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 |
$a_{2}$ |
$a_{3}$ |
$a_{5}$ |
$a_{7}$ |
882.4.g.a |
$882$ |
$4$ |
882.g |
7.c |
$3$ |
$2$ |
$1$ |
$52.040$ |
\(\Q(\sqrt{-3}) \) |
None |
|
$2$ |
$0$ |
\(-2\) |
\(0\) |
\(-22\) |
\(0\) |
$1$ |
$\mathrm{SU}(2)[C_{3}]$ |
\(q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}-22\zeta_{6}q^{5}+\cdots\) |
882.4.g.b |
$882$ |
$4$ |
882.g |
7.c |
$3$ |
$2$ |
$1$ |
$52.040$ |
\(\Q(\sqrt{-3}) \) |
None |
|
$2$ |
$0$ |
\(-2\) |
\(0\) |
\(-14\) |
\(0\) |
$1$ |
$\mathrm{SU}(2)[C_{3}]$ |
\(q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}-14\zeta_{6}q^{5}+\cdots\) |
882.4.g.c |
$882$ |
$4$ |
882.g |
7.c |
$3$ |
$2$ |
$1$ |
$52.040$ |
\(\Q(\sqrt{-3}) \) |
None |
|
$2$ |
$0$ |
\(-2\) |
\(0\) |
\(-8\) |
\(0\) |
$1$ |
$\mathrm{SU}(2)[C_{3}]$ |
\(q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}-8\zeta_{6}q^{5}+\cdots\) |
882.4.g.d |
$882$ |
$4$ |
882.g |
7.c |
$3$ |
$2$ |
$1$ |
$52.040$ |
\(\Q(\sqrt{-3}) \) |
None |
|
$2$ |
$0$ |
\(-2\) |
\(0\) |
\(-7\) |
\(0\) |
$1$ |
$\mathrm{SU}(2)[C_{3}]$ |
\(q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}-7\zeta_{6}q^{5}+\cdots\) |
882.4.g.e |
$882$ |
$4$ |
882.g |
7.c |
$3$ |
$2$ |
$1$ |
$52.040$ |
\(\Q(\sqrt{-3}) \) |
None |
|
$2$ |
$0$ |
\(-2\) |
\(0\) |
\(-6\) |
\(0\) |
$1$ |
$\mathrm{SU}(2)[C_{3}]$ |
\(q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}-6\zeta_{6}q^{5}+\cdots\) |
882.4.g.f |
$882$ |
$4$ |
882.g |
7.c |
$3$ |
$2$ |
$1$ |
$52.040$ |
\(\Q(\sqrt{-3}) \) |
None |
|
$2$ |
$0$ |
\(-2\) |
\(0\) |
\(-6\) |
\(0\) |
$1$ |
$\mathrm{SU}(2)[C_{3}]$ |
\(q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}-6\zeta_{6}q^{5}+\cdots\) |
882.4.g.g |
$882$ |
$4$ |
882.g |
7.c |
$3$ |
$2$ |
$1$ |
$52.040$ |
\(\Q(\sqrt{-3}) \) |
None |
|
$2$ |
$0$ |
\(-2\) |
\(0\) |
\(6\) |
\(0\) |
$1$ |
$\mathrm{SU}(2)[C_{3}]$ |
\(q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+6\zeta_{6}q^{5}+\cdots\) |
882.4.g.h |
$882$ |
$4$ |
882.g |
7.c |
$3$ |
$2$ |
$1$ |
$52.040$ |
\(\Q(\sqrt{-3}) \) |
None |
|
$2$ |
$0$ |
\(-2\) |
\(0\) |
\(6\) |
\(0\) |
$1$ |
$\mathrm{SU}(2)[C_{3}]$ |
\(q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+6\zeta_{6}q^{5}+\cdots\) |
882.4.g.i |
$882$ |
$4$ |
882.g |
7.c |
$3$ |
$2$ |
$1$ |
$52.040$ |
\(\Q(\sqrt{-3}) \) |
None |
|
$2$ |
$0$ |
\(-2\) |
\(0\) |
\(6\) |
\(0\) |
$1$ |
$\mathrm{SU}(2)[C_{3}]$ |
\(q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+6\zeta_{6}q^{5}+\cdots\) |
882.4.g.j |
$882$ |
$4$ |
882.g |
7.c |
$3$ |
$2$ |
$1$ |
$52.040$ |
\(\Q(\sqrt{-3}) \) |
None |
|
$2$ |
$0$ |
\(-2\) |
\(0\) |
\(8\) |
\(0\) |
$1$ |
$\mathrm{SU}(2)[C_{3}]$ |
\(q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+8\zeta_{6}q^{5}+\cdots\) |
