\cdots\) |
| 1353.1.cf.b |
$1353$ |
$1$ |
1353.cf |
1353.bf |
$10$ |
$4$ |
$1$ |
$0.675$ |
\(\Q(\zeta_{10})\) |
$D_{5}$ |
\(\Q(\sqrt{-123}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(1\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+\zeta_{10}^{3}q^{3}+\zeta_{10}^{2}q^{4}-\zeta_{10}q^{9}+\zeta_{10}^{3}q^{11}+\cdots\) |
| 1968.1.b.a |
$1968$ |
$1$ |
1968.b |
123.b |
$2$ |
$1$ |
$1$ |
$0.982$ |
\(\Q\) |
$D_{3}$ |
\(\Q(\sqrt{-123}) \) |
None |
✓ |
$2$ |
$0$ |
\(0\) |
\(-1\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-q^{3}+q^{9}+q^{11}-q^{17}+q^{25}-q^{27}+\cdots\) |
| 1968.1.b.b |
$1968$ |
$1$ |
1968.b |
123.b |
$2$ |
$1$ |
$1$ |
$0.982$ |
\(\Q\) |
$D_{3}$ |
\(\Q(\sqrt{-123}) \) |
None |
✓ |
$2$ |
$0$ |
\(0\) |
\(1\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+q^{3}+q^{9}-q^{11}+q^{17}+q^{25}+q^{27}+\cdots\) |
| 2091.1.e.e |
$2091$ |
$1$ |
2091.e |
2091.e |
$2$ |
$2$ |
$2$ |
$1.044$ |
\(\Q(\sqrt{-1}) \) |
$D_{2}$ |
\(\Q(\sqrt{-51}) \), \(\Q(\sqrt{-123}) \) |
\(\Q(\sqrt{697}) \) |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-iq^{3}+q^{4}-q^{9}-iq^{11}-iq^{12}+\cdots\) |
| 2091.1.q.a |
$2091$ |
$1$ |
2091.q |
2091.q |
$4$ |
$4$ |
$2$ |
$1.044$ |
\(\Q(\zeta_{8})\) |
$D_{4}$ |
\(\Q(\sqrt{-123}) \) |
None |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{8}^{3}q^{3}-q^{4}-\zeta_{8}^{2}q^{9}+\zeta_{8}^{3}q^{12}+\cdots\) |
| 2091.1.bk.a |
$2091$ |
$1$ |
2091.bk |
2091.ak |
$8$ |
$8$ |
$2$ |
$1.044$ |
\(\Q(\zeta_{16})\) |
$D_{8}$ |
\(\Q(\sqrt{-123}) \) |
None |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{16}q^{3}-\zeta_{16}^{4}q^{4}+\zeta_{16}^{2}q^{9}+(-\zeta_{16}+\cdots)q^{11}+\cdots\) |
| 3075.1.c.a |
$3075$ |
$1$ |
3075.c |
123.b |
$2$ |
$1$ |
$1$ |
$1.535$ |
\(\Q\) |
$D_{3}$ |
\(\Q(\sqrt{-123}) \) |
None |
✓ |
$2$ |
$0$ |
\(0\) |
\(-1\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-q^{3}+q^{4}+q^{9}-q^{11}-q^{12}+q^{16}+\cdots\) |
| 3075.1.c.b |
$3075$ |
$1$ |
3075.c |
123.b |
$2$ |
$1$ |
$1$ |
$1.535$ |
\(\Q\) |
$D_{3}$ |
\(\Q(\sqrt{-123}) \) |
None |
✓ |
$2$ |
$0$ |
\(0\) |
\(-1\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-q^{3}+q^{4}+q^{9}+q^{11}-q^{12}+q^{16}+\cdots\) |
| 3075.1.c.c |
$3075$ |
$1$ |
3075.c |
123.b |
$2$ |
$1$ |
$1$ |
$1.535$ |
\(\Q\) |
$D_{3}$ |
\(\Q(\sqrt{-123}) \) |
None |
✓ |
$2$ |
$0$ |
\(0\) |
\(1\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+q^{3}+q^{4}+q^{9}-q^{11}+q^{12}+q^{16}+\cdots\) |
| 3075.1.c.d |
$3075$ |
$1$ |
3075.c |
123.b |
$2$ |
$1$ |
$1$ |
$1.535$ |
\(\Q\) |
$D_{3}$ |
\(\Q(\sqrt{-123}) \) |
