Defining parameters
Level: | \( N \) | \(=\) | \( 669 = 3 \cdot 223 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 669.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 9 \) | ||
Sturm bound: | \(149\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(669))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 76 | 37 | 39 |
Cusp forms | 73 | 37 | 36 |
Eisenstein series | 3 | 0 | 3 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(3\) | \(223\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(11\) |
\(+\) | \(-\) | $-$ | \(7\) |
\(-\) | \(+\) | $-$ | \(14\) |
\(-\) | \(-\) | $+$ | \(5\) |
Plus space | \(+\) | \(16\) | |
Minus space | \(-\) | \(21\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(669))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(669))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(669)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(223))\)\(^{\oplus 2}\)