Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{5}(400, [\chi])\).
|
Total |
New |
Old |
Modular forms
| 516 |
74 |
442 |
Cusp forms
| 444 |
70 |
374 |
Eisenstein series
| 72 |
4 |
68 |
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 |
$a_{2}$ |
$a_{3}$ |
$a_{5}$ |
$a_{7}$ |
400.5.p.a |
$400$ |
$5$ |
400.p |
5.c |
$4$ |
$2$ |
$1$ |
$41.348$ |
\(\Q(\sqrt{-1}) \) |
None |
|
|
|
|
5.5.c.a |
$2$ |
$0$ |
\(0\) |
\(-12\) |
\(0\) |
\(-52\) |
$1$ |
$\mathrm{SU}(2)[C_{4}]$ |
\(q+(6 i-6)q^{3}+(-26 i-26)q^{7}+\cdots\) |
400.5.p.b |
$400$ |
$5$ |
400.p |
5.c |
$4$ |
$2$ |
$1$ |
$41.348$ |
\(\Q(\sqrt{-1}) \) |
None |
|
|
|
|
10.5.c.b |
$2$ |
$0$ |
\(0\) |
\(2\) |
\(0\) |
\(-38\) |
$1$ |
$\mathrm{SU}(2)[C_{4}]$ |
\(q+(-i+1)q^{3}+(-19 i-19)q^{7}+\cdots\) |
400.5.p.c |
$400$ |
$5$ |
400.p |
5.c |
$4$ |
$2$ |
$1$ |
$41.348$ |
\(\Q(\sqrt{-1}) \) |
None |
|
|
|
|
10.5.c.a |
$2$ |
$0$ |
\(0\) |
\(18\) |
\(0\) |
\(58\) |
$1$ |
$\mathrm{SU}(2)[C_{4}]$ |
\(q+(-9 i+9)q^{3}+(29 i+29)q^{7}+\cdots\) |
400.5.p.d |
$400$ |
$5$ |
400.p |
5.c |
$4$ |
$2$ |
$1$ |
$41.348$ |
\(\Q(\sqrt{-1}) \) |
None |
|
|
|
|
40.5.l.a |
$2$ |
$0$ |
\(0\) |
\(20\) |
\(0\) |
\(-84\) |
$1$ |
$\mathrm{SU}(2)[C_{4}]$ |
\(q+(-10 i+10)q^{3}+(-42 i-42)q^{7}+\cdots\) |
400.5.p.e |
$400$ |
$5$ |
400.p |
5.c |
$4$ |
$4$ |
$2$ |
$41.348$ |
\(\Q(i, \sqrt{6})\) |
None |
|
|
|
|
50.5.c.c |
$2$ |
$0$ |
\(0\) |
\(-24\) |
\(0\) |
\(-144\) |
$5^{2}$ |
$\mathrm{SU}(2)[C_{4}]$ |
\(q+(-6+\beta _{1}-6\beta _{2})q^{3}+(-6^{2}+6^{2}\beta _{2}+\cdots)q^{7}+\cdots\) |
400.5.p.f |
$400$ |
$5$ |
400.p |
5.c |
$4$ |
$4$ |
$2$ |
$41.348$ |
\(\Q(i, \sqrt{61})\) |
None |
|
|
|
|
200.5.l.b |
$2$ |
$0$ |
\(0\) |
\(-16\) |
\(0\) |
\(48\) |
$2^{3}$ |
$\mathrm{SU}(2)[C_{4}]$ |
\(q+(-4+4\beta _{1}-\beta _{3})q^{3}+(12+12\beta _{1}+\cdots)q^{7}+\cdots\) |
400.5.p.g |
$400$ |
$5$ |
400.p |
5.c |
$4$ |
$4$ |
$2$ |
$41.348$ |
\(\Q(i, \sqrt{29})\) |
None |
|
|
|
|
40.5.l.b |
$2$ |
$0$ |
\(0\) |
\(-12\) |
\(0\) |
\(44\) |
$2^{5}\cdot 5^{2}$ |
$\mathrm{SU}(2)[C_{4}]$ |
\(q+(-3+3\beta _{1})q^{3}+(11+11\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\) |
400.5.p.h |
$400$ |
$5$ |
400.p |
5.c |
$4$ |
$4$ |
$2$ |
$41.348$ |
\(\Q(i, \sqrt{241})\) |
None |
|
|
|
|
20.5.f.a |
$2$ |
$0$ |
\(0\) |
\(-10\) |
\(0\) |
\(110\) |
$2$ |
$\mathrm{SU}(2)[C_{4}]$ |
\(q+(-2+2\beta _{1}+\beta _{3})q^{3}+(26+29\beta _{1}+\cdots)q^{7}+\cdots\) |
400.5.p.i |
$400$ |
$5$ |
400.p |
5.c |
$4$ |
$4$ |
$2$ |
$41.348$ |
\(\Q(i, \sqrt{69})\) |
None |
|
|
|
|
100.5.f.b |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2^{3}$ |
$\mathrm{SU}(2)[C_{4}]$ |
\(q-\beta _{3}q^{3}+7\beta _{2}q^{7}-57\beta _{1}q^{9}-180q^{11}+\cdots\) |
400.5.p.j |
$400$ |
$5$ |
400.p |
5.c |
$4$ |
$4$ |
$2$ |
$41.348$ |
\(\Q(i, \sqrt{6})\) |
None |
|
|
|
|
25.5.c.b |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