None |
✓ |
$2$ |
$0$ |
\(0\) |
\(1\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+q^{3}+q^{4}+q^{9}+q^{11}+q^{12}+q^{16}+\cdots\) |
| 3075.1.h.a |
$3075$ |
$1$ |
3075.h |
615.h |
$2$ |
$2$ |
$2$ |
$1.535$ |
\(\Q(\sqrt{-1}) \) |
$D_{3}$ |
\(\Q(\sqrt{-123}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-iq^{3}-q^{4}-q^{9}-q^{11}+iq^{12}+\cdots\) |
| 3075.1.h.b |
$3075$ |
$1$ |
3075.h |
615.h |
$2$ |
$2$ |
$2$ |
$1.535$ |
\(\Q(\sqrt{-1}) \) |
$D_{3}$ |
\(\Q(\sqrt{-123}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-iq^{3}-q^{4}-q^{9}+q^{11}+iq^{12}+\cdots\) |
| 3321.1.k.a |
$3321$ |
$1$ |
3321.k |
369.k |
$6$ |
$2$ |
$1$ |
$1.657$ |
\(\Q(\sqrt{-3}) \) |
$D_{3}$ |
\(\Q(\sqrt{-123}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{6}q^{4}+\zeta_{6}^{2}q^{11}+\zeta_{6}^{2}q^{16}-q^{17}+\cdots\) |
| 3321.1.k.b |
$3321$ |
$1$ |
3321.k |
369.k |
$6$ |
$2$ |
$1$ |
$1.657$ |
\(\Q(\sqrt{-3}) \) |
$D_{3}$ |
\(\Q(\sqrt{-123}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{11}+\zeta_{6}^{2}q^{16}+q^{17}+\cdots\) |
| 3567.1.f.c |
$3567$ |
$1$ |
3567.f |
3567.f |
$2$ |
$2$ |
$2$ |
$1.780$ |
\(\Q(\sqrt{-1}) \) |
$D_{2}$ |
\(\Q(\sqrt{-87}) \), \(\Q(\sqrt{-123}) \) |
\(\Q(\sqrt{1189}) \) |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-iq^{3}-q^{4}-q^{9}+iq^{11}+iq^{12}+\cdots\) |
| 3567.1.bn.a |
$3567$ |
$1$ |
3567.bn |
3567.an |
$14$ |
$12$ |
$2$ |
$1.780$ |
\(\Q(\zeta_{28})\) |
$D_{14}$ |
\(\Q(\sqrt{-123}) \) |
None |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+\zeta_{28}q^{3}+\zeta_{28}^{6}q^{4}+\zeta_{28}^{2}q^{9}+(\zeta_{28}^{3}+\cdots)q^{11}+\cdots\) |
| 3567.1.br.a |
$3567$ |
$1$ |
3567.br |
3567.ar |
$14$ |
$6$ |
$1$ |
$1.780$ |
\(\Q(\zeta_{14})\) |
$D_{7}$ |
\(\Q(\sqrt{-123}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(-1\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+\zeta_{14}^{2}q^{3}-\zeta_{14}^{5}q^{4}+\zeta_{14}^{4}q^{9}+\cdots\) |
| 3567.1.br.b |
$3567$ |
$1$ |
3567.br |
3567.ar |
$14$ |
$6$ |
$1$ |
$1.780$ |
\(\Q(\zeta_{14})\) |
$D_{7}$ |
\(\Q(\sqrt{-123}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(1\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{14}^{2}q^{3}-\zeta_{14}^{5}q^{4}+\zeta_{14}^{4}q^{9}+\cdots\) |
| 3813.1.v.a |
$3813$ |
$1$ |
3813.v |
3813.v |
$6$ |
$2$ |
$1$ |
$1.903$ |
\(\Q(\sqrt{-3}) \) |
$D_{3}$ |
\(\Q(\sqrt{-123}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(-1\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+\zeta_{6}^{2}q^{3}+q^{4}-\zeta_{6}q^{9}-\zeta_{6}q^{11}+\cdots\) |
| 3813.1.v.b |
