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 |
$a_{2}$ |
$a_{3}$ |
$a_{5}$ |
$a_{7}$ |
268.1.b.a |
$268$ |
$1$ |
268.b |
67.b |
$2$ |
$1$ |
$1$ |
$0.134$ |
\(\Q\) |
$D_{3}$ |
\(\Q(\sqrt{-67}) \) |
None |
✓ |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$1$ |
|
\(q+q^{9}-q^{17}-q^{19}-q^{23}+q^{25}+\cdots\) |
603.1.b.a |
$603$ |
$1$ |
603.b |
67.b |
$2$ |
$1$ |
$1$ |
$0.301$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-67}) \) |
\(\Q(\sqrt{201}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$1$ |
|
\(q+q^{4}+q^{16}-2q^{19}+q^{25}-2q^{37}+\cdots\) |
1072.1.b.a |
$1072$ |
$1$ |
1072.b |
67.b |
$2$ |
$1$ |
$1$ |
$0.535$ |
\(\Q\) |
$D_{3}$ |
\(\Q(\sqrt{-67}) \) |
None |
✓ |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$1$ |
|
\(q+q^{9}-q^{17}+q^{19}+q^{23}+q^{25}+\cdots\) |
1139.1.c.a |
$1139$ |
$1$ |
1139.c |
1139.c |
$2$ |
$1$ |
$1$ |
$0.568$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-67}) \), \(\Q(\sqrt{-1139}) \) |
\(\Q(\sqrt{17}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$1$ |
|
\(q+q^{4}-q^{9}+q^{16}+q^{17}+2q^{19}+\cdots\) |
1139.1.g.a |
$1139$ |
$1$ |
1139.g |
1139.g |
$4$ |
$2$ |
$1$ |
$0.568$ |
\(\Q(\sqrt{-1}) \) |
$D_{4}$ |
\(\Q(\sqrt{-67}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$1$ |
|
\(q-q^{4}-iq^{9}+q^{16}+q^{17}+(-1-i+\cdots)q^{23}+\cdots\) |
1139.1.l.a |
$1139$ |
$1$ |
1139.l |
1139.l |
$8$ |
$4$ |
$1$ |
$0.568$ |
\(\Q(\zeta_{8})\) |
$D_{8}$ |
\(\Q(\sqrt{-67}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$1$ |
|
\(q+\zeta_{8}^{2}q^{4}+\zeta_{8}^{3}q^{9}-q^{16}+q^{17}+\cdots\) |
1273.1.r.a |
$1273$ |
$1$ |
1273.r |
1273.r |
$6$ |
$2$ |
$1$ |
$0.635$ |
\(\Q(\sqrt{-3}) \) |
$D_{3}$ |
\(\Q(\sqrt{-67}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$1$ |
|
\(q+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{9}-\zeta_{6}q^{16}+\zeta_{6}q^{17}+\cdots\) |
1273.1.bf.a |
$1273$ |
$1$ |
1273.bf |
1273.af |
$18$ |
$6$ |
$1$ |
$0.635$ |
\(\Q(\zeta_{18})\) |
$D_{9}$ |
\(\Q(\sqrt{-67}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$1$ |
|
\(q+\zeta_{18}^{4}q^{4}-\zeta_{18}^{7}q^{9}+\zeta_{18}^{8}q^{16}+\cdots\) |
1541.1.by.a |
$1541$ |
$1$ |
1541.by |
1541.ay |
$22$ |
$10$ |
$1$ |
$0.769$ |
\(\Q(\zeta_{22})\) |
$D_{11}$ |
\(\Q(\sqrt{-67}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$1$ |
|
\(q+\zeta_{22}^{6}q^{4}+\zeta_{22}^{4}q^{9}-\zeta_{22}q^{16}+\cdots\) |
1675.1.b.a |
$1675$ |
$1$ |
1675.b |
67.b |
$2$ |
$1$ |
$1$ |
$0.836$ |
\(\Q\) |
$D_{3}$ |
\(\Q(\sqrt{-67}) \) |
None |
✓ |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$1$ |
|
\(q+q^{4}+q^{9}+q^{16}-q^{17}-q^{19}+2q^{23}+\cdots\) |
1675.1.b.b |
$1675$ |
$1$ |
1675.b |
67.b |
$2$ |
$1$ |
$1$ |
$0.836$ |
\(\Q\) |
$D_{3}$ |
\(\Q(\sqrt{-67}) \) |
None |
