Defining parameters
Level: | \( N \) | \(=\) | \( 368 = 2^{4} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 368.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 14 \) | ||
Sturm bound: | \(192\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(368))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 150 | 33 | 117 |
Cusp forms | 138 | 33 | 105 |
Eisenstein series | 12 | 0 | 12 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(23\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | \(+\) | \(8\) |
\(+\) | \(-\) | \(-\) | \(8\) |
\(-\) | \(+\) | \(-\) | \(7\) |
\(-\) | \(-\) | \(+\) | \(10\) |
Plus space | \(+\) | \(18\) | |
Minus space | \(-\) | \(15\) |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(368))\) into newform subspaces
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(368))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_0(368)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(92))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(184))\)\(^{\oplus 2}\)