Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(4400, [\chi])\).
|
Total |
New |
Old |
Modular forms
| 756 |
90 |
666 |
Cusp forms
| 684 |
90 |
594 |
Eisenstein series
| 72 |
0 |
72 |
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 |
$a_{2}$ |
$a_{3}$ |
$a_{5}$ |
$a_{7}$ |
4400.2.b.a |
$4400$ |
$2$ |
4400.b |
5.b |
$2$ |
$2$ |
$2$ |
$35.134$ |
\(\Q(\sqrt{-1}) \) |
None |
|
|
|
|
440.2.a.d |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+3 i q^{3}-i q^{7}-6 q^{9}+q^{11}+6 i q^{13}+\cdots\) |
4400.2.b.b |
$4400$ |
$2$ |
4400.b |
5.b |
$2$ |
$2$ |
$2$ |
$35.134$ |
\(\Q(\sqrt{-1}) \) |
None |
|
|
|
|
88.2.a.a |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+3 i q^{3}-2 i q^{7}-6 q^{9}+q^{11}+\cdots\) |
4400.2.b.c |
$4400$ |
$2$ |
4400.b |
5.b |
$2$ |
$2$ |
$2$ |
$35.134$ |
\(\Q(\sqrt{-1}) \) |
None |
|
|
|
|
220.2.a.b |
$2$ |
$1$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+\beta q^{3}-q^{9}-q^{11}-2\beta q^{17}-4 q^{19}+\cdots\) |
4400.2.b.d |
$4400$ |
$2$ |
4400.b |
5.b |
$2$ |
$2$ |
$2$ |
$35.134$ |
\(\Q(\sqrt{-1}) \) |
None |
|
|
|
|
550.2.a.b |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+2 i q^{3}-q^{9}-q^{11}-3 i q^{13}-4 i q^{17}+\cdots\) |
4400.2.b.e |
$4400$ |
$2$ |
4400.b |
5.b |
$2$ |
$2$ |
$2$ |
$35.134$ |
\(\Q(\sqrt{-1}) \) |
None |
|
|
|
|
550.2.a.a |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+2 i q^{3}-4 i q^{7}-q^{9}+q^{11}+5 i q^{13}+\cdots\) |
4400.2.b.f |
$4400$ |
$2$ |
4400.b |
5.b |
$2$ |
$2$ |
$2$ |
$35.134$ |
\(\Q(\sqrt{-1}) \) |
None |
|
|
|
|
220.2.a.a |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+\beta q^{3}-2\beta q^{7}-q^{9}+q^{11}-2\beta q^{13}+\cdots\) |
4400.2.b.g |
$4400$ |
$2$ |
4400.b |
5.b |
$2$ |
$2$ |
$2$ |
$35.134$ |
\(\Q(\sqrt{-1}) \) |
None |
|
|
|
|
110.2.a.a |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+i q^{3}-5 i q^{7}+2 q^{9}-q^{11}-2 i q^{13}+\cdots\) |
4400.2.b.h |
$4400$ |
$2$ |
4400.b |
5.b |
$2$ |
$2$ |
$2$ |
$35.134$ |
\(\Q(\sqrt{-1}) \) |
None |
|
|
|
|
11.2.a.a |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+i q^{3}-2 i q^{7}+2 q^{9}-q^{11}+4 i q^{13}+\cdots\) |
4400.2.b.i |
$4400$ |
$2$ |
4400.b |
5.b |
$2$ |
$2$ |
$2$ |
$35.134$ |
\(\Q(\sqrt{-1}) \) |
None |
|
|
|
|
110.2.a.b |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+i q^{3}+3 i q^{7}+2 q^{9}-q^{11}-6 i q^{13}+\cdots\) |
4400.2.b.j |
$4400$ |
$2$ |
4400.b |
5.b |
$2$ |
$2$ |
$2$ |
$35.134$ |
\(\Q(\sqrt{-1}) \) |
None |
|
|
|
|
110.2.a.c |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+i q^{3}+i q^{7}+2 q^{9}+q^{11}-2 i q^{13}+\cdots\) |
4400.2.b.k |
$4400$ |
$2$ |
4400.b |
5.b |
$2$ |
$2$ |
$2$ |
$35.134$ |
\(\Q(\sqrt{-1}) \) |
None |
|
|
|
|
44.2.a.a |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+i q^{3}-2 i q^{7}+2 q^{9}+q^{11}+4 i q^{13}+\cdots\) |
