Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(1764, [\chi])\).
|
Total |
New |
Old |
| Modular forms
| 2112 |
100 |
2012 |
| Cusp forms
| 1920 |
100 |
1820 |
| Eisenstein series
| 192 |
0 |
192 |
| Label |
Level |
Weight |
Char |
Prim |
Char order |
Dim |
Rel. Dim |
$A$ |
Field |
CM |
Self-dual |
Twist minimal |
Largest |
Maximal |
Minimal twist |
Inner twists |
Rank* |
Traces |
Coefficient ring index |
Sato-Tate |
$q$-expansion |
| $a_{2}$ |
$a_{3}$ |
$a_{5}$ |
$a_{7}$ |
| 1764.4.k.a |
$1764$ |
$4$ |
1764.k |
7.c |
$3$ |
$2$ |
$1$ |
$104.079$ |
\(\Q(\sqrt{-3}) \) |
None |
|
|
|
|
196.4.a.a |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(-20\) |
\(0\) |
$1$ |
$\mathrm{SU}(2)[C_{3}]$ |
\(q-20\zeta_{6}q^{5}+(44-44\zeta_{6})q^{11}-44q^{13}+\cdots\) |
| 1764.4.k.b |
$1764$ |
$4$ |
1764.k |
7.c |
$3$ |
$2$ |
$1$ |
$104.079$ |
\(\Q(\sqrt{-3}) \) |
None |
|
|
|
|
12.4.a.a |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(-18\) |
\(0\) |
$1$ |
$\mathrm{SU}(2)[C_{3}]$ |
\(q-18\zeta_{6}q^{5}+(6^{2}-6^{2}\zeta_{6})q^{11}-10q^{13}+\cdots\) |
| 1764.4.k.c |
$1764$ |
$4$ |
1764.k |
7.c |
$3$ |
$2$ |
$1$ |
$104.079$ |
\(\Q(\sqrt{-3}) \) |
None |
|
|
|
|
84.4.a.b |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(-14\) |
\(0\) |
$1$ |
$\mathrm{SU}(2)[C_{3}]$ |
\(q-14\zeta_{6}q^{5}+(4-4\zeta_{6})q^{11}-54q^{13}+\cdots\) |
| 1764.4.k.d |
$1764$ |
$4$ |
1764.k |
7.c |
$3$ |
$2$ |
$1$ |
$104.079$ |
\(\Q(\sqrt{-3}) \) |
None |
|
|
|
|
28.4.a.a |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(-8\) |
\(0\) |
$1$ |
$\mathrm{SU}(2)[C_{3}]$ |
\(q-8\zeta_{6}q^{5}+(-40+40\zeta_{6})q^{11}-12q^{13}+\cdots\) |
| 1764.4.k.e |
$1764$ |
$4$ |
1764.k |
7.c |
$3$ |
$2$ |
$1$ |
$104.079$ |
\(\Q(\sqrt{-3}) \) |
None |
|
|
|
|
28.4.a.b |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(-6\) |
\(0\) |
$1$ |
$\mathrm{SU}(2)[C_{3}]$ |
\(q-6\zeta_{6}q^{5}+(-12+12\zeta_{6})q^{11}+82q^{13}+\cdots\) |
| 1764.4.k.f |
$1764$ |
$4$ |
1764.k |
7.c |
$3$ |
$2$ |
$1$ |
$104.079$ |
\(\Q(\sqrt{-3}) \) |
None |
|
|
|
|
84.4.a.a |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(-6\) |
\(0\) |
$1$ |
$\mathrm{SU}(2)[C_{3}]$ |
\(q-6\zeta_{6}q^{5}+(6^{2}-6^{2}\zeta_{6})q^{11}-62q^{13}+\cdots\) |
| 1764.4.k.g |
$1764$ |
$4$ |
1764.k |
7.c |
$3$ |
$2$ |
$1$ |
$104.079$ |
\(\Q(\sqrt{-3}) \) |
None |
|
|
|
|
588.4.a.b |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(-4\) |
\(0\) |
$1$ |
$\mathrm{SU}(2)[C_{3}]$ |
\(q-4\zeta_{6}q^{5}+(-20+20\zeta_{6})q^{11}+4q^{13}+\cdots\) |
| 1764.4.k.h |
$1764$ |
$4$ |
1764.k |
7.c |
$3$ |
$2$ |
$1$ |
$104.079$ |
\(\Q(\sqrt{-3}) \) |
\(\Q(\sqrt{-3}) \) |
|
|
|
|
252.4.k.a |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
