Defining parameters
Level: | \( N \) | \(=\) | \( 845 = 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 845.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 20 \) | ||
Sturm bound: | \(546\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(845))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 468 | 259 | 209 |
Cusp forms | 440 | 259 | 181 |
Eisenstein series | 28 | 0 | 28 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(5\) | \(13\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(61\) |
\(+\) | \(-\) | $-$ | \(68\) |
\(-\) | \(+\) | $-$ | \(68\) |
\(-\) | \(-\) | $+$ | \(62\) |
Plus space | \(+\) | \(123\) | |
Minus space | \(-\) | \(136\) |
Trace form
Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(845))\) into newform subspaces
Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(845))\) into lower level spaces
\( S_{6}^{\mathrm{old}}(\Gamma_0(845)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(13))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(65))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(169))\)\(^{\oplus 2}\)