Defining parameters
| Level: | \( N \) | = | \( 8020 = 2^{2} \cdot 5 \cdot 401 \) |
| Weight: | \( k \) | = | \( 2 \) |
| Character orbit: | \([\chi]\) | = | 8020.a (trivial) |
| Character field: | \(\Q\) | ||
| Newform subspaces: | \( 6 \) | ||
| Sturm bound: | \(2412\) | ||
| Trace bound: | \(1\) | ||
| Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8020))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 1212 | 132 | 1080 |
| Cusp forms | 1201 | 132 | 1069 |
| Eisenstein series | 11 | 0 | 11 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
| \(2\) | \(5\) | \(401\) | Fricke | Dim. |
|---|---|---|---|---|
| \(-\) | \(+\) | \(+\) | \(-\) | \(37\) |
| \(-\) | \(+\) | \(-\) | \(+\) | \(29\) |
| \(-\) | \(-\) | \(+\) | \(+\) | \(29\) |
| \(-\) | \(-\) | \(-\) | \(-\) | \(37\) |
| Plus space | \(+\) | \(58\) | ||
| Minus space | \(-\) | \(74\) | ||
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8020))\) into newform subspaces
| Label | Dim. | \(A\) | Field | CM | Traces | A-L signs | $q$-expansion | ||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(a_2\) | \(a_3\) | \(a_5\) | \(a_7\) | 2 | 5 | 401 | |||||||
| 8020.2.a.a | \(1\) | \(64.040\) | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(-2\) | \(-\) | \(+\) | \(-\) | \(q-q^{5}-2q^{7}-3q^{9}-4q^{11}+4q^{13}+\cdots\) | |
| 8020.2.a.b | \(2\) | \(64.040\) | \(\Q(\sqrt{3}) \) | None | \(0\) | \(-2\) | \(-2\) | \(0\) | \(-\) | \(+\) | \(+\) | \(q+(-1+\beta )q^{3}-q^{5}+2\beta q^{7}+(1-2\beta )q^{9}+\cdots\) | |
| 8020.2.a.c | \(28\) | \(64.040\) | None | \(0\) | \(3\) | \(-28\) | \(-4\) | \(-\) | \(+\) | \(-\) | |||
| 8020.2.a.d | \(29\) | \(64.040\) | None | \(0\) | \(-3\) | \(29\) | \(-8\) | \(-\) | \(-\) | \(+\) | |||
| 8020.2.a.e | \(35\) | \(64.040\) | None | \(0\) | \(-1\) | \(-35\) | \(6\) | \(-\) | \(+\) | \(+\) | |||
| 8020.2.a.f | \(37\) | \(64.040\) | None | \(0\) | \(3\) | \(37\) | \(4\) | \(-\) | \(-\) | \(-\) | |||
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8020))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(8020)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(401))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(802))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1604))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2005))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4010))\)\(^{\oplus 2}\)