Defining parameters
Level: | \( N \) | \(=\) | \( 5225 = 5^{2} \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5225.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 29 \) | ||
Sturm bound: | \(1200\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(2\), \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5225))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 612 | 286 | 326 |
Cusp forms | 589 | 286 | 303 |
Eisenstein series | 23 | 0 | 23 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(5\) | \(11\) | \(19\) | Fricke | Dim. |
---|---|---|---|---|
\(+\) | \(+\) | \(+\) | \(+\) | \(32\) |
\(+\) | \(+\) | \(-\) | \(-\) | \(37\) |
\(+\) | \(-\) | \(+\) | \(-\) | \(35\) |
\(+\) | \(-\) | \(-\) | \(+\) | \(30\) |
\(-\) | \(+\) | \(+\) | \(-\) | \(41\) |
\(-\) | \(+\) | \(-\) | \(+\) | \(31\) |
\(-\) | \(-\) | \(+\) | \(+\) | \(35\) |
\(-\) | \(-\) | \(-\) | \(-\) | \(45\) |
Plus space | \(+\) | \(128\) | ||
Minus space | \(-\) | \(158\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5225))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5225))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(5225)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(95))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(209))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(275))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(475))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1045))\)\(^{\oplus 2}\)