Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of M3(1152,[χ]).
|
Total |
New |
Old |
Modular forms
| 416 |
32 |
384 |
Cusp forms
| 352 |
32 |
320 |
Eisenstein series
| 64 |
0 |
64 |
Decomposition of S3new(1152,[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 |
1152.3.e.a |
1152 |
3 |
1152.e |
3.b |
2 |
4 |
4 |
31.390 |
Q(−2,−11) |
None |
|
✓ |
|
|
1152.3.e.a |
2 |
0 |
0 |
0 |
0 |
−8 |
24 |
SU(2)[C2] |
q+(β1−β3)q5−2q7+(6β1−2β3)q11+⋯ |
1152.3.e.b |
1152 |
3 |
1152.e |
3.b |
2 |
4 |
4 |
31.390 |
Q(−2,−3) |
None |
|
✓ |
|
|
1152.3.e.b |
2 |
0 |
0 |
0 |
0 |
−8 |
24 |
SU(2)[C2] |
q+(−β1+β2)q5+(−2+2β3)q7+⋯ |
1152.3.e.c |
1152 |
3 |
1152.e |
3.b |
2 |
4 |
4 |
31.390 |
Q(−2,−11) |
None |
|
✓ |
|
|
1152.3.e.a |
2 |
0 |
0 |
0 |
0 |
−8 |
24 |
SU(2)[C2] |
q+(β1−β3)q5−2q7+(6β1−2β3)q11+⋯ |
1152.3.e.d |
1152 |
3 |
1152.e |
3.b |
2 |
4 |
4 |
31.390 |
Q(−2,−3) |
None |
|
✓ |
|
|
1152.3.e.b |
2 |
0 |
0 |
0 |
0 |
−8 |
24 |
SU(2)[C2] |
q+(−β1+β2)q5+(−2+2β3)q7+⋯ |
1152.3.e.e |
1152 |
3 |
1152.e |
3.b |
2 |
4 |
4 |
31.390 |
Q(−2,−11) |
None |
|
✓ |
|
|
1152.3.e.a |
2 |
0 |
0 |
0 |
0 |
8 |
24 |
SU(2)[C2] |
q+(β1−β3)q5+2q7+(−6β1+2β3)q11+⋯ |
1152.3.e.f |
1152 |
3 |
1152.e |
3.b |
2 |
4 |
4 |
31.390 |
Q(−2,−3) |
None |
|
✓ |
|
|
1152.3.e.b |
2 |
0 |
0 |
0 |
0 |
8 |
24 |
SU(2)[C2] |
q+(−β1+β2)q5+(2−2β3)q7+(−2β1+⋯)q11+⋯ |
1152.3.e.g |
1152 |
3 |
1152.e |
3.b |
2 |
4 |
4 |
31.390 |
Q(−2,−11) |
None |
|
✓ |
|
|
1152.3.e.a |
2 |
0 |
0 |
0 |
0 |
8 |
24 |
SU(2)[C2] |
q+(β1−β3)q5+2q7+(−6β1+2β3)q11+⋯ |
1152.3.e.h |
1152 |
3 |
1152.e |
3.b |
2 |
4 |
4 |
31.390 |
Q(−2,−3) |
None |
|
✓ |
|
|
1152.3.e.b |
2 |
0 |
0 |
0 |
0 |
8 |
24 |
SU(2)[C2] |
q+(−β1+β2)q5+(2−2β3)q7+(−2β1+⋯)q11+⋯ |
Decomposition of S3old(1152,[χ]) into lower level spaces
S3old(1152,[χ])≃ S3new(12,[χ])⊕12⊕S3new(18,[χ])⊕7⊕S3new(24,[χ])⊕10⊕S3new(48,[χ])⊕8⊕S3new(72,[χ])⊕5⊕S3new(96,[χ])⊕6⊕S3new(144,[χ])⊕4⊕S3new(192,[χ])⊕4⊕S3new(288,[χ])⊕3⊕S3new(384,[χ])⊕2⊕S3new(576,[χ])⊕2