882.4.g.k |
$882$ |
$4$ |
882.g |
7.c |
$3$ |
$2$ |
$1$ |
$52.040$ |
\(\Q(\sqrt{-3}) \) |
None |
|
$2$ |
$0$ |
\(-2\) |
\(0\) |
\(14\) |
\(0\) |
$1$ |
$\mathrm{SU}(2)[C_{3}]$ |
\(q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+14\zeta_{6}q^{5}+\cdots\) |
882.4.g.l |
$882$ |
$4$ |
882.g |
7.c |
$3$ |
$2$ |
$1$ |
$52.040$ |
\(\Q(\sqrt{-3}) \) |
None |
|
$2$ |
$0$ |
\(-2\) |
\(0\) |
\(15\) |
\(0\) |
$1$ |
$\mathrm{SU}(2)[C_{3}]$ |
\(q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+15\zeta_{6}q^{5}+\cdots\) |
882.4.g.m |
$882$ |
$4$ |
882.g |
7.c |
$3$ |
$2$ |
$1$ |
$52.040$ |
\(\Q(\sqrt{-3}) \) |
None |
|
$2$ |
$0$ |
\(-2\) |
\(0\) |
\(22\) |
\(0\) |
$1$ |
$\mathrm{SU}(2)[C_{3}]$ |
\(q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+22\zeta_{6}q^{5}+\cdots\) |
882.4.g.n |
$882$ |
$4$ |
882.g |
7.c |
$3$ |
$2$ |
$1$ |
$52.040$ |
\(\Q(\sqrt{-3}) \) |
None |
|
$2$ |
$0$ |
\(2\) |
\(0\) |
\(-22\) |
\(0\) |
$1$ |
$\mathrm{SU}(2)[C_{3}]$ |
\(q+2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}-22\zeta_{6}q^{5}+\cdots\) |
882.4.g.o |
$882$ |
$4$ |
882.g |
7.c |
$3$ |
$2$ |
$1$ |
$52.040$ |
\(\Q(\sqrt{-3}) \) |
None |
|
$2$ |
$0$ |
\(2\) |
\(0\) |
\(-18\) |
\(0\) |
$1$ |
$\mathrm{SU}(2)[C_{3}]$ |
\(q+2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}-18\zeta_{6}q^{5}+\cdots\) |
882.4.g.p |
$882$ |
$4$ |
882.g |
7.c |
$3$ |
$2$ |
$1$ |
$52.040$ |
\(\Q(\sqrt{-3}) \) |
None |
|
$2$ |
$0$ |
\(2\) |
\(0\) |
\(-12\) |
\(0\) |
$1$ |
$\mathrm{SU}(2)[C_{3}]$ |
\(q+2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}-12\zeta_{6}q^{5}+\cdots\) |
882.4.g.q |
$882$ |
$4$ |
882.g |
7.c |
$3$ |
$2$ |
$1$ |
$52.040$ |
\(\Q(\sqrt{-3}) \) |
None |
|
$2$ |
$0$ |
\(2\) |
\(0\) |
\(-6\) |
\(0\) |
$1$ |
$\mathrm{SU}(2)[C_{3}]$ |
\(q+2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}-6\zeta_{6}q^{5}+\cdots\) |
882.4.g.r |
$882$ |
$4$ |
882.g |
7.c |
$3$ |
$2$ |
$1$ |
$52.040$ |
\(\Q(\sqrt{-3}) \) |
None |
|
$2$ |
$0$ |
\(2\) |
\(0\) |
\(-2\) |
\(0\) |
$1$ |
$\mathrm{SU}(2)[C_{3}]$ |
\(q+2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}-2\zeta_{6}q^{5}+\cdots\) |
882.4.g.s |
$882$ |
$4$ |
882.g |
7.c |
$3$ |
$2$ |
$1$ |
$52.040$ |
\(\Q(\sqrt{-3}) \) |
None |
|
$2$ |
$1$ |
\(2\) |
\(0\) |
\(2\) |
\(0\) |
$1$ |
$\mathrm{SU}(2)[C_{3}]$ |
\(q+2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+2\zeta_{6}q^{5}+\cdots\) |
882.4.g.t |
$882$ |
$4$ |
882.g |
7.c |
$3$ |
$2$ |
$1$ |
$52.040$ |
\(\Q(\sqrt{-3}) \) |
None |
|
$2$ |
$0$ |
\(2\) |
\(0\) |
\(6\) |
\(0\) |
$1$ |
$\mathrm{SU}(2)[C_{3}]$ |
\(q+2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+6\zeta_{6}q^{5}+\cdots\) |
882.4.g.u |
$882$ |
$4$ |
882.g |
7.c |
$3$ |
$2$ |
$1$ |
