Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(4032, [\chi])\).
|
Total |
New |
Old |
| Modular forms
| 1584 |
96 |
1488 |
| Cusp forms
| 1488 |
96 |
1392 |
| Eisenstein series
| 96 |
0 |
96 |
| 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 |
| $a_{2}$ |
$a_{3}$ |
$a_{5}$ |
$a_{7}$ |
| 4032.3.d.a |
$4032$ |
$3$ |
4032.d |
3.b |
$2$ |
$4$ |
$4$ |
$109.864$ |
\(\Q(\sqrt{-2}, \sqrt{7})\) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+2\beta _{1}q^{5}-\beta _{3}q^{7}+3\beta _{2}q^{11}-14q^{13}+\cdots\) |
| 4032.3.d.b |
$4032$ |
$3$ |
4032.d |
3.b |
$2$ |
$4$ |
$4$ |
$109.864$ |
\(\Q(\sqrt{-2}, \sqrt{7})\) |
None |
|
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2\cdot 3$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+\beta _{1}q^{5}+\beta _{3}q^{7}+(-2\beta _{1}+\beta _{2})q^{11}+\cdots\) |
| 4032.3.d.c |
$4032$ |
$3$ |
4032.d |
3.b |
$2$ |
$4$ |
$4$ |
$109.864$ |
\(\Q(\sqrt{-2}, \sqrt{7})\) |
None |
|
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2\cdot 3$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+\beta _{1}q^{5}-\beta _{3}q^{7}+(2\beta _{1}-\beta _{2})q^{11}+\cdots\) |
| 4032.3.d.d |
$4032$ |
$3$ |
4032.d |
3.b |
$2$ |
$4$ |
$4$ |
$109.864$ |
\(\Q(\sqrt{-2}, \sqrt{7})\) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q-5\beta _{1}q^{5}+\beta _{3}q^{7}+4\beta _{2}q^{11}+11\beta _{1}q^{17}+\cdots\) |
| 4032.3.d.e |
$4032$ |
$3$ |
4032.d |
3.b |
$2$ |
$4$ |
$4$ |
$109.864$ |
\(\Q(\sqrt{-2}, \sqrt{7})\) |
None |
|
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2\cdot 3$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+\beta _{1}q^{5}-\beta _{3}q^{7}+(-2\beta _{1}-\beta _{2})q^{11}+\cdots\) |
| 4032.3.d.f |
$4032$ |
$3$ |
4032.d |
3.b |
$2$ |
$4$ |
$4$ |
$109.864$ |
\(\Q(\sqrt{-2}, \sqrt{7})\) |
None |
|
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+(-3\beta _{1}+\beta _{2})q^{5}-\beta _{3}q^{7}+(-\beta _{1}+\cdots)q^{11}+\cdots\) |
| 4032.3.d.g |
$4032$ |
$3$ |
4032.d |
3.b |
$2$ |
$4$ |
$4$ |
$109.864$ |
\(\Q(\sqrt{-2}, \sqrt{7})\) |
None |
|
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+(-3\beta _{1}+\beta _{2})q^{5}+\beta _{3}q^{7}+(\beta _{1}-2\beta _{2}+\cdots)q^{11}+\cdots\) |
| 4032.3.d.h |
$4032$ |
$3$ |
4032.d |
3.b |
$2$ |
$4$ |
$4$ |
$109.864$ |
\(\Q(\sqrt{-2}, \sqrt{7})\) |
None |
|
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2\cdot 3$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+\beta _{1}q^{5}+\beta _{3}q^{7}+(2\beta _{1}+\beta _{2})q^{11}+\cdots\) |
| 4032.3.d.i |
$4032$ |
$3$ |
4032.d |
3.b |
$2$ |
$4$ |
$4$ |
$109.864$ |
\(\Q(\sqrt{-2}, \sqrt{7})\) |
None |
|
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2\cdot 3$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+(2\beta _{1}-\beta _{3})q^{5}-\beta _{2}q^{7}+(4\beta _{1}-2\beta _{3})q^{11}+\cdots\) |
| 4032.3.d.j |
$4032$ |
$3$ |
4032.d |
3.b |
$2$ |
$4$ |
$4$ |
$109.864$ |
\(\Q(\sqrt{-2}, \sqrt{7})\) |
None |
|
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2\cdot 3$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+(2\beta _{1}-\beta _{3})q^{5}+\beta _{2}q^{7}+(-4\beta _{1}+2\beta _{3})q^{11}+\cdots\) |
| 4032.3.d.k |
$4032$ |
$3$ |
4032.d |
3.b |
$2$ |
$4$ |
$4$ |
$109.864$ |
\(\Q(\sqrt{-2}, \sqrt{7})\) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+\beta _{3}q^{7}+\beta _{2}q^{11}+10q^{13}+14\beta _{1}q^{17}+\cdots\) |
| 4032.3.d.l |
$4032$ |
$3$ |
4032.d |
3.b |
$2$ |
$8$ |
$8$ |
