Defining parameters
Level: | \( N \) | \(=\) | \( 75 = 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 22 \) |
Character orbit: | \([\chi]\) | \(=\) | 75.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 14 \) | ||
Sturm bound: | \(220\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{22}(\Gamma_0(75))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 216 | 66 | 150 |
Cusp forms | 204 | 66 | 138 |
Eisenstein series | 12 | 0 | 12 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(3\) | \(5\) | Fricke | Dim. |
---|---|---|---|
\(+\) | \(+\) | \(+\) | \(15\) |
\(+\) | \(-\) | \(-\) | \(18\) |
\(-\) | \(+\) | \(-\) | \(17\) |
\(-\) | \(-\) | \(+\) | \(16\) |
Plus space | \(+\) | \(31\) | |
Minus space | \(-\) | \(35\) |
Trace form
Decomposition of \(S_{22}^{\mathrm{new}}(\Gamma_0(75))\) into newform subspaces
Decomposition of \(S_{22}^{\mathrm{old}}(\Gamma_0(75))\) into lower level spaces
\( S_{22}^{\mathrm{old}}(\Gamma_0(75)) \cong \) \(S_{22}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_0(25))\)\(^{\oplus 2}\)