✓ |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$1$ |
|
\(q+q^{4}+q^{9}+q^{16}+q^{17}-q^{19}-2q^{23}+\cdots\) |
1675.1.d.a |
$1675$ |
$1$ |
1675.d |
335.d |
$2$ |
$2$ |
$2$ |
$0.836$ |
\(\Q(\sqrt{-1}) \) |
$D_{3}$ |
\(\Q(\sqrt{-67}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$1$ |
|
\(q-q^{4}-q^{9}+q^{16}-iq^{17}+q^{19}+\cdots\) |
1943.1.d.a |
$1943$ |
$1$ |
1943.d |
1943.d |
$2$ |
$1$ |
$1$ |
$0.970$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-67}) \), \(\Q(\sqrt{-1943}) \) |
\(\Q(\sqrt{29}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$1$ |
|
\(q-q^{4}-q^{9}+q^{16}+2q^{23}+q^{25}+\cdots\) |
1943.1.o.a |
$1943$ |
$1$ |
1943.o |
1943.o |
$14$ |
$6$ |
$1$ |
$0.970$ |
\(\Q(\zeta_{14})\) |
$D_{14}$ |
\(\Q(\sqrt{-67}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$1$ |
|
\(q+\zeta_{14}^{5}q^{4}-\zeta_{14}^{4}q^{9}-\zeta_{14}^{3}q^{16}+\cdots\) |
1943.1.q.a |
$1943$ |
$1$ |
1943.q |
1943.q |
$14$ |
$6$ |
$1$ |
$0.970$ |
\(\Q(\zeta_{14})\) |
$D_{7}$ |
\(\Q(\sqrt{-67}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$1$ |
|
\(q-\zeta_{14}^{3}q^{4}-\zeta_{14}q^{9}+\zeta_{14}^{6}q^{16}+\cdots\) |
2412.1.b.a |
$2412$ |
$1$ |
2412.b |
67.b |
$2$ |
$1$ |
$1$ |
$1.204$ |
\(\Q\) |
$D_{3}$ |
\(\Q(\sqrt{-67}) \) |
None |
✓ |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$1$ |
|
\(q+q^{17}-q^{19}+q^{23}+q^{25}+q^{29}+\cdots\) |
2412.1.b.b |
$2412$ |
$1$ |
2412.b |
67.b |
$2$ |
$2$ |
$2$ |
$1.204$ |
\(\Q(\sqrt{3}) \) |
$D_{6}$ |
\(\Q(\sqrt{-67}) \) |
None |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$1$ |
|
\(q-\beta q^{17}+q^{19}+\beta q^{23}+q^{25}+\beta q^{29}+\cdots\) |
2479.1.d.b |
$2479$ |
$1$ |
2479.d |
2479.d |
$2$ |
$1$ |
$1$ |
$1.237$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-67}) \), \(\Q(\sqrt{-2479}) \) |
\(\Q(\sqrt{37}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$1$ |
|
\(q-q^{4}+q^{9}+q^{16}-q^{25}-q^{36}+q^{37}+\cdots\) |
2479.1.n.a |
$2479$ |
$1$ |
2479.n |
2479.n |
$6$ |
$2$ |
$1$ |
$1.237$ |
\(\Q(\sqrt{-3}) \) |
$D_{6}$ |
\(\Q(\sqrt{-67}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$1$ |
|
\(q+\zeta_{6}q^{4}+\zeta_{6}^{2}q^{9}+\zeta_{6}^{2}q^{16}+(-1+\cdots)q^{19}+\cdots\) |
2479.1.t.a |
$2479$ |
$1$ |
2479.t |
2479.t |
$6$ |
$2$ |
$1$ |
$1.237$ |
\(\Q(\sqrt{-3}) \) |
$D_{3}$ |
\(\Q(\sqrt{-67}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$1$ |
|
\(q+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{9}-\zeta_{6}q^{16}-\zeta_{6}q^{17}+\cdots\) |
2479.1.bi.a |
$2479$ |
$1$ |
2479.bi |
2479.ai |
$18$ |
$6$ |
$1$ |
$1.237$ |
\(\Q(\zeta_{18})\) |
$D_{18}$ |
\(\Q(\sqrt{-67}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$1$ |
|
\(q-\zeta_{18}^{8}q^{4}-\zeta_{18}q^{9}-\zeta_{18}^{7}q^{16}+\cdots\) |
2479.1.bq.a |
$2479$ |
$1$ |
2479.bq |
2479.aq |
$18$ |
$6$ |
$1$ |
