Defining parameters
Level: | \( N \) | \(=\) | \( 2 \) |
Weight: | \( k \) | \(=\) | \( 84 \) |
Character orbit: | \([\chi]\) | \(=\) | 2.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(21\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{84}(\Gamma_0(2))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 22 | 6 | 16 |
Cusp forms | 20 | 6 | 14 |
Eisenstein series | 2 | 0 | 2 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | Dim |
---|---|
\(+\) | \(3\) |
\(-\) | \(3\) |
Trace form
Decomposition of \(S_{84}^{\mathrm{new}}(\Gamma_0(2))\) into newform subspaces
Decomposition of \(S_{84}^{\mathrm{old}}(\Gamma_0(2))\) into lower level spaces
\( S_{84}^{\mathrm{old}}(\Gamma_0(2)) \cong \) \(S_{84}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 2}\)