Defining parameters
Level: | \( N \) | \(=\) | \( 448 = 2^{6} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 448.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 24 \) | ||
Sturm bound: | \(256\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(3\), \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(448))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 204 | 36 | 168 |
Cusp forms | 180 | 36 | 144 |
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.
\(2\) | \(7\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | \(+\) | \(9\) |
\(+\) | \(-\) | \(-\) | \(8\) |
\(-\) | \(+\) | \(-\) | \(9\) |
\(-\) | \(-\) | \(+\) | \(10\) |
Plus space | \(+\) | \(19\) | |
Minus space | \(-\) | \(17\) |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(448))\) into newform subspaces
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(448))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_0(448)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 7}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(28))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(224))\)\(^{\oplus 2}\)