$\mathrm{U}(1)[D_{3}]$ |
\(q-89q^{13}-163\zeta_{6}q^{19}+(5^{3}-5^{3}\zeta_{6})q^{25}+\cdots\) |
| 1764.4.k.i |
$1764$ |
$4$ |
1764.k |
7.c |
$3$ |
$2$ |
$1$ |
$104.079$ |
\(\Q(\sqrt{-3}) \) |
\(\Q(\sqrt{-3}) \) |
|
|
|
|
252.4.k.b |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
$\mathrm{U}(1)[D_{3}]$ |
\(q+19q^{13}+107\zeta_{6}q^{19}+(5^{3}-5^{3}\zeta_{6})q^{25}+\cdots\) |
| 1764.4.k.j |
$1764$ |
$4$ |
1764.k |
7.c |
$3$ |
$2$ |
$1$ |
$104.079$ |
\(\Q(\sqrt{-3}) \) |
None |
|
|
|
|
588.4.a.b |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(4\) |
\(0\) |
$1$ |
$\mathrm{SU}(2)[C_{3}]$ |
\(q+4\zeta_{6}q^{5}+(-20+20\zeta_{6})q^{11}-4q^{13}+\cdots\) |
| 1764.4.k.k |
$1764$ |
$4$ |
1764.k |
7.c |
$3$ |
$2$ |
$1$ |
$104.079$ |
\(\Q(\sqrt{-3}) \) |
None |
|
|
|
|
28.4.a.b |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(6\) |
\(0\) |
$1$ |
$\mathrm{SU}(2)[C_{3}]$ |
\(q+6\zeta_{6}q^{5}+(-12+12\zeta_{6})q^{11}-82q^{13}+\cdots\) |
| 1764.4.k.l |
$1764$ |
$4$ |
1764.k |
7.c |
$3$ |
$2$ |
$1$ |
$104.079$ |
\(\Q(\sqrt{-3}) \) |
None |
|
|
|
|
84.4.a.a |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(6\) |
\(0\) |
$1$ |
$\mathrm{SU}(2)[C_{3}]$ |
\(q+6\zeta_{6}q^{5}+(6^{2}-6^{2}\zeta_{6})q^{11}+62q^{13}+\cdots\) |
| 1764.4.k.m |
$1764$ |
$4$ |
1764.k |
7.c |
$3$ |
$2$ |
$1$ |
$104.079$ |
\(\Q(\sqrt{-3}) \) |
None |
|
|
|
|
28.4.a.a |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(8\) |
\(0\) |
$1$ |
$\mathrm{SU}(2)[C_{3}]$ |
\(q+8\zeta_{6}q^{5}+(-40+40\zeta_{6})q^{11}+12q^{13}+\cdots\) |
| 1764.4.k.n |
$1764$ |
$4$ |
1764.k |
7.c |
$3$ |
$2$ |
$1$ |
$104.079$ |
\(\Q(\sqrt{-3}) \) |
None |
|
|
|
|
84.4.a.b |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(14\) |
\(0\) |
$1$ |
$\mathrm{SU}(2)[C_{3}]$ |
\(q+14\zeta_{6}q^{5}+(4-4\zeta_{6})q^{11}+54q^{13}+\cdots\) |
| 1764.4.k.o |
$1764$ |
$4$ |
1764.k |
7.c |
$3$ |
$2$ |
$1$ |
$104.079$ |
\(\Q(\sqrt{-3}) \) |
None |
|
|
|
|
12.4.a.a |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(18\) |
\(0\) |
$1$ |
$\mathrm{SU}(2)[C_{3}]$ |
\(q+18\zeta_{6}q^{5}+(6^{2}-6^{2}\zeta_{6})q^{11}+10q^{13}+\cdots\) |
| 1764.4.k.p |
$1764$ |
$4$ |
1764.k |
7.c |
$3$ |
$2$ |
$1$ |
$104.079$ |
\(\Q(\sqrt{-3}) \) |
None |
|
|
|
|
196.4.a.a |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(20\) |
\(0\) |
$1$ |
$\mathrm{SU}(2)[C_{3}]$ |
\(q+20\zeta_{6}q^{5}+(44-44\zeta_{6})q^{11}+44q^{13}+\cdots\) |
| 1764.4.k.q |
$1764$ |
$4$ |
1764.k |
7.c |
$3$ |
$4$ |
$2$ |
$104.079$ |
\(\Q(\sqrt{-3}, \sqrt{193})\) |
None |
|
|
|
|
84.4.i.a |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(-11\) |
\(0\) |
$1$ |
$\mathrm{SU}(2)[C_{3}]$ |
