Defining parameters
Level: | \( N \) | \(=\) | \( 7225 = 5^{2} \cdot 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7225.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 54 \) | ||
Sturm bound: | \(1530\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(2\), \(3\), \(7\), \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(7225))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 818 | 451 | 367 |
Cusp forms | 711 | 406 | 305 |
Eisenstein series | 107 | 45 | 62 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(5\) | \(17\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(96\) |
\(+\) | \(-\) | $-$ | \(100\) |
\(-\) | \(+\) | $-$ | \(109\) |
\(-\) | \(-\) | $+$ | \(101\) |
Plus space | \(+\) | \(197\) | |
Minus space | \(-\) | \(209\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7225))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7225))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(7225)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(85))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(289))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(425))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1445))\)\(^{\oplus 2}\)