Defining parameters
Level: | \( N \) | \(=\) | \( 112 = 2^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 112.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 12 \) | ||
Sturm bound: | \(192\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_0(112))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 182 | 33 | 149 |
Cusp forms | 170 | 33 | 137 |
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.
\(2\) | \(7\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(8\) |
\(+\) | \(-\) | $-$ | \(8\) |
\(-\) | \(+\) | $-$ | \(8\) |
\(-\) | \(-\) | $+$ | \(9\) |
Plus space | \(+\) | \(17\) | |
Minus space | \(-\) | \(16\) |
Trace form
Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_0(112))\) into newform subspaces
Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_0(112))\) into lower level spaces
\( S_{12}^{\mathrm{old}}(\Gamma_0(112)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 5}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(28))\)\(^{\oplus 3}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 2}\)