Defining parameters
Level: | \( N \) | \(=\) | \( 207 = 3^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 207.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 8 \) | ||
Sturm bound: | \(96\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(207))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 76 | 27 | 49 |
Cusp forms | 68 | 27 | 41 |
Eisenstein series | 8 | 0 | 8 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(3\) | \(23\) | Fricke | Total | Cusp | Eisenstein | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
All | New | Old | All | New | Old | All | New | Old | ||||||
\(+\) | \(+\) | \(+\) | \(22\) | \(5\) | \(17\) | \(20\) | \(5\) | \(15\) | \(2\) | \(0\) | \(2\) | |||
\(+\) | \(-\) | \(-\) | \(16\) | \(5\) | \(11\) | \(14\) | \(5\) | \(9\) | \(2\) | \(0\) | \(2\) | |||
\(-\) | \(+\) | \(-\) | \(19\) | \(7\) | \(12\) | \(17\) | \(7\) | \(10\) | \(2\) | \(0\) | \(2\) | |||
\(-\) | \(-\) | \(+\) | \(19\) | \(10\) | \(9\) | \(17\) | \(10\) | \(7\) | \(2\) | \(0\) | \(2\) | |||
Plus space | \(+\) | \(41\) | \(15\) | \(26\) | \(37\) | \(15\) | \(22\) | \(4\) | \(0\) | \(4\) | ||||
Minus space | \(-\) | \(35\) | \(12\) | \(23\) | \(31\) | \(12\) | \(19\) | \(4\) | \(0\) | \(4\) |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(207))\) into newform subspaces
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(207))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_0(207)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(69))\)\(^{\oplus 2}\)