$52.040$ |
\(\Q(\sqrt{-3}) \) |
None |
|
$2$ |
$0$ |
\(2\) |
\(0\) |
\(9\) |
\(0\) |
$1$ |
$\mathrm{SU}(2)[C_{3}]$ |
\(q+2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+9\zeta_{6}q^{5}+\cdots\) |
882.4.g.v |
$882$ |
$4$ |
882.g |
7.c |
$3$ |
$2$ |
$1$ |
$52.040$ |
\(\Q(\sqrt{-3}) \) |
None |
|
$2$ |
$0$ |
\(2\) |
\(0\) |
\(12\) |
\(0\) |
$1$ |
$\mathrm{SU}(2)[C_{3}]$ |
\(q+2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+12\zeta_{6}q^{5}+\cdots\) |
882.4.g.w |
$882$ |
$4$ |
882.g |
7.c |
$3$ |
$2$ |
$1$ |
$52.040$ |
\(\Q(\sqrt{-3}) \) |
None |
|
$2$ |
$0$ |
\(2\) |
\(0\) |
\(18\) |
\(0\) |
$1$ |
$\mathrm{SU}(2)[C_{3}]$ |
\(q+2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+18\zeta_{6}q^{5}+\cdots\) |
882.4.g.x |
$882$ |
$4$ |
882.g |
7.c |
$3$ |
$2$ |
$1$ |
$52.040$ |
\(\Q(\sqrt{-3}) \) |
None |
|
$2$ |
$0$ |
\(2\) |
\(0\) |
\(22\) |
\(0\) |
$1$ |
$\mathrm{SU}(2)[C_{3}]$ |
\(q+2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+22\zeta_{6}q^{5}+\cdots\) |
882.4.g.y |
$882$ |
$4$ |
882.g |
7.c |
$3$ |
$4$ |
$2$ |
$52.040$ |
\(\Q(\sqrt{2}, \sqrt{-3})\) |
None |
|
$2$ |
$0$ |
\(-4\) |
\(0\) |
\(-12\) |
\(0\) |
$7^{2}$ |
$\mathrm{SU}(2)[C_{3}]$ |
\(q+(-2-2\beta _{2})q^{2}+4\beta _{2}q^{4}+(-6-\beta _{1}+\cdots)q^{5}+\cdots\) |
882.4.g.z |
$882$ |
$4$ |
882.g |
7.c |
$3$ |
$4$ |
$2$ |
$52.040$ |
\(\Q(\sqrt{-3}, \sqrt{193})\) |
None |
|
$2$ |
$0$ |
\(-4\) |
\(0\) |
\(-7\) |
\(0\) |
$1$ |
$\mathrm{SU}(2)[C_{3}]$ |
\(q-2\beta _{2}q^{2}+(-4+4\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\) |
882.4.g.ba |
$882$ |
$4$ |
882.g |
7.c |
$3$ |
$4$ |
$2$ |
$52.040$ |
\(\Q(\sqrt{2}, \sqrt{-3})\) |
None |
|
$4$ |
$0$ |
\(-4\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
$\mathrm{SU}(2)[C_{3}]$ |
\(q+(-2-2\beta _{2})q^{2}+4\beta _{2}q^{4}+14\beta _{1}q^{5}+\cdots\) |
882.4.g.bb |
$882$ |
$4$ |
882.g |
7.c |
$3$ |
$4$ |
$2$ |
$52.040$ |
\(\Q(\sqrt{-3}, \sqrt{58})\) |
None |
|
$4$ |
$0$ |
\(-4\) |
\(0\) |
\(0\) |
\(0\) |
$2^{2}$ |
$\mathrm{SU}(2)[C_{3}]$ |
\(q+(-2-2\beta _{2})q^{2}+4\beta _{2}q^{4}+\beta _{1}q^{5}+\cdots\) |
882.4.g.bc |
$882$ |
$4$ |
882.g |
7.c |
$3$ |
$4$ |
$2$ |
$52.040$ |
\(\Q(\sqrt{2}, \sqrt{-3})\) |
None |
|
$4$ |
$0$ |
\(-4\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
$\mathrm{SU}(2)[C_{3}]$ |
\(q+(-2-2\beta _{2})q^{2}+4\beta _{2}q^{4}+5\beta _{1}q^{5}+\cdots\) |
882.4.g.bd |
$882$ |
$4$ |
882.g |
7.c |
$3$ |
$4$ |
$2$ |
$52.040$ |
\(\Q(\sqrt{2}, \sqrt{-3})\) |
None |
|
$2$ |
$0$ |
\(-4\) |
\(0\) |
\(12\) |
\(0\) |
$7^{2}$ |
$\mathrm{SU}(2)[C_{3}]$ |
\(q+(-2-2\beta _{2})q^{2}+4\beta _{2}q^{4}+(6+\beta _{1}+\cdots)q^{5}+\cdots\) |
882.4.g.be |
$882$ |
$4$ |
882.g |
7.c |
$3$ |
$4$ |
$2$ |
$52.040$ |
