Defining parameters
Level: | \( N \) | \(=\) | \( 1911 = 3 \cdot 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1911.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 33 \) | ||
Sturm bound: | \(1045\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(2\), \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(1911))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 800 | 246 | 554 |
Cusp forms | 768 | 246 | 522 |
Eisenstein series | 32 | 0 | 32 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(3\) | \(7\) | \(13\) | Fricke | Dim. |
---|---|---|---|---|
\(+\) | \(+\) | \(+\) | \(+\) | \(33\) |
\(+\) | \(+\) | \(-\) | \(-\) | \(27\) |
\(+\) | \(-\) | \(+\) | \(-\) | \(30\) |
\(+\) | \(-\) | \(-\) | \(+\) | \(33\) |
\(-\) | \(+\) | \(+\) | \(-\) | \(25\) |
\(-\) | \(+\) | \(-\) | \(+\) | \(35\) |
\(-\) | \(-\) | \(+\) | \(+\) | \(36\) |
\(-\) | \(-\) | \(-\) | \(-\) | \(27\) |
Plus space | \(+\) | \(137\) | ||
Minus space | \(-\) | \(109\) |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(1911))\) into newform subspaces
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(1911))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_0(1911)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(13))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(91))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(147))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(273))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(637))\)\(^{\oplus 2}\)