Defining parameters
Level: | \( N \) | \(=\) | \( 63 = 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 63.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 8 \) | ||
Sturm bound: | \(48\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(63))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 44 | 13 | 31 |
Cusp forms | 36 | 13 | 23 |
Eisenstein series | 8 | 0 | 8 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(3\) | \(7\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(2\) |
\(+\) | \(-\) | $-$ | \(4\) |
\(-\) | \(+\) | $-$ | \(4\) |
\(-\) | \(-\) | $+$ | \(3\) |
Plus space | \(+\) | \(5\) | |
Minus space | \(-\) | \(8\) |
Trace form
Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(63))\) into newform subspaces
Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(63))\) into lower level spaces
\( S_{6}^{\mathrm{old}}(\Gamma_0(63)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 2}\)