$\mathrm{SU}(2)[C_{4}]$ |
\(q+7\beta _{1}q^{3}+28\beta _{3}q^{7}+66\beta _{2}q^{9}-117q^{11}+\cdots\) |
400.5.p.k |
$400$ |
$5$ |
400.p |
5.c |
$4$ |
$4$ |
$2$ |
$41.348$ |
\(\Q(i, \sqrt{6})\) |
None |
|
|
|
|
100.5.f.a |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
$\mathrm{SU}(2)[C_{4}]$ |
\(q+\beta _{1}q^{3}-12\beta _{3}q^{7}-78\beta _{2}q^{9}-45q^{11}+\cdots\) |
400.5.p.l |
$400$ |
$5$ |
400.p |
5.c |
$4$ |
$4$ |
$2$ |
$41.348$ |
\(\Q(i, \sqrt{21})\) |
None |
|
|
|
|
25.5.c.c |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2^{3}$ |
$\mathrm{SU}(2)[C_{4}]$ |
\(q-\beta _{3}q^{3}-9\beta _{2}q^{7}+39\beta _{1}q^{9}+108q^{11}+\cdots\) |
400.5.p.m |
$400$ |
$5$ |
400.p |
5.c |
$4$ |
$4$ |
$2$ |
$41.348$ |
\(\Q(i, \sqrt{61})\) |
None |
|
|
|
|
200.5.l.b |
$2$ |
$0$ |
\(0\) |
\(16\) |
\(0\) |
\(-48\) |
$2^{3}$ |
$\mathrm{SU}(2)[C_{4}]$ |
\(q+(4+4\beta _{1}-\beta _{2})q^{3}+(-12+12\beta _{1}+\cdots)q^{7}+\cdots\) |
400.5.p.n |
$400$ |
$5$ |
400.p |
5.c |
$4$ |
$4$ |
$2$ |
$41.348$ |
\(\Q(i, \sqrt{6})\) |
None |
|
|
|
|
50.5.c.c |
$2$ |
$0$ |
\(0\) |
\(24\) |
\(0\) |
\(144\) |
$5^{2}$ |
$\mathrm{SU}(2)[C_{4}]$ |
\(q+(6+\beta _{1}+6\beta _{2})q^{3}+(6^{2}-6^{2}\beta _{2}+4\beta _{3})q^{7}+\cdots\) |
400.5.p.o |
$400$ |
$5$ |
400.p |
5.c |
$4$ |
$6$ |
$3$ |
$41.348$ |
6.0.313431616.3 |
None |
|
|
|
|
40.5.l.c |
$2$ |
$0$ |
\(0\) |
\(-8\) |
\(0\) |
\(-40\) |
$2^{6}\cdot 5^{2}$ |
$\mathrm{SU}(2)[C_{4}]$ |
\(q+(-1-\beta _{1}-\beta _{3})q^{3}+(-6+6\beta _{1}+\cdots)q^{7}+\cdots\) |
400.5.p.p |
$400$ |
$5$ |
400.p |
5.c |
$4$ |
$8$ |
$4$ |
$41.348$ |
8.0.\(\cdots\).18 |
None |
|
|
|
|
200.5.l.f |
$2$ |
$0$ |
\(0\) |
\(-8\) |
\(0\) |
\(-48\) |
$2^{6}\cdot 5^{4}$ |
$\mathrm{SU}(2)[C_{4}]$ |
\(q+(-1-\beta _{1}+\beta _{3})q^{3}+(-6+6\beta _{1}+\cdots)q^{7}+\cdots\) |
400.5.p.q |
$400$ |
$5$ |
400.p |
5.c |
$4$ |
$8$ |
$4$ |
$41.348$ |
8.0.\(\cdots\).18 |
None |
|
|
|
|
200.5.l.f |
$2$ |
$0$ |
\(0\) |
\(8\) |
\(0\) |
\(48\) |
$2^{6}\cdot 5^{4}$ |
$\mathrm{SU}(2)[C_{4}]$ |
\(q+(1-\beta _{1}-\beta _{2})q^{3}+(6+6\beta _{1}-2\beta _{3}+\cdots)q^{7}+\cdots\) |
\( S_{5}^{\mathrm{old}}(400, [\chi]) \simeq \)
\(S_{5}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 10}\)\(\oplus\)
\(S_{5}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 8}\)\(\oplus\)
\(S_{5}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 6}\)\(\oplus\)
\(S_{5}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 5}\)\(\oplus\)
\(S_{5}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)
\(S_{5}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 4}\)\(\oplus\)
\(S_{5}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 2}\)\(\oplus\)
\(S_{5}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 3}\)\(\oplus\)
\(S_{5}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 2}\)