Defining parameters
Level: | \( N \) | \(=\) | \( 5052 = 2^{2} \cdot 3 \cdot 421 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5052.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 7 \) | ||
Sturm bound: | \(1688\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5052))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 850 | 70 | 780 |
Cusp forms | 839 | 70 | 769 |
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.
\(2\) | \(3\) | \(421\) | Fricke | Dim |
---|---|---|---|---|
\(-\) | \(+\) | \(+\) | \(-\) | \(15\) |
\(-\) | \(+\) | \(-\) | \(+\) | \(20\) |
\(-\) | \(-\) | \(+\) | \(+\) | \(15\) |
\(-\) | \(-\) | \(-\) | \(-\) | \(20\) |
Plus space | \(+\) | \(35\) | ||
Minus space | \(-\) | \(35\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5052))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5052))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(5052)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(421))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(842))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1263))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1684))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2526))\)\(^{\oplus 2}\)