$3813$ |
$1$ |
3813.v |
3813.v |
$6$ |
$2$ |
$1$ |
$1.903$ |
\(\Q(\sqrt{-3}) \) |
$D_{3}$ |
\(\Q(\sqrt{-123}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(1\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{6}^{2}q^{3}+q^{4}-\zeta_{6}q^{9}+\zeta_{6}q^{11}+\cdots\) |
| 3813.1.bz.a |
$3813$ |
$1$ |
3813.bz |
3813.az |
$10$ |
$4$ |
$1$ |
$1.903$ |
\(\Q(\zeta_{10})\) |
$D_{5}$ |
\(\Q(\sqrt{-123}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(-1\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{10}^{3}q^{3}+\zeta_{10}^{4}q^{4}-\zeta_{10}q^{9}+(-\zeta_{10}+\cdots)q^{11}+\cdots\) |
| 3813.1.bz.b |
$3813$ |
$1$ |
3813.bz |
3813.az |
$10$ |
$4$ |
$1$ |
$1.903$ |
\(\Q(\zeta_{10})\) |
$D_{5}$ |
\(\Q(\sqrt{-123}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(1\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+\zeta_{10}^{3}q^{3}+\zeta_{10}^{4}q^{4}-\zeta_{10}q^{9}+(\zeta_{10}+\cdots)q^{11}+\cdots\) |
| 3813.1.fq.a |
$3813$ |
$1$ |
3813.fq |
3813.eq |
$30$ |
$8$ |
$1$ |
$1.903$ |
\(\Q(\zeta_{15})\) |
$D_{15}$ |
\(\Q(\sqrt{-123}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(-1\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+\zeta_{30}^{11}q^{3}-\zeta_{30}^{3}q^{4}-\zeta_{30}^{7}q^{9}+\cdots\) |
| 3813.1.fq.b |
$3813$ |
$1$ |
3813.fq |
3813.eq |
$30$ |
$8$ |
$1$ |
$1.903$ |
\(\Q(\zeta_{15})\) |
$D_{15}$ |
\(\Q(\sqrt{-123}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(1\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{30}^{11}q^{3}-\zeta_{30}^{3}q^{4}-\zeta_{30}^{7}q^{9}+\cdots\) |
| 369.2.d.b |
$369$ |
$2$ |
369.d |
41.b |
$2$ |
$2$ |
$2$ |
$2.946$ |
\(\Q(\sqrt{-41}) \) |
$_{}$ |
\(\Q(\sqrt{-123}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q-2q^{4}+\beta q^{11}+4q^{16}+\beta q^{17}-5q^{25}+\cdots\) |
| 123.3.b.a |
$123$ |
$3$ |
123.b |
123.b |
$2$ |
$1$ |
$1$ |
$3.352$ |
\(\Q\) |
$_{}$ |
\(\Q(\sqrt{-123}) \) |
None |
✓ |
$2$ |
$0$ |
\(0\) |
\(-3\) |
\(0\) |
\(0\) |
$1$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q-3q^{3}+4q^{4}+9q^{9}+19q^{11}-12q^{12}+\cdots\) |
| 123.3.b.b |
$123$ |
$3$ |
123.b |
123.b |
$2$ |
$1$ |
$1$ |
$3.352$ |
\(\Q\) |
$_{}$ |
\(\Q(\sqrt{-123}) \) |
None |
✓ |
$2$ |
$0$ |
\(0\) |
\(3\) |
\(0\) |
\(0\) |
$1$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q+3q^{3}+4q^{4}+9q^{9}-19q^{11}+12q^{12}+\cdots\) |
| 1107.2.d.a |
$1107$ |
$2$ |
1107.d |
41.b |
$2$ |
$4$ |
$4$ |
$8.839$ |
\(\Q(i, \sqrt{41})\) |
$_{}$ |
\(\Q(\sqrt{-123}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$3^{2}$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q-2q^{4}+\beta _{1}q^{11}+4q^{16}+(-2\beta _{1}+\cdots)q^{17}+\cdots\) |