\(\Q(\sqrt{2}, \sqrt{-3})\) |
None |
|
$2$ |
$0$ |
\(4\) |
\(0\) |
\(-12\) |
\(0\) |
$1$ |
$\mathrm{SU}(2)[C_{3}]$ |
\(q-2\beta _{2}q^{2}+(-4-4\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\) |
882.4.g.bf |
$882$ |
$4$ |
882.g |
7.c |
$3$ |
$4$ |
$2$ |
$52.040$ |
\(\Q(\sqrt{-3}, \sqrt{1345})\) |
None |
|
$2$ |
$0$ |
\(4\) |
\(0\) |
\(-5\) |
\(0\) |
$1$ |
$\mathrm{SU}(2)[C_{3}]$ |
\(q+2\beta _{2}q^{2}+(-4+4\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\) |
882.4.g.bg |
$882$ |
$4$ |
882.g |
7.c |
$3$ |
$4$ |
$2$ |
$52.040$ |
\(\Q(\sqrt{2}, \sqrt{-3})\) |
None |
|
$4$ |
$0$ |
\(4\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
$\mathrm{SU}(2)[C_{3}]$ |
\(q+(2+2\beta _{2})q^{2}+4\beta _{2}q^{4}+5\beta _{1}q^{5}+\cdots\) |
882.4.g.bh |
$882$ |
$4$ |
882.g |
7.c |
$3$ |
$4$ |
$2$ |
$52.040$ |
\(\Q(\sqrt{-3}, \sqrt{58})\) |
None |
|
$4$ |
$0$ |
\(4\) |
\(0\) |
\(0\) |
\(0\) |
$2^{2}$ |
$\mathrm{SU}(2)[C_{3}]$ |
\(q+(2+2\beta _{2})q^{2}+4\beta _{2}q^{4}+\beta _{1}q^{5}-8q^{8}+\cdots\) |
882.4.g.bi |
$882$ |
$4$ |
882.g |
7.c |
$3$ |
$4$ |
$2$ |
$52.040$ |
\(\Q(\sqrt{-3}, \sqrt{22})\) |
None |
|
$4$ |
$0$ |
\(4\) |
\(0\) |
\(0\) |
\(0\) |
$2^{2}$ |
$\mathrm{SU}(2)[C_{3}]$ |
\(q+(2+2\beta _{2})q^{2}+4\beta _{2}q^{4}+\beta _{1}q^{5}-8q^{8}+\cdots\) |
882.4.g.bj |
$882$ |
$4$ |
882.g |
7.c |
$3$ |
$4$ |
$2$ |
$52.040$ |
\(\Q(\sqrt{-3}, \sqrt{193})\) |
None |
|
$2$ |
$0$ |
\(4\) |
\(0\) |
\(7\) |
\(0\) |
$1$ |
$\mathrm{SU}(2)[C_{3}]$ |
\(q+2\beta _{2}q^{2}+(-4+4\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\) |
882.4.g.bk |
$882$ |
$4$ |
882.g |
7.c |
$3$ |
$4$ |
$2$ |
$52.040$ |
\(\Q(\sqrt{2}, \sqrt{-3})\) |
None |
|
$2$ |
$0$ |
\(4\) |
\(0\) |
\(12\) |
\(0\) |
$1$ |
$\mathrm{SU}(2)[C_{3}]$ |
\(q-2\beta _{2}q^{2}+(-4-4\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\) |
\( S_{4}^{\mathrm{old}}(882, [\chi]) \cong \)
\(S_{4}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 12}\)\(\oplus\)
\(S_{4}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 6}\)\(\oplus\)
\(S_{4}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 8}\)\(\oplus\)
\(S_{4}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 4}\)\(\oplus\)
\(S_{4}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 6}\)\(\oplus\)
\(S_{4}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 4}\)\(\oplus\)
\(S_{4}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 3}\)\(\oplus\)
\(S_{4}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 2}\)\(\oplus\)
\(S_{4}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 4}\)\(\oplus\)
\(S_{4}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 2}\)\(\oplus\)
\(S_{4}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 2}\)