Defining parameters
Level: | \( N \) | \(=\) | \( 325 = 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 325.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 11 \) | ||
Sturm bound: | \(70\) | ||
Trace bound: | \(6\) | ||
Distinguishing \(T_p\): | \(2\), \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(325))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 40 | 19 | 21 |
Cusp forms | 29 | 19 | 10 |
Eisenstein series | 11 | 0 | 11 |
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 |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(3\) |
\(+\) | \(-\) | $-$ | \(6\) |
\(-\) | \(+\) | $-$ | \(6\) |
\(-\) | \(-\) | $+$ | \(4\) |
Plus space | \(+\) | \(7\) | |
Minus space | \(-\) | \(12\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(325))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(325))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(325)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(65))\)\(^{\oplus 2}\)