Defining parameters
Level: | \( N \) | \(=\) | \( 1408 = 2^{7} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1408.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 20 \) | ||
Sturm bound: | \(384\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(3\), \(5\), \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1408))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 208 | 40 | 168 |
Cusp forms | 177 | 40 | 137 |
Eisenstein series | 31 | 0 | 31 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(11\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | \(+\) | \(9\) |
\(+\) | \(-\) | \(-\) | \(11\) |
\(-\) | \(+\) | \(-\) | \(11\) |
\(-\) | \(-\) | \(+\) | \(9\) |
Plus space | \(+\) | \(18\) | |
Minus space | \(-\) | \(22\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1408))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1408))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(1408)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(88))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(128))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(176))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(352))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(704))\)\(^{\oplus 2}\)