4400.2.b.l |
$4400$ |
$2$ |
4400.b |
5.b |
$2$ |
$2$ |
$2$ |
$35.134$ |
\(\Q(\sqrt{-1}) \) |
None |
|
|
|
|
440.2.a.b |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q-\beta q^{7}+3 q^{9}-q^{11}-2\beta q^{13}+2\beta q^{17}+\cdots\) |
4400.2.b.m |
$4400$ |
$2$ |
4400.b |
5.b |
$2$ |
$2$ |
$2$ |
$35.134$ |
\(\Q(\sqrt{-1}) \) |
None |
|
|
|
|
440.2.a.a |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q-\beta q^{7}+3 q^{9}+q^{11}-8 q^{19}+4\beta q^{23}+\cdots\) |
4400.2.b.n |
$4400$ |
$2$ |
4400.b |
5.b |
$2$ |
$2$ |
$2$ |
$35.134$ |
\(\Q(\sqrt{-1}) \) |
None |
|
|
|
|
55.2.a.a |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+3 q^{9}+q^{11}-\beta q^{13}+3\beta q^{17}+\cdots\) |
4400.2.b.o |
$4400$ |
$2$ |
4400.b |
5.b |
$2$ |
$2$ |
$2$ |
$35.134$ |
\(\Q(\sqrt{-1}) \) |
None |
|
|
|
|
440.2.a.c |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q-2\beta q^{7}+3 q^{9}+q^{11}-3\beta q^{13}+\cdots\) |
4400.2.b.p |
$4400$ |
$2$ |
4400.b |
5.b |
$2$ |
$4$ |
$4$ |
$35.134$ |
\(\Q(i, \sqrt{33})\) |
None |
|
|
|
|
110.2.a.d |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+\beta _{1}q^{3}+\beta _{1}q^{7}+(-6+\beta _{3})q^{9}+q^{11}+\cdots\) |
4400.2.b.q |
$4400$ |
$2$ |
4400.b |
5.b |
$2$ |
$4$ |
$4$ |
$35.134$ |
\(\Q(\zeta_{8})\) |
None |
|
|
|
|
55.2.a.b |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2^{5}$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+\beta_{2} q^{3}-\beta_1 q^{7}-5 q^{9}-q^{11}+\cdots\) |
4400.2.b.r |
$4400$ |
$2$ |
4400.b |
5.b |
$2$ |
$4$ |
$4$ |
$35.134$ |
\(\Q(i, \sqrt{13})\) |
None |
|
|
|
|
1100.2.a.f |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+(\beta _{1}-\beta _{2})q^{3}+(-\beta _{1}+2\beta _{2})q^{7}+(-4+\cdots)q^{9}+\cdots\) |
4400.2.b.s |
$4400$ |
$2$ |
4400.b |
5.b |
$2$ |
$4$ |
$4$ |
$35.134$ |
\(\Q(i, \sqrt{21})\) |
None |
|
|
|
|
1100.2.a.g |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+\beta _{1}q^{3}+(\beta _{1}+3\beta _{2})q^{7}+(-3+\beta _{3})q^{9}+\cdots\) |
4400.2.b.t |
$4400$ |
$2$ |
4400.b |
5.b |
$2$ |
$4$ |
$4$ |
$35.134$ |
\(\Q(i, \sqrt{17})\) |
None |
|
|
|
|
440.2.a.e |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+\beta _{1}q^{3}-\beta _{1}q^{7}+(-2+\beta _{3})q^{9}-q^{11}+\cdots\) |
4400.2.b.u |
$4400$ |
$2$ |
4400.b |
5.b |
$2$ |
$4$ |
$4$ |
$35.134$ |
\(\Q(i, \sqrt{17})\) |
None |
|
|
|
|
440.2.a.f |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+\beta _{1}q^{3}+(\beta _{1}+\beta _{2})q^{7}+(-2+\beta _{3})q^{9}+\cdots\) |
4400.2.b.v |
$4400$ |
$2$ |
4400.b |
5.b |
$2$ |
$4$ |
$4$ |
$35.134$ |
\(\Q(i, \sqrt{17})\) |
None |
|
|
|
|
88.2.a.b |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+\beta _{1}q^{3}+2\beta _{1}q^{7}+(-2+\beta _{3})q^{9}+\cdots\) |
4400.2.b.w |
$4400$ |
$2$ |
4400.b |
5.b |
$2$ |
$4$ |
$4$ |
$35.134$ |
\(\Q(i, \sqrt{17})\) |
