Defining parameters
Level: | \( N \) | \(=\) | \( 8752 = 2^{4} \cdot 547 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8752.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 26 \) | ||
Sturm bound: | \(2192\) | ||
Trace bound: | \(11\) | ||
Distinguishing \(T_p\): | \(3\), \(5\), \(7\), \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8752))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1102 | 273 | 829 |
Cusp forms | 1091 | 273 | 818 |
Eisenstein series | 11 | 0 | 11 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(547\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(64\) |
\(+\) | \(-\) | $-$ | \(73\) |
\(-\) | \(+\) | $-$ | \(68\) |
\(-\) | \(-\) | $+$ | \(68\) |
Plus space | \(+\) | \(132\) | |
Minus space | \(-\) | \(141\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8752))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8752))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(8752)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(547))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1094))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2188))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4376))\)\(^{\oplus 2}\)