Defining parameters
Level: | \( N \) | \(=\) | \( 99 = 3^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 14 \) |
Character orbit: | \([\chi]\) | \(=\) | 99.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 9 \) | ||
Sturm bound: | \(168\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{14}(\Gamma_0(99))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 160 | 54 | 106 |
Cusp forms | 152 | 54 | 98 |
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.
\(3\) | \(11\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(11\) |
\(+\) | \(-\) | $-$ | \(11\) |
\(-\) | \(+\) | $-$ | \(17\) |
\(-\) | \(-\) | $+$ | \(15\) |
Plus space | \(+\) | \(26\) | |
Minus space | \(-\) | \(28\) |
Trace form
Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_0(99))\) into newform subspaces
Decomposition of \(S_{14}^{\mathrm{old}}(\Gamma_0(99))\) into lower level spaces
\( S_{14}^{\mathrm{old}}(\Gamma_0(99)) \cong \) \(S_{14}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 3}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 2}\)