Label |
Level |
Weight |
Char |
Prim |
Char order |
Dim |
Rel. Dim |
$A$ |
Field |
CM |
Self-dual |
Inner twists |
Rank* |
Traces |
Coefficient ring index |
Sato-Tate |
$q$-expansion |
$a_{2}$ |
$a_{3}$ |
$a_{5}$ |
$a_{7}$ |
3600.3.e.a |
$3600$ |
$3$ |
3600.e |
4.b |
$2$ |
$1$ |
$1$ |
$98.093$ |
\(\Q\) |
\(\Q(\sqrt{-1}) \) |
✓ |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q-24q^{13}-30q^{17}+40q^{29}-24q^{37}+\cdots\) |
3600.3.e.b |
$3600$ |
$3$ |
3600.e |
4.b |
$2$ |
$1$ |
$1$ |
$98.093$ |
\(\Q\) |
\(\Q(\sqrt{-1}) \) |
✓ |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q-24q^{13}+30q^{17}-40q^{29}-24q^{37}+\cdots\) |
3600.3.e.c |
$3600$ |
$3$ |
3600.e |
4.b |
$2$ |
$1$ |
$1$ |
$98.093$ |
\(\Q\) |
\(\Q(\sqrt{-1}) \) |
✓ |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q-10q^{13}-30q^{17}-42q^{29}+70q^{37}+\cdots\) |
3600.3.e.d |
$3600$ |
$3$ |
3600.e |
4.b |
$2$ |
$1$ |
$1$ |
$98.093$ |
\(\Q\) |
\(\Q(\sqrt{-1}) \) |
✓ |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q+24q^{13}-30q^{17}-40q^{29}+24q^{37}+\cdots\) |
3600.3.e.e |
$3600$ |
$3$ |
3600.e |
4.b |
$2$ |
$1$ |
$1$ |
$98.093$ |
\(\Q\) |
\(\Q(\sqrt{-1}) \) |
✓ |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q+24q^{13}+30q^{17}+40q^{29}+24q^{37}+\cdots\) |
3600.3.e.f |
$3600$ |
$3$ |
3600.e |
4.b |
$2$ |
$2$ |
$2$ |
$98.093$ |
\(\Q(\sqrt{-3}) \) |
None |
|
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2^{3}$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q-\zeta_{6}q^{7}+2\zeta_{6}q^{11}-24q^{13}-24q^{17}+\cdots\) |
3600.3.e.g |
$3600$ |
$3$ |
3600.e |
4.b |
$2$ |
$2$ |
$2$ |
$98.093$ |
\(\Q(\sqrt{-3}) \) |
\(\Q(\sqrt{-3}) \) |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q-3\zeta_{6}q^{7}-23q^{13}-21\zeta_{6}q^{19}-11\zeta_{6}q^{31}+\cdots\) |
3600.3.e.h |
$3600$ |
$3$ |
3600.e |
4.b |
$2$ |
$2$ |
$2$ |
$98.093$ |
\(\Q(\sqrt{-3}) \) |
\(\Q(\sqrt{-3}) \) |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2^{4}$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q-\zeta_{6}q^{7}-22q^{13}+2\zeta_{6}q^{19}-3\zeta_{6}q^{31}+\cdots\) |
3600.3.e.i |
$3600$ |
$3$ |
3600.e |
4.b |
$2$ |
$2$ |
$2$ |
$98.093$ |
\(\Q(\sqrt{-15}) \) |
None |
|
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q-2\beta q^{7}-5\beta q^{11}-20q^{13}+15q^{17}+\cdots\) |
3600.3.e.j |
$3600$ |
$3$ |
3600.e |
4.b |
$2$ |
$2$ |
$2$ |
$98.093$ |
\(\Q(\sqrt{-3}) \) |
None |
|
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q-2\zeta_{6}q^{7}+7\zeta_{6}q^{11}-2^{4}q^{13}-3q^{17}+\cdots\) |
3600.3.e.k |
$3600$ |
$3$ |
3600.e |
4.b |
$2$ |
$2$ |
$2$ |
$98.093$ |
\(\Q(\sqrt{-3}) \) |
None |
|
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q-3\zeta_{6}q^{7}+2\zeta_{6}q^{11}-13q^{13}+18q^{17}+\cdots\) |
3600.3.e.l |
$3600$ |
$3$ |
3600.e |
4.b |
$2$ |
$2$ |
$2$ |
$98.093$ |
\(\Q(\sqrt{-3}) \) |
None |
|
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q-\zeta_{6}q^{7}-2\zeta_{6}q^{11}-11q^{13}-6q^{17}+\cdots\) |
3600.3.e.m |
$3600$ |
$3$ |
3600.e |
4.b |
$2$ |
$2$ |
$2$ |
$98.093$ |
\(\Q(\sqrt{-3}) \) |
None |
|
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2^{2}$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q-\zeta_{6}q^{7}+\zeta_{6}q^{11}-6q^{13}-18q^{17}+\cdots\) |
3600.3.e.n |
$3600$ |
$3$ |
3600.e |
4.b |
$2$ |
$2$ |
$2$ |
$98.093$ |
\(\Q(\sqrt{-3}) \) |
\(\Q(\sqrt{-3}) \) |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2\cdot 5$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q-\zeta_{6}q^{7}-q^{13}-\zeta_{6}q^{19}-7\zeta_{6}q^{31}+\cdots\) |
3600.3.e.o |
$3600$ |
$3$ |
3600.e |
4.b |
$2$ |
$2$ |
$2$ |
$98.093$ |
\(\Q(\sqrt{-5}) \) |