$1.237$ |
\(\Q(\zeta_{18})\) |
$D_{9}$ |
\(\Q(\sqrt{-67}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$1$ |
|
\(q-\zeta_{18}^{5}q^{4}+\zeta_{18}^{4}q^{9}-\zeta_{18}q^{16}+\cdots\) |
3149.1.q.a |
$3149$ |
$1$ |
3149.q |
3149.q |
$46$ |
$22$ |
$1$ |
$1.572$ |
\(\Q(\zeta_{46})\) |
$D_{23}$ |
\(\Q(\sqrt{-67}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$1$ |
|
\(q+\zeta_{46}^{6}q^{4}+\zeta_{46}^{22}q^{9}+\zeta_{46}^{12}q^{16}+\cdots\) |
3283.1.b.a |
$3283$ |
$1$ |
3283.b |
67.b |
$2$ |
$1$ |
$1$ |
$1.638$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-67}) \) |
\(\Q(\sqrt{469}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$1$ |
|
\(q+q^{4}+q^{9}+q^{16}-2q^{23}+q^{25}+\cdots\) |
3283.1.b.c |
$3283$ |
$1$ |
3283.b |
67.b |
$2$ |
$2$ |
$2$ |
$1.638$ |
\(\Q(\sqrt{2}) \) |
$D_{4}$ |
\(\Q(\sqrt{-67}) \) |
None |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$1$ |
|
\(q+q^{4}+q^{9}+q^{16}-\beta q^{17}+\beta q^{19}+\cdots\) |
3283.1.r.b |
$3283$ |
$1$ |
3283.r |
469.r |
$6$ |
$2$ |
$1$ |
$1.638$ |
\(\Q(\sqrt{-3}) \) |
$D_{2}$ |
\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-67}) \) |
\(\Q(\sqrt{469}) \) |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$1$ |
|
\(q-\zeta_{6}q^{4}+\zeta_{6}^{2}q^{9}+\zeta_{6}^{2}q^{16}-\zeta_{6}^{2}q^{23}+\cdots\) |
3283.1.r.d |
$3283$ |
$1$ |
3283.r |
469.r |
$6$ |
$4$ |
$2$ |
$1.638$ |
\(\Q(\sqrt{2}, \sqrt{-3})\) |
$D_{4}$ |
\(\Q(\sqrt{-67}) \) |
None |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$1$ |
|
\(q+\beta _{2}q^{4}+(-1-\beta _{2})q^{9}+(-1-\beta _{2}+\cdots)q^{16}+\cdots\) |
67.3.b.a |
$67$ |
$3$ |
67.b |
67.b |
$2$ |
$1$ |
$1$ |
$1.826$ |
\(\Q\) |
$_{}$ |
\(\Q(\sqrt{-67}) \) |
None |
✓ |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$1$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q+4q^{4}+9q^{9}+2^{4}q^{16}-33q^{17}+\cdots\) |
3953.1.q.a |
$3953$ |
$1$ |
3953.q |
3953.q |
$58$ |
$28$ |
$1$ |
$1.973$ |
\(\Q(\zeta_{58})\) |
$D_{29}$ |
\(\Q(\sqrt{-67}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$1$ |
|
\(q-\zeta_{58}^{19}q^{4}+\zeta_{58}^{22}q^{9}-\zeta_{58}^{9}q^{16}+\cdots\) |
603.2.d.a |
$603$ |
$2$ |
603.d |
201.d |
$2$ |
$4$ |
$4$ |
$4.815$ |
\(\Q(\sqrt{-2}, \sqrt{67})\) |
$_{}$ |
\(\Q(\sqrt{-67}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$3$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q-2q^{4}+4q^{16}+\beta _{1}q^{17}+\beta _{3}q^{19}+\cdots\) |
67.5.b.a |
$67$ |
$5$ |
67.b |
67.b |
$2$ |
$1$ |
$1$ |
$6.926$ |
\(\Q\) |
$_{}$ |
\(\Q(\sqrt{-67}) \) |
None |
✓ |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$1$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q+2^{4}q^{4}+3^{4}q^{9}+2^{8}q^{16}+511q^{17}+\cdots\) |
268.3.b.a |
$268$ |
$3$ |
268.b |
67.b |
$2$ |
$2$ |
$2$ |
$7.302$ |
\(\Q(\sqrt{201}) \) |
