Defining parameters
| Level: | \( N \) | \(=\) | \( 572 = 2^{2} \cdot 11 \cdot 13 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 572.a (trivial) |
| Character field: | \(\Q\) | ||
| Newform subspaces: | \( 5 \) | ||
| Sturm bound: | \(168\) | ||
| Trace bound: | \(5\) | ||
| Distinguishing \(T_p\): | \(3\), \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(572))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 90 | 10 | 80 |
| Cusp forms | 79 | 10 | 69 |
| 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.
| \(2\) | \(11\) | \(13\) | Fricke | Dim. |
|---|---|---|---|---|
| \(-\) | \(+\) | \(+\) | \(-\) | \(2\) |
| \(-\) | \(+\) | \(-\) | \(+\) | \(2\) |
| \(-\) | \(-\) | \(+\) | \(+\) | \(3\) |
| \(-\) | \(-\) | \(-\) | \(-\) | \(3\) |
| Plus space | \(+\) | \(5\) | ||
| Minus space | \(-\) | \(5\) | ||
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(572))\) into newform subspaces
| Label | Dim. | \(A\) | Field | CM | Traces | A-L signs | $q$-expansion | ||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(a_2\) | \(a_3\) | \(a_5\) | \(a_7\) | 2 | 11 | 13 | |||||||
| 572.2.a.a | \(1\) | \(4.567\) | \(\Q\) | None | \(0\) | \(1\) | \(3\) | \(2\) | \(-\) | \(-\) | \(-\) | \(q+q^{3}+3q^{5}+2q^{7}-2q^{9}+q^{11}+\cdots\) | |
| 572.2.a.b | \(2\) | \(4.567\) | \(\Q(\sqrt{13}) \) | None | \(0\) | \(-3\) | \(0\) | \(-3\) | \(-\) | \(+\) | \(-\) | \(q+(-1-\beta )q^{3}+(-2+\beta )q^{7}+(1+3\beta )q^{9}+\cdots\) | |
| 572.2.a.c | \(2\) | \(4.567\) | \(\Q(\sqrt{21}) \) | None | \(0\) | \(1\) | \(-4\) | \(3\) | \(-\) | \(-\) | \(-\) | \(q+\beta q^{3}-2q^{5}+(1+\beta )q^{7}+(2+\beta )q^{9}+\cdots\) | |
| 572.2.a.d | \(2\) | \(4.567\) | \(\Q(\sqrt{21}) \) | None | \(0\) | \(1\) | \(4\) | \(5\) | \(-\) | \(+\) | \(+\) | \(q+\beta q^{3}+2q^{5}+(3-\beta )q^{7}+(2+\beta )q^{9}+\cdots\) | |
| 572.2.a.e | \(3\) | \(4.567\) | 3.3.229.1 | None | \(0\) | \(-2\) | \(-1\) | \(-7\) | \(-\) | \(-\) | \(+\) | \(q+(-1-\beta _{2})q^{3}+(\beta _{1}+\beta _{2})q^{5}+(-2+\cdots)q^{7}+\cdots\) | |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(572))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(572)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(143))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(286))\)\(^{\oplus 2}\)