Defining parameters
Level: | \( N \) | \(=\) | \( 1335 = 3 \cdot 5 \cdot 89 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1335.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 11 \) | ||
Sturm bound: | \(360\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1335))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 184 | 59 | 125 |
Cusp forms | 177 | 59 | 118 |
Eisenstein series | 7 | 0 | 7 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(3\) | \(5\) | \(89\) | Fricke | Dim |
---|---|---|---|---|
\(+\) | \(+\) | \(+\) | $+$ | \(6\) |
\(+\) | \(+\) | \(-\) | $-$ | \(9\) |
\(+\) | \(-\) | \(+\) | $-$ | \(10\) |
\(+\) | \(-\) | \(-\) | $+$ | \(3\) |
\(-\) | \(+\) | \(+\) | $-$ | \(11\) |
\(-\) | \(+\) | \(-\) | $+$ | \(4\) |
\(-\) | \(-\) | \(+\) | $+$ | \(3\) |
\(-\) | \(-\) | \(-\) | $-$ | \(13\) |
Plus space | \(+\) | \(16\) | ||
Minus space | \(-\) | \(43\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1335))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1335))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(1335)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(89))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(267))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(445))\)\(^{\oplus 2}\)