\(\Q(\sqrt{-5}) \) |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2\cdot 3$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q+\beta q^{7}+\beta q^{23}-22q^{29}+62q^{41}+\cdots\) |
3600.3.e.p |
$3600$ |
$3$ |
3600.e |
4.b |
$2$ |
$2$ |
$2$ |
$98.093$ |
\(\Q(\sqrt{-3}) \) |
\(\Q(\sqrt{-3}) \) |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2\cdot 5$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q-\zeta_{6}q^{7}+q^{13}+\zeta_{6}q^{19}+7\zeta_{6}q^{31}+\cdots\) |
3600.3.e.q |
$3600$ |
$3$ |
3600.e |
4.b |
$2$ |
$2$ |
$2$ |
$98.093$ |
\(\Q(\sqrt{-3}) \) |
None |
|
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2^{2}$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q-\zeta_{6}q^{7}-\zeta_{6}q^{11}+6q^{13}+18q^{17}+\cdots\) |
3600.3.e.r |
$3600$ |
$3$ |
3600.e |
4.b |
$2$ |
$2$ |
$2$ |
$98.093$ |
\(\Q(\sqrt{-3}) \) |
None |
|
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q-\zeta_{6}q^{7}+2\zeta_{6}q^{11}+11q^{13}+6q^{17}+\cdots\) |
3600.3.e.s |
$3600$ |
$3$ |
3600.e |
4.b |
$2$ |
$2$ |
$2$ |
$98.093$ |
\(\Q(\sqrt{-3}) \) |
None |
|
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q-3\zeta_{6}q^{7}-2\zeta_{6}q^{11}+13q^{13}-18q^{17}+\cdots\) |
3600.3.e.t |
$3600$ |
$3$ |
3600.e |
4.b |
$2$ |
$2$ |
$2$ |
$98.093$ |
\(\Q(\sqrt{-3}) \) |
None |
|
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2^{3}$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q-\zeta_{6}q^{7}+3\zeta_{6}q^{11}+14q^{13}-6q^{17}+\cdots\) |
3600.3.e.u |
$3600$ |
$3$ |
3600.e |
4.b |
$2$ |
$2$ |
$2$ |
$98.093$ |
\(\Q(\sqrt{-3}) \) |
None |
|
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q-2\zeta_{6}q^{7}-7\zeta_{6}q^{11}+2^{4}q^{13}+3q^{17}+\cdots\) |
3600.3.e.v |
$3600$ |
$3$ |
3600.e |
4.b |
$2$ |
$2$ |
$2$ |
$98.093$ |
\(\Q(\sqrt{-15}) \) |
None |
|
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q-2\beta q^{7}+5\beta q^{11}+20q^{13}-15q^{17}+\cdots\) |
3600.3.e.w |
$3600$ |
$3$ |
3600.e |
4.b |
$2$ |
$2$ |
$2$ |
$98.093$ |
\(\Q(\sqrt{-3}) \) |
\(\Q(\sqrt{-3}) \) |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q-3\zeta_{6}q^{7}+23q^{13}+21\zeta_{6}q^{19}+11\zeta_{6}q^{31}+\cdots\) |
3600.3.e.x |
$3600$ |
$3$ |
3600.e |
4.b |
$2$ |
$2$ |
$2$ |
$98.093$ |
\(\Q(\sqrt{-3}) \) |
None |
|
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2^{3}$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q-\zeta_{6}q^{7}-2\zeta_{6}q^{11}+24q^{13}+24q^{17}+\cdots\) |
3600.3.e.y |
$3600$ |
$3$ |
3600.e |
4.b |
$2$ |
$4$ |
$4$ |
$98.093$ |
\(\Q(\sqrt{-3}, \sqrt{-10})\) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2^{4}\cdot 3^{2}$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+3\beta _{2}q^{7}-\beta _{1}q^{11}-13q^{13}-\beta _{3}q^{17}+\cdots\) |
3600.3.e.z |
$3600$ |
$3$ |
3600.e |
4.b |
$2$ |
$4$ |
$4$ |
$98.093$ |
\(\Q(\sqrt{-3}, \sqrt{5})\) |
None |
|
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2^{8}\cdot 3$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+\beta _{1}q^{7}+\beta _{1}q^{11}+(-4-\beta _{3})q^{13}+\cdots\) |
3600.3.e.ba |
$3600$ |
$3$ |
3600.e |
4.b |
$2$ |
$4$ |
$4$ |
$98.093$ |
\(\Q(\sqrt{-3}, \sqrt{5})\) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2^{7}\cdot 3\cdot 5$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q-\beta _{1}q^{7}+\beta _{2}q^{11}-4q^{13}-\beta _{3}q^{17}+\cdots\) |
3600.3.e.bb |
$3600$ |
$3$ |
3600.e |
4.b |
$2$ |
$4$ |
$4$ |
$98.093$ |
\(\Q(\sqrt{-3}, \sqrt{5})\) |
None |
|
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2^{7}\cdot 3$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+\beta _{1}q^{7}+2\beta _{2}q^{11}+(-4+\beta _{3})q^{13}+\cdots\) |
3600.3.e.bc |
$3600$ |
$3$ |
3600.e |
4.b |
$2$ |
$4$ |
$4$ |
$98.093$ |
\(\Q(\sqrt{-3}, \sqrt{11})\) |