$_{}$ |
\(\Q(\sqrt{-67}) \) |
None |
✓ |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$1$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q+9q^{9}+(17-\beta )q^{17}+(13+3\beta )q^{19}+\cdots\) |
1072.2.g.a |
$1072$ |
$2$ |
1072.g |
268.d |
$2$ |
$2$ |
$2$ |
$8.560$ |
\(\Q(\sqrt{-67}) \) |
$_{}$ |
\(\Q(\sqrt{-67}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$2$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q-3q^{9}-q^{17}-\beta q^{19}-\beta q^{23}+5q^{25}+\cdots\) |
1072.2.g.c |
$1072$ |
$2$ |
1072.g |
268.d |
$2$ |
$4$ |
$4$ |
$8.560$ |
\(\Q(\sqrt{-3}, \sqrt{-67})\) |
$_{}$ |
\(\Q(\sqrt{-67}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$2^{2}$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q-3q^{9}+(1-\beta _{2})q^{17}+(-2\beta _{1}-\beta _{3})q^{19}+\cdots\) |
67.7.b.a |
$67$ |
$7$ |
67.b |
67.b |
$2$ |
$1$ |
$1$ |
$15.414$ |
\(\Q\) |
$_{}$ |
\(\Q(\sqrt{-67}) \) |
None |
✓ |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$1$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q+2^{6}q^{4}+3^{6}q^{9}+2^{12}q^{16}-7326q^{17}+\cdots\) |
603.3.b.a |
$603$ |
$3$ |
603.b |
67.b |
$2$ |
$1$ |
$1$ |
$16.431$ |
\(\Q\) |
$_{}$ |
\(\Q(\sqrt{-67}) \) |
None |
✓ |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$1$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q+4q^{4}+2^{4}q^{16}+33q^{17}-29q^{19}+\cdots\) |
603.3.b.b |
$603$ |
$3$ |
603.b |
67.b |
$2$ |
$2$ |
$2$ |
$16.431$ |
\(\Q(\sqrt{67}) \) |
$_{}$ |
\(\Q(\sqrt{-67}) \) |
None |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$1$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q+4q^{4}+2^{4}q^{16}+\beta q^{17}+29q^{19}+\cdots\) |
2412.2.g.a |
$2412$ |
$2$ |
2412.g |
201.d |
$2$ |
$8$ |
$8$ |
$19.260$ |
8.0.\(\cdots\).23 |
$_{}$ |
\(\Q(\sqrt{-67}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$2\cdot 3^{4}$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q-\beta _{3}q^{17}+\beta _{1}q^{19}+\beta _{5}q^{23}-5q^{25}+\cdots\) |
67.9.b.a |
$67$ |
$9$ |
67.b |
67.b |
$2$ |
$1$ |
$1$ |
$27.294$ |
\(\Q\) |
$_{}$ |
\(\Q(\sqrt{-67}) \) |
None |
✓ |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$1$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q+2^{8}q^{4}+3^{8}q^{9}+2^{16}q^{16}+94079q^{17}+\cdots\) |
268.5.b.a |
$268$ |
$5$ |
268.b |
67.b |
$2$ |
$2$ |
$2$ |
$27.703$ |
\(\Q(\sqrt{201}) \) |
$_{}$ |
\(\Q(\sqrt{-67}) \) |
None |
✓ |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$3$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q+3^{4}q^{9}+(-250+11\beta )q^{17}+(-74+\cdots)q^{19}+\cdots\) |
1072.3.b.a |
$1072$ |
$3$ |
1072.b |
67.b |
$2$ |
$1$ |
$1$ |
$29.210$ |
\(\Q\) |
$_{}$ |
\(\Q(\sqrt{-67}) \) |
None |
✓ |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$1$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q+9q^{9}-33q^{17}+29q^{19}+21q^{23}+\cdots\) |
