Defining parameters
Level: | \( N \) | \(=\) | \( 847 = 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 847.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 18 \) | ||
Sturm bound: | \(352\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(847))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 276 | 163 | 113 |
Cusp forms | 252 | 163 | 89 |
Eisenstein series | 24 | 0 | 24 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(7\) | \(11\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | \(+\) | \(41\) |
\(+\) | \(-\) | \(-\) | \(40\) |
\(-\) | \(+\) | \(-\) | \(37\) |
\(-\) | \(-\) | \(+\) | \(45\) |
Plus space | \(+\) | \(86\) | |
Minus space | \(-\) | \(77\) |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(847))\) into newform subspaces
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(847))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_0(847)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 2}\)