| 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 |
| $a_{2}$ |
$a_{3}$ |
$a_{5}$ |
$a_{7}$ |
| 259.1.b.a |
$259$ |
$1$ |
259.b |
259.b |
$2$ |
$1$ |
$1$ |
$0.129$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-259}) \) |
\(\Q(\sqrt{37}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(-1\) |
$1$ |
|
\(q+q^{4}-q^{7}+q^{9}-2q^{11}+q^{16}-q^{25}+\cdots\) |
| 1036.1.e.a |
$1036$ |
$1$ |
1036.e |
259.b |
$2$ |
$1$ |
$1$ |
$0.517$ |
\(\Q\) |
$D_{3}$ |
\(\Q(\sqrt{-259}) \) |
None |
✓ |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(-1\) |
\(1\) |
$1$ |
|
\(q-q^{5}+q^{7}+q^{9}-q^{11}-q^{13}+2q^{17}+\cdots\) |
| 1036.1.e.b |
$1036$ |
$1$ |
1036.e |
259.b |
$2$ |
$1$ |
$1$ |
$0.517$ |
\(\Q\) |
$D_{3}$ |
\(\Q(\sqrt{-259}) \) |
None |
✓ |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(1\) |
\(1\) |
$1$ |
|
\(q+q^{5}+q^{7}+q^{9}-q^{11}+q^{13}-2q^{17}+\cdots\) |
| 1036.1.e.c |
$1036$ |
$1$ |
1036.e |
259.b |
$2$ |
$2$ |
$2$ |
$0.517$ |
\(\Q(\sqrt{3}) \) |
$D_{6}$ |
\(\Q(\sqrt{-259}) \) |
None |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(-2\) |
$1$ |
|
\(q-\beta q^{5}-q^{7}+q^{9}+q^{11}+\beta q^{13}+\cdots\) |
| 1295.1.h.i |
$1295$ |
$1$ |
1295.h |
1295.h |
$2$ |
$4$ |
$4$ |
$0.646$ |
\(\Q(\zeta_{8})\) |
$D_{4}$ |
\(\Q(\sqrt{-259}) \) |
None |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-q^{4}-\zeta_{8}q^{5}-\zeta_{8}^{2}q^{7}-q^{9}+(\zeta_{8}+\cdots)q^{13}+\cdots\) |
| 1813.1.t.a |
$1813$ |
$1$ |
1813.t |
259.t |
$6$ |
$2$ |
$1$ |
$0.905$ |
\(\Q(\sqrt{-3}) \) |
$D_{2}$ |
\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-259}) \) |
\(\Q(\sqrt{37}) \) |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{9}-\zeta_{6}^{2}q^{11}-\zeta_{6}q^{16}+\cdots\) |
| 2331.1.e.a |
$2331$ |
$1$ |
2331.e |
259.b |
$2$ |
$1$ |
$1$ |
$1.163$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-111}) \), \(\Q(\sqrt{-259}) \) |
\(\Q(\sqrt{21}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(-2\) |
\(-1\) |
$1$ |
|
\(q+q^{4}-2q^{5}-q^{7}+q^{16}+2q^{17}+\cdots\) |
| 2331.1.e.b |
$2331$ |
$1$ |
2331.e |
259.b |
$2$ |
$1$ |
$1$ |
$1.163$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-259}) \) |
\(\Q(\sqrt{37}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(-1\) |
$1$ |
|
\(q+q^{4}-q^{7}+2q^{11}+q^{16}-q^{25}+\cdots\) |
| 2331.1.e.c |
$2331$ |
$1$ |
2331.e |
259.b |
$2$ |
$1$ |
$1$ |
$1.163$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-259}) \) |
\(\Q(\sqrt{777}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(1\) |
$1$ |
|
\(q+q^{4}+q^{7}-2q^{13}+q^{16}+2q^{19}+\cdots\) |
| 2331.1.e.d |
$2331$ |
$1$ |
2331.e |
259.b |
$2$ |
$1$ |
$1$ |
$1.163$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-259}) \) |
\(\Q(\sqrt{777}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(1\) |
$1$ |
|
\(q+q^{4}+q^{7}+2q^{13}+q^{16}-2q^{19}+\cdots\) |
| 2331.1.e.e |
$2331$ |
$1$ |
2331.e |
259.b |
