Defining parameters
Level: | \( N \) | \(=\) | \( 2057 = 11^{2} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2057.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 22 \) | ||
Sturm bound: | \(792\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(2\), \(3\), \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(2057))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 606 | 436 | 170 |
Cusp forms | 582 | 436 | 146 |
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.
\(11\) | \(17\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(112\) |
\(+\) | \(-\) | $-$ | \(104\) |
\(-\) | \(+\) | $-$ | \(105\) |
\(-\) | \(-\) | $+$ | \(115\) |
Plus space | \(+\) | \(227\) | |
Minus space | \(-\) | \(209\) |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(2057))\) into newform subspaces
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(2057))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_0(2057)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(187))\)\(^{\oplus 2}\)