Defining parameters
Level: | \( N \) | \(=\) | \( 693 = 3^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 693.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 21 \) | ||
Sturm bound: | \(384\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(2\), \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(693))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 296 | 76 | 220 |
Cusp forms | 280 | 76 | 204 |
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.
\(3\) | \(7\) | \(11\) | Fricke | Dim |
---|---|---|---|---|
\(+\) | \(+\) | \(+\) | \(+\) | \(8\) |
\(+\) | \(+\) | \(-\) | \(-\) | \(8\) |
\(+\) | \(-\) | \(+\) | \(-\) | \(8\) |
\(+\) | \(-\) | \(-\) | \(+\) | \(8\) |
\(-\) | \(+\) | \(+\) | \(-\) | \(11\) |
\(-\) | \(+\) | \(-\) | \(+\) | \(11\) |
\(-\) | \(-\) | \(+\) | \(+\) | \(13\) |
\(-\) | \(-\) | \(-\) | \(-\) | \(9\) |
Plus space | \(+\) | \(40\) | ||
Minus space | \(-\) | \(36\) |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(693))\) into newform subspaces
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(693))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_0(693)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(99))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(231))\)\(^{\oplus 2}\)