$2$ |
$1$ |
$1$ |
$1.163$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-111}) \), \(\Q(\sqrt{-259}) \) |
\(\Q(\sqrt{21}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(2\) |
\(-1\) |
$1$ |
|
\(q+q^{4}+2q^{5}-q^{7}+q^{16}-2q^{17}+\cdots\) |
| 2849.1.cb.a |
$2849$ |
$1$ |
2849.cb |
2849.bb |
$10$ |
$4$ |
$1$ |
$1.422$ |
\(\Q(\zeta_{10})\) |
$D_{5}$ |
\(\Q(\sqrt{-259}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(-2\) |
\(-1\) |
$1$ |
|
\(q+\zeta_{10}^{2}q^{4}+(-\zeta_{10}+\zeta_{10}^{2})q^{5}+\zeta_{10}^{2}q^{7}+\cdots\) |
| 2849.1.cb.d |
$2849$ |
$1$ |
2849.cb |
2849.bb |
$10$ |
$4$ |
$1$ |
$1.422$ |
\(\Q(\zeta_{10})\) |
$D_{5}$ |
\(\Q(\sqrt{-259}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(2\) |
\(-1\) |
$1$ |
|
\(q+\zeta_{10}^{2}q^{4}+(\zeta_{10}-\zeta_{10}^{2})q^{5}+\zeta_{10}^{2}q^{7}+\cdots\) |
| 2849.1.cb.e |
$2849$ |
$1$ |
2849.cb |
2849.bb |
$10$ |
$8$ |
$2$ |
$1.422$ |
\(\Q(\zeta_{20})\) |
$D_{10}$ |
\(\Q(\sqrt{-259}) \) |
None |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(2\) |
$5$ |
|
\(q+\zeta_{20}^{4}q^{4}+(\zeta_{20}^{7}+\zeta_{20}^{9})q^{5}-\zeta_{20}^{4}q^{7}+\cdots\) |
| 3367.1.f.e |
$3367$ |
$1$ |
3367.f |
3367.f |
$2$ |
$4$ |
$4$ |
$1.680$ |
\(\Q(\zeta_{8})\) |
$D_{4}$ |
\(\Q(\sqrt{-259}) \) |
None |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-q^{4}+(-\zeta_{8}-\zeta_{8}^{3})q^{5}+\zeta_{8}^{2}q^{7}+\cdots\) |
| 3367.1.cm.a |
$3367$ |
$1$ |
3367.cm |
3367.bm |
$6$ |
$8$ |
$4$ |
$1.680$ |
\(\Q(\zeta_{24})\) |
$D_{12}$ |
\(\Q(\sqrt{-259}) \) |
None |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+\zeta_{24}^{4}q^{4}+(-\zeta_{24}^{3}-\zeta_{24}^{9})q^{5}+\cdots\) |
| 3367.1.dy.a |
$3367$ |
$1$ |
3367.dy |
3367.cy |
$6$ |
$2$ |
$1$ |
$1.680$ |
\(\Q(\sqrt{-3}) \) |
$D_{3}$ |
\(\Q(\sqrt{-259}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(-4\) |
\(-1\) |
$1$ |
|
\(q+\zeta_{6}^{2}q^{4}-q^{5}+\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}+\cdots\) |
| 3367.1.dy.b |
$3367$ |
$1$ |
3367.dy |
3367.cy |
$6$ |
$2$ |
$1$ |
$1.680$ |
\(\Q(\sqrt{-3}) \) |
$D_{3}$ |
\(\Q(\sqrt{-259}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(4\) |
\(-1\) |
$1$ |
|
\(q+\zeta_{6}^{2}q^{4}+q^{5}+\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}+\cdots\) |
| 3367.1.dy.c |
$3367$ |
$1$ |
3367.dy |
3367.cy |
$6$ |
$4$ |
$2$ |
$1.680$ |
\(\Q(\zeta_{12})\) |
$D_{6}$ |
\(\Q(\sqrt{-259}) \) |
None |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(2\) |
$1$ |
|
\(q-\zeta_{12}^{2}q^{4}+\zeta_{12}^{2}q^{7}-\zeta_{12}^{2}q^{9}+\cdots\) |
| 259.3.b.b |
$259$ |
$3$ |
259.b |
259.b |
$2$ |
$2$ |
$2$ |
$7.057$ |
\(\Q(\sqrt{37}) \) |
$_{}$ |
\(\Q(\sqrt{-259}) \) |
None |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(-14\) |
$2$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q+4q^{4}+\beta q^{5}-7q^{7}+9q^{9}+15q^{11}+\cdots\) |
| 259.3.b.c |
$259$ |
$3$ |