\(q+(\beta _{1}-6\beta _{2})q^{5}+(1-7\beta _{1}+6\beta _{2}-7\beta _{3})q^{11}+\cdots\) |
| 1764.4.k.r |
$1764$ |
$4$ |
1764.k |
7.c |
$3$ |
$4$ |
$2$ |
$104.079$ |
\(\Q(\sqrt{2}, \sqrt{-3})\) |
None |
|
✓ |
|
|
1764.4.a.q |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
$\mathrm{SU}(2)[C_{3}]$ |
\(q+7\beta _{1}q^{5}+28\beta _{2}q^{11}+3\beta _{3}q^{13}+\cdots\) |
| 1764.4.k.s |
$1764$ |
$4$ |
1764.k |
7.c |
$3$ |
$4$ |
$2$ |
$104.079$ |
\(\Q(\sqrt{2}, \sqrt{-3})\) |
None |
|
|
|
|
196.4.a.f |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
$\mathrm{SU}(2)[C_{3}]$ |
\(q+2\beta _{1}q^{5}+26\beta _{2}q^{11}-24\beta _{3}q^{13}+\cdots\) |
| 1764.4.k.t |
$1764$ |
$4$ |
1764.k |
7.c |
$3$ |
$4$ |
$2$ |
$104.079$ |
\(\Q(\sqrt{-3}, \sqrt{7})\) |
None |
|
|
|
|
252.4.a.e |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2^{2}$ |
$\mathrm{SU}(2)[C_{3}]$ |
\(q+\beta _{1}q^{5}+(13\beta _{1}+13\beta _{3})q^{11}-30q^{13}+\cdots\) |
| 1764.4.k.u |
$1764$ |
$4$ |
1764.k |
7.c |
$3$ |
$4$ |
$2$ |
$104.079$ |
\(\Q(\sqrt{-3}, \sqrt{7})\) |
None |
|
|
|
|
252.4.a.f |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2^{2}\cdot 3^{2}$ |
$\mathrm{SU}(2)[C_{3}]$ |
\(q+\beta _{1}q^{5}+(\beta _{1}+\beta _{3})q^{11}-26q^{13}+\cdots\) |
| 1764.4.k.v |
$1764$ |
$4$ |
1764.k |
7.c |
$3$ |
$4$ |
$2$ |
$104.079$ |
\(\Q(\sqrt{-3}, \sqrt{7})\) |
None |
|
|
|
|
252.4.a.f |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2^{2}\cdot 3^{2}$ |
$\mathrm{SU}(2)[C_{3}]$ |
\(q+\beta _{1}q^{5}+(-\beta _{1}-\beta _{3})q^{11}+26q^{13}+\cdots\) |
| 1764.4.k.w |
$1764$ |
$4$ |
1764.k |
7.c |
$3$ |
$4$ |
$2$ |
$104.079$ |
\(\Q(\sqrt{-3}, \sqrt{7})\) |
None |
|
|
|
|
252.4.a.e |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2^{2}$ |
$\mathrm{SU}(2)[C_{3}]$ |
\(q+\beta _{1}q^{5}+(-13\beta _{1}-13\beta _{3})q^{11}+30q^{13}+\cdots\) |
| 1764.4.k.x |
$1764$ |
$4$ |
1764.k |
7.c |
$3$ |
$4$ |
$2$ |
$104.079$ |
\(\Q(\sqrt{-3}, \sqrt{385})\) |
None |
|
|
|
|
252.4.k.e |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2^{2}$ |
$\mathrm{SU}(2)[C_{3}]$ |
\(q-\beta _{2}q^{5}+(\beta _{2}+\beta _{3})q^{11}+54q^{13}+\cdots\) |
| 1764.4.k.y |
$1764$ |
$4$ |
1764.k |
7.c |
$3$ |
$4$ |
$2$ |
$104.079$ |
\(\Q(\sqrt{2}, \sqrt{-3})\) |
None |
|
✓ |
|
|
1764.4.a.q |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
$\mathrm{SU}(2)[C_{3}]$ |
\(q+7\beta _{1}q^{5}-28\beta _{2}q^{11}-3\beta _{3}q^{13}+\cdots\) |
| 1764.4.k.z |
$1764$ |
$4$ |
1764.k |
7.c |
$3$ |
$4$ |
$2$ |
$104.079$ |
\(\Q(\sqrt{-3}, \sqrt{-19})\) |
None |
|
|
|
|
84.4.i.b |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(3\) |
\(0\) |
$3^{3}$ |
$\mathrm{SU}(2)[C_{3}]$ |
\(q+(1+\beta _{1}+\beta _{3})q^{5}+(-1+5^{2}\beta _{1}-\beta _{2}+\cdots)q^{11}+\cdots\) |
