Defining parameters
Level: | \( N \) | \(=\) | \( 50 = 2 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 50.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 10 \) | ||
Sturm bound: | \(90\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_0(50))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 89 | 17 | 72 |
Cusp forms | 77 | 17 | 60 |
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.
\(2\) | \(5\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | \(+\) | \(5\) |
\(+\) | \(-\) | \(-\) | \(4\) |
\(-\) | \(+\) | \(-\) | \(3\) |
\(-\) | \(-\) | \(+\) | \(5\) |
Plus space | \(+\) | \(10\) | |
Minus space | \(-\) | \(7\) |
Trace form
Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_0(50))\) into newform subspaces
Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_0(50))\) into lower level spaces
\( S_{12}^{\mathrm{old}}(\Gamma_0(50)) \simeq \) \(S_{12}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(10))\)\(^{\oplus 2}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(25))\)\(^{\oplus 2}\)