| 1476.2.f.c |
$1476$ |
$2$ |
1476.f |
41.b |
$2$ |
$4$ |
$4$ |
$11.786$ |
\(\Q(i, \sqrt{41})\) |
$_{}$ |
\(\Q(\sqrt{-123}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$3^{2}$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q+\beta _{1}q^{11}+(\beta _{1}-2\beta _{2})q^{17}-5q^{25}+\cdots\) |
| 123.5.b.a |
$123$ |
$5$ |
123.b |
123.b |
$2$ |
$1$ |
$1$ |
$12.715$ |
\(\Q\) |
$_{}$ |
\(\Q(\sqrt{-123}) \) |
None |
✓ |
$2$ |
$0$ |
\(0\) |
\(-9\) |
\(0\) |
\(0\) |
$1$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q-9q^{3}+2^{4}q^{4}+3^{4}q^{9}-119q^{11}+\cdots\) |
| 123.5.b.b |
$123$ |
$5$ |
123.b |
123.b |
$2$ |
$1$ |
$1$ |
$12.715$ |
\(\Q\) |
$_{}$ |
\(\Q(\sqrt{-123}) \) |
None |
✓ |
$2$ |
$0$ |
\(0\) |
\(9\) |
\(0\) |
\(0\) |
$1$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q+9q^{3}+2^{4}q^{4}+3^{4}q^{9}+119q^{11}+\cdots\) |
| 492.3.b.a |
$492$ |
$3$ |
492.b |
123.b |
$2$ |
$2$ |
$2$ |
$13.406$ |
\(\Q(\sqrt{41}) \) |
$_{}$ |
\(\Q(\sqrt{-123}) \) |
None |
✓ |
$2$ |
$0$ |
\(0\) |
\(-6\) |
\(0\) |
\(0\) |
$3$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q-3q^{3}+9q^{9}+(-9+\beta )q^{11}+(-5+\cdots)q^{17}+\cdots\) |
| 492.3.b.b |
$492$ |
$3$ |
492.b |
123.b |
$2$ |
$2$ |
$2$ |
$13.406$ |
\(\Q(\sqrt{41}) \) |
$_{}$ |
\(\Q(\sqrt{-123}) \) |
None |
✓ |
$2$ |
$0$ |
\(0\) |
\(6\) |
\(0\) |
\(0\) |
$3$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q+3q^{3}+9q^{9}+(10+\beta )q^{11}+(2-3\beta )q^{17}+\cdots\) |
| 1968.2.g.a |
$1968$ |
$2$ |
1968.g |
492.d |
$2$ |
$4$ |
$4$ |
$15.715$ |
\(\Q(\sqrt{-3}, \sqrt{41})\) |
$_{}$ |
\(\Q(\sqrt{-123}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2^{2}$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q+\beta _{1}q^{3}-3q^{9}+\beta _{2}q^{11}+(-5+\beta _{3})q^{17}+\cdots\) |
| 1968.2.g.b |
$1968$ |
$2$ |
1968.g |
492.d |
$2$ |
$4$ |
$4$ |
$15.715$ |
\(\Q(\sqrt{-3}, \sqrt{41})\) |
$_{}$ |
\(\Q(\sqrt{-123}) \) |
None |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2^{4}$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q+\beta _{1}q^{3}-3q^{9}-\beta _{1}q^{11}-\beta _{2}q^{17}+\cdots\) |
| 1968.2.g.c |
$1968$ |
$2$ |
1968.g |
492.d |
$2$ |
$4$ |
$4$ |
$15.715$ |
\(\Q(\sqrt{-3}, \sqrt{41})\) |
$_{}$ |
\(\Q(\sqrt{-123}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2^{2}$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q-\beta _{1}q^{3}-3q^{9}-\beta _{2}q^{11}+(5-\beta _{3})q^{17}+\cdots\) |
| 369.4.d.a |
$369$ |
$4$ |
369.d |