1072.3.b.b |
$1072$ |
$3$ |
1072.b |
67.b |
$2$ |
$2$ |
$2$ |
$29.210$ |
\(\Q(\sqrt{201}) \) |
$_{}$ |
\(\Q(\sqrt{-67}) \) |
None |
✓ |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$1$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q+9q^{9}+(2^{4}+\beta )q^{17}+(-2^{4}+3\beta )q^{19}+\cdots\) |
603.4.d.a |
$603$ |
$4$ |
603.d |
201.d |
$2$ |
$4$ |
$4$ |
$35.578$ |
\(\Q(\sqrt{-2}, \sqrt{67})\) |
$_{}$ |
\(\Q(\sqrt{-67}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$2\cdot 3^{2}$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q-8q^{4}+2^{6}q^{16}+(8\beta _{1}-\beta _{2})q^{17}+\cdots\) |
4489.2.a.b |
$4489$ |
$2$ |
4489.a |
1.a |
$1$ |
$1$ |
$1$ |
$35.845$ |
\(\Q\) |
$_{}$ |
\(\Q(\sqrt{-67}) \) |
None |
✓ |
$2$ |
$1$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$+$ |
$1$ |
$N(\mathrm{U}(1))$ |
\(q-2q^{4}-3q^{9}+4q^{16}-q^{17}+3q^{19}+\cdots\) |
67.11.b.a |
$67$ |
$11$ |
67.b |
67.b |
$2$ |
$1$ |
$1$ |
$42.569$ |
\(\Q\) |
$_{}$ |
\(\Q(\sqrt{-67}) \) |
None |
✓ |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$1$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q+2^{10}q^{4}+3^{10}q^{9}+2^{20}q^{16}-987393q^{17}+\cdots\) |
67.13.b.a |
$67$ |
$13$ |
67.b |
67.b |
$2$ |
$1$ |
$1$ |
$61.238$ |
\(\Q\) |
$_{}$ |
\(\Q(\sqrt{-67}) \) |
None |
✓ |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$1$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q+2^{12}q^{4}+3^{12}q^{9}+2^{24}q^{16}+5395138q^{17}+\cdots\) |
268.7.b.a |
$268$ |
$7$ |
268.b |
67.b |
$2$ |
$2$ |
$2$ |
$61.654$ |
\(\Q(\sqrt{201}) \) |
$_{}$ |
\(\Q(\sqrt{-67}) \) |
None |
✓ |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$2^{3}\cdot 5$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q+3^{6}q^{9}+(3663-20\beta )q^{17}+(-3509+\cdots)q^{19}+\cdots\) |
2412.3.b.a |
$2412$ |
$3$ |
2412.b |
67.b |
$2$ |
$2$ |
$2$ |
$65.722$ |
\(\Q(\sqrt{201}) \) |
$_{}$ |
\(\Q(\sqrt{-67}) \) |
None |
✓ |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$1$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q+(-17+\beta )q^{17}+(13+3\beta )q^{19}+(-13+\cdots)q^{23}+\cdots\) |
2412.3.b.c |
$2412$ |
$3$ |
2412.b |
67.b |
$2$ |
$4$ |
$4$ |
$65.722$ |
\(\Q(\sqrt{3}, \sqrt{67})\) |
$_{}$ |
\(\Q(\sqrt{-67}) \) |
None |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$2^{3}\cdot 3^{2}$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q+(\beta _{1}+2\beta _{2})q^{17}+(-15-\beta _{3})q^{19}+\cdots\) |
67.15.b.a |
$67$ |
$15$ |
67.b |
67.b |
$2$ |
$1$ |
$1$ |
$83.300$ |
\(\Q\) |
$_{}$ |
\(\Q(\sqrt{-67}) \) |
None |
✓ |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
$1$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q+2^{14}q^{4}+3^{14}q^{9}+2^{28}q^{16}+107317023q^{17}+\cdots\) |