Defining parameters
Level: | \( N \) | \(=\) | \( 800 = 2^{5} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 800.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 14 \) | ||
Sturm bound: | \(240\) | ||
Trace bound: | \(13\) | ||
Distinguishing \(T_p\): | \(3\), \(11\), \(13\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(800))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 144 | 19 | 125 |
Cusp forms | 97 | 19 | 78 |
Eisenstein series | 47 | 0 | 47 |
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 |
---|---|---|---|
\(+\) | \(+\) | \(+\) | \(3\) |
\(+\) | \(-\) | \(-\) | \(6\) |
\(-\) | \(+\) | \(-\) | \(6\) |
\(-\) | \(-\) | \(+\) | \(4\) |
Plus space | \(+\) | \(7\) | |
Minus space | \(-\) | \(12\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(800))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(800))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(800)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(100))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(160))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(200))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(400))\)\(^{\oplus 2}\)