Defining parameters
Level: | \( N \) | \(=\) | \( 663 = 3 \cdot 13 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 663.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 10 \) | ||
Sturm bound: | \(336\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(663))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 256 | 96 | 160 |
Cusp forms | 248 | 96 | 152 |
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.
\(3\) | \(13\) | \(17\) | Fricke | Dim |
---|---|---|---|---|
\(+\) | \(+\) | \(+\) | $+$ | \(13\) |
\(+\) | \(+\) | \(-\) | $-$ | \(9\) |
\(+\) | \(-\) | \(+\) | $-$ | \(11\) |
\(+\) | \(-\) | \(-\) | $+$ | \(15\) |
\(-\) | \(+\) | \(+\) | $-$ | \(11\) |
\(-\) | \(+\) | \(-\) | $+$ | \(15\) |
\(-\) | \(-\) | \(+\) | $+$ | \(13\) |
\(-\) | \(-\) | \(-\) | $-$ | \(9\) |
Plus space | \(+\) | \(56\) | ||
Minus space | \(-\) | \(40\) |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(663))\) into newform subspaces
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(663))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_0(663)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(13))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(51))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(221))\)\(^{\oplus 2}\)