$109.864$ |
\(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
None |
|
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2^{4}$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+(\beta _{2}-\beta _{4}+\beta _{5})q^{5}-\beta _{3}q^{7}+(\beta _{2}-\beta _{4}+\cdots)q^{11}+\cdots\) |
| 4032.3.d.m |
$4032$ |
$3$ |
4032.d |
3.b |
$2$ |
$8$ |
$8$ |
$109.864$ |
\(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
None |
|
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2^{4}$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+(\beta _{2}-\beta _{4}+\beta _{5})q^{5}+\beta _{3}q^{7}+(-\beta _{2}+\cdots)q^{11}+\cdots\) |
| 4032.3.d.n |
$4032$ |
$3$ |
4032.d |
3.b |
$2$ |
$12$ |
$12$ |
$109.864$ |
\(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
None |
|
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2^{13}$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+\beta _{8}q^{5}-\beta _{4}q^{7}-\beta _{6}q^{11}+(-1-\beta _{9}+\cdots)q^{13}+\cdots\) |
| 4032.3.d.o |
$4032$ |
$3$ |
4032.d |
3.b |
$2$ |
$12$ |
$12$ |
$109.864$ |
\(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
None |
|
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2^{13}$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+\beta _{8}q^{5}+\beta _{4}q^{7}+\beta _{6}q^{11}+(-1-\beta _{9}+\cdots)q^{13}+\cdots\) |
| 4032.3.d.p |
$4032$ |
$3$ |
4032.d |
3.b |
$2$ |
$12$ |
$12$ |
$109.864$ |
12.0.\(\cdots\).4 |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2^{13}$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+(\beta _{5}-\beta _{7})q^{5}-\beta _{1}q^{7}+(\beta _{8}-\beta _{10}+\cdots)q^{11}+\cdots\) |
\( S_{3}^{\mathrm{old}}(4032, [\chi]) \cong \)
\(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 20}\)\(\oplus\)
\(S_{3}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 12}\)\(\oplus\)
\(S_{3}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 14}\)\(\oplus\)
\(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 16}\)\(\oplus\)
\(S_{3}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 10}\)\(\oplus\)
\(S_{3}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 12}\)\(\oplus\)
\(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 12}\)\(\oplus\)
\(S_{3}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 7}\)\(\oplus\)
\(S_{3}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 8}\)\(\oplus\)
\(S_{3}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 10}\)\(\oplus\)
\(S_{3}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 8}\)\(\oplus\)
\(S_{3}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 6}\)\(\oplus\)
\(S_{3}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 6}\)\(\oplus\)
\(S_{3}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 8}\)\(\oplus\)
\(S_{3}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 4}\)\(\oplus\)
\(S_{3}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 5}\)\(\oplus\)
\(S_{3}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 4}\)\(\oplus\)
\(S_{3}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 6}\)\(\oplus\)
\(S_{3}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 4}\)\(\oplus\)
\(S_{3}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 2}\)\(\oplus\)
\(S_{3}^{\mathrm{new}}(672, [\chi])\)\(^{\oplus 4}\)\(\oplus\)
\(S_{3}^{\mathrm{new}}(1008, [\chi])\)\(^{\oplus 3}\)\(\oplus\)
\(S_{3}^{\mathrm{new}}(1344, [\chi])\)\(^{\oplus 2}\)\(\oplus\)
\(S_{3}^{\mathrm{new}}(2016, [\chi])\)\(^{\oplus 2}\)
