Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of M3(300,[χ]).
|
Total |
New |
Old |
Modular forms
| 264 |
152 |
112 |
Cusp forms
| 216 |
136 |
80 |
Eisenstein series
| 48 |
16 |
32 |
Decomposition of S3new(300,[χ]) into newform subspaces
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 |
a2 |
a3 |
a5 |
a7 |
300.3.l.a |
300 |
3 |
300.l |
60.l |
4 |
4 |
2 |
8.174 |
Q(i,14) |
None |
|
✓ |
|
|
300.3.l.a |
4 |
0 |
−8 |
4 |
0 |
0 |
1 |
SU(2)[C4] |
q−2q2+(1+β2+β3)q3+4q4+(−2+⋯)q6+⋯ |
300.3.l.b |
300 |
3 |
300.l |
60.l |
4 |
4 |
2 |
8.174 |
Q(i,14) |
None |
|
✓ |
|
|
300.3.l.a |
4 |
0 |
0 |
−4 |
0 |
0 |
1 |
SU(2)[C4] |
q−2β2q2+(−1−β2+β3)q3−4q4+⋯ |
300.3.l.c |
300 |
3 |
300.l |
60.l |
4 |
4 |
2 |
8.174 |
Q(i,14) |
None |
|
✓ |
|
|
300.3.l.a |
4 |
0 |
0 |
4 |
0 |
0 |
1 |
SU(2)[C4] |
q−2β2q2+(1+β1−β2)q3−4q4+⋯ |
300.3.l.d |
300 |
3 |
300.l |
60.l |
4 |
4 |
2 |
8.174 |
Q(i,14) |
None |
|
✓ |
|
|
300.3.l.a |
4 |
0 |
8 |
−4 |
0 |
0 |
1 |
SU(2)[C4] |
q+2q2+(−1+β1+β2)q3+4q4+⋯ |
300.3.l.e |
300 |
3 |
300.l |
60.l |
4 |
8 |
4 |
8.174 |
8.0.3317760000.4 |
Q(−15) |
|
✓ |
|
|
300.3.l.e |
16 |
0 |
0 |
0 |
0 |
0 |
1 |
U(1)[D4] |
q+β1q2+3β5q3+(4β4+β6)q4+⋯ |
300.3.l.f |
300 |
3 |
300.l |
60.l |
4 |
8 |
4 |
8.174 |
8.0.40960000.1 |
Q(−5) |
|
✓ |
|
|
300.3.l.f |
16 |
0 |
0 |
0 |
0 |
0 |
28 |
U(1)[D4] |
q−β6q2+(−β3+β7)q3−4β2q4+⋯ |
300.3.l.g |
300 |
3 |
300.l |
60.l |
4 |
40 |
20 |
8.174 |
|
None |
|
|
|
|
60.3.l.a |
8 |
0 |
0 |
0 |
0 |
0 |
|
SU(2)[C4] |
|
300.3.l.h |
300 |
3 |
300.l |
60.l |
4 |
64 |
32 |
8.174 |
|
None |
|
✓ |
✓ |
|
300.3.l.h |
16 |
0 |
0 |
0 |
0 |
0 |
|
SU(2)[C4] |
|
Decomposition of S3old(300,[χ]) into lower level spaces