Defining parameters
Level: | \( N \) | \(=\) | \( 325 = 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 325.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 12 \) | ||
Sturm bound: | \(350\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_0(325))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 320 | 171 | 149 |
Cusp forms | 308 | 171 | 137 |
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.
\(5\) | \(13\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | \(+\) | \(39\) |
\(+\) | \(-\) | \(-\) | \(42\) |
\(-\) | \(+\) | \(-\) | \(46\) |
\(-\) | \(-\) | \(+\) | \(44\) |
Plus space | \(+\) | \(83\) | |
Minus space | \(-\) | \(88\) |
Trace form
Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(325))\) into newform subspaces
Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_0(325))\) into lower level spaces
\( S_{10}^{\mathrm{old}}(\Gamma_0(325)) \simeq \) \(S_{10}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(13))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(25))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(65))\)\(^{\oplus 2}\)