Defining parameters
Level: | \( N \) | \(=\) | \( 528 = 2^{4} \cdot 3 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 528.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 10 \) | ||
Sturm bound: | \(192\) | ||
Trace bound: | \(11\) | ||
Distinguishing \(T_p\): | \(5\), \(7\), \(13\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(528))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 108 | 10 | 98 |
Cusp forms | 85 | 10 | 75 |
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.
\(2\) | \(3\) | \(11\) | Fricke | Dim |
---|---|---|---|---|
\(+\) | \(+\) | \(+\) | $+$ | \(1\) |
\(+\) | \(+\) | \(-\) | $-$ | \(2\) |
\(+\) | \(-\) | \(+\) | $-$ | \(1\) |
\(-\) | \(+\) | \(+\) | $-$ | \(2\) |
\(-\) | \(+\) | \(-\) | $+$ | \(1\) |
\(-\) | \(-\) | \(+\) | $+$ | \(1\) |
\(-\) | \(-\) | \(-\) | $-$ | \(2\) |
Plus space | \(+\) | \(3\) | ||
Minus space | \(-\) | \(7\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(528))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(528))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(528)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(88))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(132))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(176))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(264))\)\(^{\oplus 2}\)