None |
|
|
|
|
440.2.a.g |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$2$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+\beta _{1}q^{3}+(-\beta _{1}+\beta _{2})q^{7}+(-2+\beta _{3})q^{9}+\cdots\) |
4400.2.b.x |
$4400$ |
$2$ |
4400.b |
5.b |
$2$ |
$4$ |
$4$ |
$35.134$ |
\(\Q(i, \sqrt{5})\) |
None |
|
|
|
|
275.2.a.d |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+(\beta _{1}-\beta _{3})q^{3}+(3\beta _{1}+2\beta _{3})q^{7}+(1+\cdots)q^{9}+\cdots\) |
4400.2.b.y |
$4400$ |
$2$ |
4400.b |
5.b |
$2$ |
$4$ |
$4$ |
$35.134$ |
\(\Q(i, \sqrt{13})\) |
None |
|
|
|
|
275.2.a.e |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+\beta _{1}q^{3}+(\beta _{1}+3\beta _{2})q^{7}+(-1+\beta _{3})q^{9}+\cdots\) |
4400.2.b.z |
$4400$ |
$2$ |
4400.b |
5.b |
$2$ |
$4$ |
$4$ |
$35.134$ |
\(\Q(i, \sqrt{5})\) |
None |
|
|
|
|
2200.2.a.p |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+\beta _{1}q^{3}+(\beta _{1}-\beta _{3})q^{7}+(2+\beta _{2})q^{9}+\cdots\) |
4400.2.b.ba |
$4400$ |
$2$ |
4400.b |
5.b |
$2$ |
$4$ |
$4$ |
$35.134$ |
\(\Q(i, \sqrt{5})\) |
None |
|
|
|
|
2200.2.a.n |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{3})q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\) |
4400.2.b.bb |
$4400$ |
$2$ |
4400.b |
5.b |
$2$ |
$6$ |
$6$ |
$35.134$ |
6.0.96668224.1 |
None |
|
|
|
|
2200.2.a.u |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+\beta _{1}q^{3}+(-\beta _{2}-\beta _{4})q^{7}+(-2+\beta _{3}+\cdots)q^{9}+\cdots\) |
4400.2.b.bc |
$4400$ |
$2$ |
4400.b |
5.b |
$2$ |
$6$ |
$6$ |
$35.134$ |
6.0.44836416.1 |
None |
|
|
|
|
2200.2.a.t |
$2$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
$\mathrm{SU}(2)[C_{2}]$ |
\(q+(\beta _{1}+\beta _{3})q^{3}+(-\beta _{3}-\beta _{5})q^{7}+(-2+\cdots)q^{9}+\cdots\) |
\( S_{2}^{\mathrm{old}}(4400, [\chi]) \simeq \)
\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 8}\)\(\oplus\)
\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 8}\)\(\oplus\)
\(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 10}\)\(\oplus\)
\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 4}\)\(\oplus\)
\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 6}\)\(\oplus\)
\(S_{2}^{\mathrm{new}}(110, [\chi])\)\(^{\oplus 8}\)\(\oplus\)
\(S_{2}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 4}\)\(\oplus\)
\(S_{2}^{\mathrm{new}}(220, [\chi])\)\(^{\oplus 6}\)\(\oplus\)
\(S_{2}^{\mathrm{new}}(275, [\chi])\)\(^{\oplus 5}\)\(\oplus\)
\(S_{2}^{\mathrm{new}}(400, [\chi])\)\(^{\oplus 2}\)\(\oplus\)
\(S_{2}^{\mathrm{new}}(440, [\chi])\)\(^{\oplus 4}\)\(\oplus\)
\(S_{2}^{\mathrm{new}}(550, [\chi])\)\(^{\oplus 4}\)\(\oplus\)
\(S_{2}^{\mathrm{new}}(880, [\chi])\)\(^{\oplus 2}\)\(\oplus\)
\(S_{2}^{\mathrm{new}}(1100, [\chi])\)\(^{\oplus 3}\)\(\oplus\)
\(S_{2}^{\mathrm{new}}(2200, [\chi])\)\(^{\oplus 2}\)