Defining parameters
Level: | \( N \) | \(=\) | \( 605 = 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 605.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 13 \) | ||
Sturm bound: | \(132\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(2\), \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(605))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 78 | 37 | 41 |
Cusp forms | 55 | 37 | 18 |
Eisenstein series | 23 | 0 | 23 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(5\) | \(11\) | Fricke | Dim. |
---|---|---|---|
\(+\) | \(+\) | \(+\) | \(6\) |
\(+\) | \(-\) | \(-\) | \(12\) |
\(-\) | \(+\) | \(-\) | \(12\) |
\(-\) | \(-\) | \(+\) | \(7\) |
Plus space | \(+\) | \(13\) | |
Minus space | \(-\) | \(24\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(605))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(605))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(605)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 2}\)