259.b |
259.b |
$2$ |
$2$ |
$2$ |
$7.057$ |
\(\Q(\sqrt{7}) \) |
$_{}$ |
\(\Q(\sqrt{-259}) \) |
None |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(14\) |
$1$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q+4q^{4}+3\beta q^{5}+7q^{7}+9q^{9}-15q^{11}+\cdots\) |
| 259.5.b.a |
$259$ |
$5$ |
259.b |
259.b |
$2$ |
$1$ |
$1$ |
$26.773$ |
\(\Q\) |
$_{}$ |
\(\Q(\sqrt{-259}) \) |
None |
✓ |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(-13\) |
\(49\) |
$1$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q+2^{4}q^{4}-13q^{5}+7^{2}q^{7}+3^{4}q^{9}+\cdots\) |
| 259.5.b.b |
$259$ |
$5$ |
259.b |
259.b |
$2$ |
$1$ |
$1$ |
$26.773$ |
\(\Q\) |
$_{}$ |
\(\Q(\sqrt{-259}) \) |
None |
✓ |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(13\) |
\(49\) |
$1$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q+2^{4}q^{4}+13q^{5}+7^{2}q^{7}+3^{4}q^{9}+\cdots\) |
| 259.5.b.d |
$259$ |
$5$ |
259.b |
259.b |
$2$ |
$2$ |
$2$ |
$26.773$ |
\(\Q(\sqrt{259}) \) |
$_{}$ |
\(\Q(\sqrt{-259}) \) |
None |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(-98\) |
$3$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q+2^{4}q^{4}-\beta q^{5}-7^{2}q^{7}+3^{4}q^{9}+17q^{11}+\cdots\) |
| 1036.3.e.a |
$1036$ |
$3$ |
1036.e |
259.b |
$2$ |
$4$ |
$4$ |
$28.229$ |
\(\Q(\sqrt{21}, \sqrt{37})\) |
$_{}$ |
\(\Q(\sqrt{-259}) \) |
None |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(-28\) |
$2^{3}$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q-\beta _{2}q^{5}-7q^{7}+9q^{9}+(-7+\beta _{3})q^{11}+\cdots\) |
| 1036.3.e.b |
$1036$ |
$3$ |
1036.e |
259.b |
$2$ |
$4$ |
$4$ |
$28.229$ |
\(\Q(\sqrt{7}, \sqrt{111})\) |
$_{}$ |
\(\Q(\sqrt{-259}) \) |
None |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(28\) |
$2^{2}$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q-\beta _{1}q^{5}+7q^{7}+9q^{9}+(7-\beta _{3})q^{11}+\cdots\) |
| 1036.5.e.a |
$1036$ |
$5$ |
1036.e |
259.b |
$2$ |
$2$ |
$2$ |
$107.091$ |
\(\Q(\sqrt{777}) \) |
$_{}$ |
\(\Q(\sqrt{-259}) \) |
None |
✓ |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(-13\) |
\(98\) |
$3$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q+(-6+\beta )q^{5}+7^{2}q^{7}+3^{4}q^{9}+(6+\cdots)q^{11}+\cdots\) |
| 1036.5.e.b |
$1036$ |
$5$ |
1036.e |
259.b |
$2$ |
$2$ |
$2$ |
$107.091$ |
\(\Q(\sqrt{777}) \) |
$_{}$ |
\(\Q(\sqrt{-259}) \) |
None |
✓ |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(13\) |
\(98\) |
$3$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q+(7+\beta )q^{5}+7^{2}q^{7}+3^{4}q^{9}+(11+5\beta )q^{11}+\cdots\) |
| 1036.5.e.c |
$1036$ |
$5$ |
1036.e |
259.b |
$2$ |
$4$ |
$4$ |
$107.091$ |
\(\Q(\sqrt{3}, \sqrt{259})\) |
$_{}$ |
\(\Q(\sqrt{-259}) \) |
None |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(-196\) |
$2^{3}\cdot 3^{2}$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q+(-\beta _{1}+\beta _{2})q^{5}-7^{2}q^{7}+3^{4}q^{9}+\cdots\) |
