Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(3200, [\chi])\).
|
Total |
New |
Old |
Modular forms
| 528 |
76 |
452 |
Cusp forms
| 432 |
76 |
356 |
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 |
$a_{2}$ |
$a_{3}$ |
$a_{5}$ |
$a_{7}$ |
3200.2.d.a |
$3200$ |
$2$ |
3200.d |
8.b |
$2$ |
$2$ |
$2$ |
$25.552$ |
\(\Q(\sqrt{-1}) \) |
None |
|
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(-8\) |
$1$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+iq^{3}-4q^{7}+2q^{9}-3iq^{11}-q^{17}+\cdots\) |
3200.2.d.b |
$3200$ |
$2$ |
3200.d |
8.b |
$2$ |
$2$ |
$2$ |
$25.552$ |
\(\Q(\sqrt{-1}) \) |
None |
|
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(-8\) |
$1$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+iq^{3}-4q^{7}+2q^{9}+3iq^{11}+q^{17}+\cdots\) |
3200.2.d.c |
$3200$ |
$2$ |
3200.d |
8.b |
$2$ |
$2$ |
$2$ |
$25.552$ |
\(\Q(\sqrt{-2}) \) |
\(\Q(\sqrt{-2}) \) |
|
$4$ |
$1$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q+\beta q^{3}-5q^{9}-\beta q^{11}-6q^{17}+3\beta q^{19}+\cdots\) |
3200.2.d.d |
$3200$ |
$2$ |
3200.d |
8.b |
$2$ |
$2$ |
$2$ |
$25.552$ |
\(\Q(\sqrt{-1}) \) |
\(\Q(\sqrt{-1}) \) |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q+3q^{9}-3iq^{13}-8q^{17}-2iq^{29}+\cdots\) |
3200.2.d.e |
$3200$ |
$2$ |
3200.d |
8.b |
$2$ |
$2$ |
$2$ |
$25.552$ |
\(\Q(\sqrt{-1}) \) |
\(\Q(\sqrt{-1}) \) |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2^{2}$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q+3q^{9}-iq^{13}+2q^{17}+iq^{29}-3iq^{37}+\cdots\) |
3200.2.d.f |
$3200$ |
$2$ |
3200.d |
8.b |
$2$ |
$2$ |
$2$ |
$25.552$ |
\(\Q(\sqrt{-1}) \) |
\(\Q(\sqrt{-1}) \) |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q+3q^{9}+3iq^{13}+8q^{17}-2iq^{29}+\cdots\) |
3200.2.d.g |
$3200$ |
$2$ |
3200.d |
8.b |
$2$ |
$2$ |
$2$ |
$25.552$ |
\(\Q(\sqrt{-1}) \) |
None |
|
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(8\) |
$1$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+iq^{3}+4q^{7}+2q^{9}-3iq^{11}-q^{17}+\cdots\) |
3200.2.d.h |
$3200$ |
$2$ |
3200.d |
8.b |
$2$ |
$2$ |
$2$ |
$25.552$ |
\(\Q(\sqrt{-1}) \) |
None |
|
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(8\) |
$1$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+iq^{3}+4q^{7}+2q^{9}+3iq^{11}+q^{17}+\cdots\) |
3200.2.d.i |
$3200$ |
$2$ |
3200.d |
8.b |
$2$ |
$4$ |
$4$ |
$25.552$ |
\(\Q(\sqrt{2}, \sqrt{-5})\) |
\(\Q(\sqrt{-5}) \) |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2^{2}$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q+\beta _{2}q^{3}-3\beta _{1}q^{7}-7q^{9}+3\beta _{3}q^{21}+\cdots\) |
3200.2.d.j |
$3200$ |
$2$ |
3200.d |
8.b |
$2$ |
$4$ |
$4$ |
$25.552$ |
\(\Q(i, \sqrt{10})\) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2^{2}$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+\beta _{2}q^{3}-\beta _{3}q^{7}-7q^{9}+3\beta _{1}q^{13}+\cdots\) |
3200.2.d.k |
$3200$ |
$2$ |
3200.d |
8.b |
$2$ |
$4$ |
$4$ |
$25.552$ |
\(\Q(i, \sqrt{6})\) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2^{2}$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+\beta _{2}q^{3}-\beta _{3}q^{7}-3q^{9}-2\beta _{2}q^{11}+\cdots\) |
3200.2.d.l |
$3200$ |
$2$ |
3200.d |
8.b |
$2$ |
$4$ |
$4$ |
$25.552$ |
\(\Q(i, \sqrt{6})\) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2^{2}$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+\beta _{2}q^{3}+\beta _{3}q^{7}-3q^{9}+2\beta _{2}q^{11}+\cdots\) |
3200.2.d.m |
$3200$ |
$2$ |
3200.d |
8.b |
$2$ |
$4$ |
$4$ |
$25.552$ |
\(\Q(\sqrt{2}, \sqrt{-5})\) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2^{3}$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+\beta _{3}q^{3}+\beta _{1}q^{7}-2q^{9}+\beta _{3}q^{11}+\cdots\) |
