Defining parameters
Level: | \( N \) | \(=\) | \( 522 = 2 \cdot 3^{2} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 522.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 17 \) | ||
Sturm bound: | \(360\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(522))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 278 | 35 | 243 |
Cusp forms | 262 | 35 | 227 |
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.
\(2\) | \(3\) | \(29\) | Fricke | Dim |
---|---|---|---|---|
\(+\) | \(+\) | \(+\) | $+$ | \(4\) |
\(+\) | \(+\) | \(-\) | $-$ | \(3\) |
\(+\) | \(-\) | \(+\) | $-$ | \(6\) |
\(+\) | \(-\) | \(-\) | $+$ | \(5\) |
\(-\) | \(+\) | \(+\) | $-$ | \(3\) |
\(-\) | \(+\) | \(-\) | $+$ | \(4\) |
\(-\) | \(-\) | \(+\) | $+$ | \(6\) |
\(-\) | \(-\) | \(-\) | $-$ | \(4\) |
Plus space | \(+\) | \(19\) | ||
Minus space | \(-\) | \(16\) |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(522))\) into newform subspaces
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(522))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_0(522)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(18))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(29))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(58))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(87))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(174))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(261))\)\(^{\oplus 2}\)