41.b |
$2$ |
$2$ |
$2$ |
$21.772$ |
\(\Q(\sqrt{-41}) \) |
$_{}$ |
\(\Q(\sqrt{-123}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q-8q^{4}-8\beta q^{11}+2^{6}q^{16}+10\beta q^{17}+\cdots\) |
| 123.7.b.a |
$123$ |
$7$ |
123.b |
123.b |
$2$ |
$1$ |
$1$ |
$28.297$ |
\(\Q\) |
$_{}$ |
\(\Q(\sqrt{-123}) \) |
None |
✓ |
$2$ |
$0$ |
\(0\) |
\(-27\) |
\(0\) |
\(0\) |
$1$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q-3^{3}q^{3}+2^{6}q^{4}+3^{6}q^{9}-38q^{11}+\cdots\) |
| 123.7.b.b |
$123$ |
$7$ |
123.b |
123.b |
$2$ |
$1$ |
$1$ |
$28.297$ |
\(\Q\) |
$_{}$ |
\(\Q(\sqrt{-123}) \) |
None |
✓ |
$2$ |
$0$ |
\(0\) |
\(27\) |
\(0\) |
\(0\) |
$1$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q+3^{3}q^{3}+2^{6}q^{4}+3^{6}q^{9}+38q^{11}+\cdots\) |
| 4428.2.f.a |
$4428$ |
$2$ |
4428.f |
41.b |
$2$ |
$4$ |
$4$ |
$35.358$ |
\(\Q(i, \sqrt{41})\) |
$_{}$ |
\(\Q(\sqrt{-123}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$3^{2}$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q+\beta _{1}q^{11}+(\beta _{1}+\beta _{2})q^{17}-5q^{25}+\cdots\) |
| 4428.2.f.b |
$4428$ |
$2$ |
4428.f |
41.b |
$2$ |
$4$ |
$4$ |
$35.358$ |
\(\Q(i, \sqrt{41})\) |
$_{}$ |
\(\Q(\sqrt{-123}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$3^{2}$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q+(-2\beta _{1}+\beta _{2})q^{11}+(\beta _{1}+\beta _{2})q^{17}+\cdots\) |
| 492.5.b.a |
$492$ |
$5$ |
492.b |
123.b |
$2$ |
$2$ |
$2$ |
$50.858$ |
\(\Q(\sqrt{41}) \) |
$_{}$ |
\(\Q(\sqrt{-123}) \) |
None |
✓ |
$2$ |
$0$ |
\(0\) |
\(-18\) |
\(0\) |
\(0\) |
$3$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q-9q^{3}+3^{4}q^{9}+(69+19\beta )q^{11}+(-275+\cdots)q^{17}+\cdots\) |
| 492.5.b.b |
$492$ |
$5$ |
492.b |
123.b |
$2$ |
$2$ |
$2$ |
$50.858$ |
\(\Q(\sqrt{41}) \) |
$_{}$ |
\(\Q(\sqrt{-123}) \) |
None |
✓ |
$2$ |
$0$ |
\(0\) |
\(18\) |
\(0\) |
\(0\) |
$3$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q+9q^{3}+3^{4}q^{9}+(-69-19\beta )q^{11}+\cdots\) |
| 369.6.d.a |
$369$ |
$6$ |
369.d |
41.b |
$2$ |
$2$ |
$2$ |
$59.182$ |
\(\Q(\sqrt{-41}) \) |
$_{}$ |
\(\Q(\sqrt{-123}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q-2^{5}q^{4}+31\beta q^{11}+2^{10}q^{16}-359\beta q^{17}+\cdots\) |
| 1476.4.f.b |
$1476$ |
$4$ |
1476.f |
41.b |
$2$ |
$4$ |
$4$ |
$87.087$ |
\(\Q(i, \sqrt{41})\) |
$_{}$ |
\(\Q(\sqrt{-123}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2^{2}\cdot 3^{4}$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q+(-4\beta _{1}-5\beta _{2})q^{11}+(5\beta _{1}+12\beta _{2}+\cdots)q^{17}+\cdots\) |
