Defining parameters
Level: | \( N \) | \(=\) | \( 8092 = 2^{2} \cdot 7 \cdot 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8092.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 26 \) | ||
Sturm bound: | \(2448\) | ||
Trace bound: | \(11\) | ||
Distinguishing \(T_p\): | \(3\), \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8092))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1278 | 136 | 1142 |
Cusp forms | 1171 | 136 | 1035 |
Eisenstein series | 107 | 0 | 107 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(7\) | \(17\) | Fricke | Dim |
---|---|---|---|---|
\(-\) | \(+\) | \(+\) | \(-\) | \(32\) |
\(-\) | \(+\) | \(-\) | \(+\) | \(36\) |
\(-\) | \(-\) | \(+\) | \(+\) | \(32\) |
\(-\) | \(-\) | \(-\) | \(-\) | \(36\) |
Plus space | \(+\) | \(68\) | ||
Minus space | \(-\) | \(68\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8092))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8092))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(8092)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(68))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(119))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(238))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(289))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(476))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(578))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1156))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2023))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4046))\)\(^{\oplus 2}\)