Defining parameters
Level: | \( N \) | \(=\) | \( 567 = 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 567.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 9 \) | ||
Sturm bound: | \(144\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(567))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 84 | 24 | 60 |
Cusp forms | 61 | 24 | 37 |
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.
\(3\) | \(7\) | Fricke | Total | Cusp | Eisenstein | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
All | New | Old | All | New | Old | All | New | Old | ||||||
\(+\) | \(+\) | \(+\) | \(18\) | \(5\) | \(13\) | \(13\) | \(5\) | \(8\) | \(5\) | \(0\) | \(5\) | |||
\(+\) | \(-\) | \(-\) | \(24\) | \(9\) | \(15\) | \(18\) | \(9\) | \(9\) | \(6\) | \(0\) | \(6\) | |||
\(-\) | \(+\) | \(-\) | \(24\) | \(7\) | \(17\) | \(18\) | \(7\) | \(11\) | \(6\) | \(0\) | \(6\) | |||
\(-\) | \(-\) | \(+\) | \(18\) | \(3\) | \(15\) | \(12\) | \(3\) | \(9\) | \(6\) | \(0\) | \(6\) | |||
Plus space | \(+\) | \(36\) | \(8\) | \(28\) | \(25\) | \(8\) | \(17\) | \(11\) | \(0\) | \(11\) | ||||
Minus space | \(-\) | \(48\) | \(16\) | \(32\) | \(36\) | \(16\) | \(20\) | \(12\) | \(0\) | \(12\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(567))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(567))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(567)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(81))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(189))\)\(^{\oplus 2}\)