Defining parameters
Level: | \( N \) | \(=\) | \( 245 = 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 245.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 15 \) | ||
Sturm bound: | \(280\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(2\), \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_0(245))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 260 | 123 | 137 |
Cusp forms | 244 | 123 | 121 |
Eisenstein series | 16 | 0 | 16 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(5\) | \(7\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | \(+\) | \(29\) |
\(+\) | \(-\) | \(-\) | \(33\) |
\(-\) | \(+\) | \(-\) | \(31\) |
\(-\) | \(-\) | \(+\) | \(30\) |
Plus space | \(+\) | \(59\) | |
Minus space | \(-\) | \(64\) |
Trace form
Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(245))\) into newform subspaces
Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_0(245))\) into lower level spaces
\( S_{10}^{\mathrm{old}}(\Gamma_0(245)) \simeq \) \(S_{10}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 2}\)