Defining parameters
Level: | \( N \) | \(=\) | \( 162 = 2 \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 162.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 8 \) | ||
Sturm bound: | \(108\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(162))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 93 | 12 | 81 |
Cusp forms | 69 | 12 | 57 |
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.
\(2\) | \(3\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(3\) |
\(+\) | \(-\) | $-$ | \(3\) |
\(-\) | \(+\) | $-$ | \(2\) |
\(-\) | \(-\) | $+$ | \(4\) |
Plus space | \(+\) | \(7\) | |
Minus space | \(-\) | \(5\) |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(162))\) into newform subspaces
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(162))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_0(162)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(18))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(54))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(81))\)\(^{\oplus 2}\)