Defining parameters
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 24 \) | ||
Sturm bound: | \(320\) | ||
Trace bound: | \(11\) | ||
Distinguishing \(T_p\): | \(2\), \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(525))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 252 | 56 | 196 |
Cusp forms | 228 | 56 | 172 |
Eisenstein series | 24 | 0 | 24 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(3\) | \(5\) | \(7\) | Fricke | Dim |
---|---|---|---|---|
\(+\) | \(+\) | \(+\) | \(+\) | \(6\) |
\(+\) | \(+\) | \(-\) | \(-\) | \(8\) |
\(+\) | \(-\) | \(+\) | \(-\) | \(7\) |
\(+\) | \(-\) | \(-\) | \(+\) | \(7\) |
\(-\) | \(+\) | \(+\) | \(-\) | \(5\) |
\(-\) | \(+\) | \(-\) | \(+\) | \(9\) |
\(-\) | \(-\) | \(+\) | \(+\) | \(9\) |
\(-\) | \(-\) | \(-\) | \(-\) | \(5\) |
Plus space | \(+\) | \(31\) | ||
Minus space | \(-\) | \(25\) |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(525))\) into newform subspaces
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(525))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_0(525)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(105))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(175))\)\(^{\oplus 2}\)