3200.2.d.n |
$3200$ |
$2$ |
3200.d |
8.b |
$2$ |
$4$ |
$4$ |
$25.552$ |
\(\Q(\sqrt{-2}, \sqrt{-3})\) |
\(\Q(\sqrt{-2}) \) |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2^{4}$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q+\beta _{2}q^{3}+(-2+\beta _{3})q^{9}+(\beta _{1}+2\beta _{2}+\cdots)q^{11}+\cdots\) |
3200.2.d.o |
$3200$ |
$2$ |
3200.d |
8.b |
$2$ |
$4$ |
$4$ |
$25.552$ |
\(\Q(i, \sqrt{5})\) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2^{6}$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q-\beta _{1}q^{3}-2q^{9}+\beta _{1}q^{11}-\beta _{2}q^{13}+\cdots\) |
3200.2.d.p |
$3200$ |
$2$ |
3200.d |
8.b |
$2$ |
$4$ |
$4$ |
$25.552$ |
\(\Q(i, \sqrt{5})\) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2^{6}$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+\beta _{1}q^{3}-2q^{9}+\beta _{1}q^{11}-\beta _{2}q^{13}+\cdots\) |
3200.2.d.q |
$3200$ |
$2$ |
3200.d |
8.b |
$2$ |
$4$ |
$4$ |
$25.552$ |
\(\Q(\sqrt{-2}, \sqrt{-3})\) |
\(\Q(\sqrt{-2}) \) |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2^{4}$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q+\beta _{2}q^{3}+(-2+\beta _{3})q^{9}+(-\beta _{1}-2\beta _{2}+\cdots)q^{11}+\cdots\) |
3200.2.d.r |
$3200$ |
$2$ |
3200.d |
8.b |
$2$ |
$4$ |
$4$ |
$25.552$ |
\(\Q(\sqrt{2}, \sqrt{-5})\) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2^{3}$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+\beta _{3}q^{3}-\beta _{1}q^{7}-2q^{9}-\beta _{3}q^{11}+\cdots\) |
3200.2.d.s |
$3200$ |
$2$ |
3200.d |
8.b |
$2$ |
$4$ |
$4$ |
$25.552$ |
\(\Q(\zeta_{8})\) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2^{2}$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+\zeta_{8}^{2}q^{3}+3\zeta_{8}^{3}q^{7}+q^{9}+4\zeta_{8}^{2}q^{11}+\cdots\) |
3200.2.d.t |
$3200$ |
$2$ |
3200.d |
8.b |
$2$ |
$4$ |
$4$ |
$25.552$ |
\(\Q(\zeta_{8})\) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2^{2}$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+\zeta_{8}^{2}q^{3}-\zeta_{8}^{3}q^{7}+q^{9}-2\zeta_{8}^{2}q^{11}+\cdots\) |
3200.2.d.u |
$3200$ |
$2$ |
3200.d |
8.b |
$2$ |
$4$ |
$4$ |
$25.552$ |
\(\Q(\sqrt{-2}, \sqrt{-5})\) |
\(\Q(\sqrt{-5}) \) |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2^{2}$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q+\beta _{1}q^{3}+\beta _{2}q^{7}+q^{9}+\beta _{3}q^{21}-3\beta _{2}q^{23}+\cdots\) |
3200.2.d.v |
$3200$ |
$2$ |
3200.d |
8.b |
$2$ |
$4$ |
$4$ |
$25.552$ |
\(\Q(\zeta_{8})\) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2^{2}\cdot 3^{2}$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+\zeta_{8}^{2}q^{3}-\zeta_{8}^{3}q^{7}+q^{9}+2\zeta_{8}^{2}q^{11}+\cdots\) |
3200.2.d.w |
$3200$ |
$2$ |
3200.d |
8.b |
$2$ |
$4$ |
$4$ |
$25.552$ |
\(\Q(\sqrt{2}, \sqrt{-5})\) |
\(\Q(\sqrt{-10}) \) |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2^{4}$ |
$\mathrm{U}(1)[D_{2}]$ |
\(q-\beta _{1}q^{7}+3q^{9}-\beta _{2}q^{11}+\beta _{3}q^{13}+\cdots\) |
\( S_{2}^{\mathrm{old}}(3200, [\chi]) \cong \)
\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 10}\)\(\oplus\)
\(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 6}\)\(\oplus\)
\(S_{2}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 3}\)\(\oplus\)
\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 6}\)\(\oplus\)
\(S_{2}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 5}\)\(\oplus\)
\(S_{2}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 4}\)\(\oplus\)
\(S_{2}^{\mathrm{new}}(640, [\chi])\)\(^{\oplus 2}\)\(\oplus\)
\(S_{2}^{\mathrm{new}}(800, [\chi])\)\(^{\oplus 3}\)\(\oplus\)
\(S_{2}^{\mathrm{new}}(1600, [\chi])\)\(^{\oplus 2}\)