None |
|
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2^{4}\cdot 3$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+(\beta _{1}+\beta _{2})q^{7}+\beta _{1}q^{11}-q^{13}+(-12+\cdots)q^{17}+\cdots\) |
3600.3.e.bd |
$3600$ |
$3$ |
3600.e |
4.b |
$2$ |
$4$ |
$4$ |
$98.093$ |
\(\Q(\sqrt{-2}, \sqrt{-3})\) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2^{8}\cdot 3$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+\beta _{2}q^{7}+\beta _{3}q^{11}-\beta _{1}q^{13}+2\beta _{1}q^{17}+\cdots\) |
3600.3.e.be |
$3600$ |
$3$ |
3600.e |
4.b |
$2$ |
$4$ |
$4$ |
$98.093$ |
\(\Q(\sqrt{-3}, \sqrt{-7})\) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2^{7}\cdot 3$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+\beta _{2}q^{7}-\beta _{3}q^{11}-\beta _{1}q^{13}+\beta _{1}q^{17}+\cdots\) |
3600.3.e.bf |
$3600$ |
$3$ |
3600.e |
4.b |
$2$ |
$4$ |
$4$ |
$98.093$ |
\(\Q(\sqrt{-3}, \sqrt{11})\) |
None |
|
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2^{4}\cdot 3$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+(\beta _{1}+\beta _{2})q^{7}-\beta _{1}q^{11}+q^{13}+(12+\cdots)q^{17}+\cdots\) |
3600.3.e.bg |
$3600$ |
$3$ |
3600.e |
4.b |
$2$ |
$4$ |
$4$ |
$98.093$ |
\(\Q(\sqrt{-3}, \sqrt{5})\) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2^{7}\cdot 3$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+\beta _{1}q^{7}+\beta _{2}q^{11}+8q^{13}-\beta _{3}q^{17}+\cdots\) |
3600.3.e.bh |
$3600$ |
$3$ |
3600.e |
4.b |
$2$ |
$4$ |
$4$ |
$98.093$ |
\(\Q(\sqrt{-3}, \sqrt{5})\) |
None |
|
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2^{8}\cdot 3$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+\beta _{1}q^{7}+(\beta _{1}-\beta _{2})q^{11}+(8+\beta _{3})q^{13}+\cdots\) |
3600.3.e.bi |
$3600$ |
$3$ |
3600.e |
4.b |
$2$ |
$4$ |
$4$ |
$98.093$ |
\(\Q(\sqrt{-3}, \sqrt{-10})\) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2^{4}\cdot 3^{2}$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+3\beta _{2}q^{7}+\beta _{1}q^{11}+13q^{13}+\beta _{3}q^{17}+\cdots\) |
3600.3.e.bj |
$3600$ |
$3$ |
3600.e |
4.b |
$2$ |
$8$ |
$8$ |
$98.093$ |
8.0.3317760000.8 |
None |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2^{15}\cdot 3^{2}$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+\beta _{3}q^{7}+\beta _{1}q^{11}+\beta _{4}q^{13}+\beta _{2}q^{17}+\cdots\) |
\( S_{3}^{\mathrm{old}}(3600, [\chi]) \cong \)
\(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 18}\)\(\oplus\)
\(S_{3}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 9}\)\(\oplus\)
\(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 12}\)\(\oplus\)
\(S_{3}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 9}\)\(\oplus\)
\(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 6}\)\(\oplus\)
\(S_{3}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 12}\)\(\oplus\)
\(S_{3}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 6}\)\(\oplus\)
\(S_{3}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 8}\)\(\oplus\)
\(S_{3}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 3}\)\(\oplus\)
\(S_{3}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 6}\)\(\oplus\)
\(S_{3}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 4}\)\(\oplus\)
\(S_{3}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 6}\)\(\oplus\)
\(S_{3}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 4}\)\(\oplus\)
\(S_{3}^{\mathrm{new}}(600, [\chi])\)\(^{\oplus 4}\)\(\oplus\)
\(S_{3}^{\mathrm{new}}(720, [\chi])\)\(^{\oplus 2}\)\(\oplus\)
\(S_{3}^{\mathrm{new}}(900, [\chi])\)\(^{\oplus 3}\)\(\oplus\)
\(S_{3}^{\mathrm{new}}(1200, [\chi])\)\(^{\oplus 2}\)\(\oplus\)
\(S_{3}^{\mathrm{new}}(1800, [\chi])\)\(^{\oplus 2}\)