| 1764.4.k.ba |
$1764$ |
$4$ |
1764.k |
7.c |
$3$ |
$4$ |
$2$ |
$104.079$ |
\(\Q(\sqrt{-3}, \sqrt{37})\) |
None |
|
|
|
|
28.4.e.a |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(14\) |
\(0\) |
$2^{2}$ |
$\mathrm{SU}(2)[C_{3}]$ |
\(q+(7\beta _{1}+2\beta _{2})q^{5}+(2^{4}-2^{4}\beta _{1}+7\beta _{2}+\cdots)q^{11}+\cdots\) |
| 1764.4.k.bb |
$1764$ |
$4$ |
1764.k |
7.c |
$3$ |
$8$ |
$4$ |
$104.079$ |
\(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
None |
|
|
|
|
588.4.a.j |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2^{8}\cdot 7^{2}$ |
$\mathrm{SU}(2)[C_{3}]$ |
\(q+\beta _{6}q^{5}+(-3\beta _{2}-\beta _{4})q^{11}+(3\beta _{4}+\cdots)q^{13}+\cdots\) |
| 1764.4.k.bc |
$1764$ |
$4$ |
1764.k |
7.c |
$3$ |
$8$ |
$4$ |
$104.079$ |
8.0.\(\cdots\).42 |
None |
|
✓ |
|
|
1764.4.a.bb |
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2^{16}$ |
$\mathrm{SU}(2)[C_{3}]$ |
\(q-\beta _{5}q^{5}+(\beta _{2}+\beta _{3})q^{11}+\beta _{6}q^{13}+\cdots\) |
| 1764.4.k.bd |
$1764$ |
$4$ |
1764.k |
7.c |
$3$ |
$8$ |
$4$ |
$104.079$ |
\(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
None |
|
|
|
|
588.4.a.j |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2^{8}\cdot 7^{2}$ |
$\mathrm{SU}(2)[C_{3}]$ |
\(q-\beta _{6}q^{5}+(-3\beta _{2}-\beta _{4})q^{11}+(-3\beta _{4}+\cdots)q^{13}+\cdots\) |
\( S_{4}^{\mathrm{old}}(1764, [\chi]) \simeq \)
\(S_{4}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 18}\)\(\oplus\)
\(S_{4}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 12}\)\(\oplus\)
\(S_{4}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 12}\)\(\oplus\)
\(S_{4}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 6}\)\(\oplus\)
\(S_{4}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 8}\)\(\oplus\)
\(S_{4}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 9}\)\(\oplus\)
\(S_{4}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 6}\)\(\oplus\)
\(S_{4}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 4}\)\(\oplus\)
\(S_{4}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 6}\)\(\oplus\)
\(S_{4}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 4}\)\(\oplus\)
\(S_{4}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 6}\)\(\oplus\)
\(S_{4}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 3}\)\(\oplus\)
\(S_{4}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 2}\)\(\oplus\)
\(S_{4}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 4}\)\(\oplus\)
\(S_{4}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 3}\)\(\oplus\)
\(S_{4}^{\mathrm{new}}(588, [\chi])\)\(^{\oplus 2}\)\(\oplus\)
\(S_{4}^{\mathrm{new}}(882, [\chi])\)\(^{\oplus 2}\)
