Defining parameters
Level: | \( N \) | \(=\) | \( 275 = 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 275.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 11 \) | ||
Sturm bound: | \(120\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(275))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 96 | 48 | 48 |
Cusp forms | 84 | 48 | 36 |
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.
\(5\) | \(11\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | \(+\) | \(12\) |
\(+\) | \(-\) | \(-\) | \(10\) |
\(-\) | \(+\) | \(-\) | \(11\) |
\(-\) | \(-\) | \(+\) | \(15\) |
Plus space | \(+\) | \(27\) | |
Minus space | \(-\) | \(21\) |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(275))\) into newform subspaces
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(275))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_0(275)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(25))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 2}\)