Defining parameters
Level: | \( N \) | \(=\) | \( 1734 = 2 \cdot 3 \cdot 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1734.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 23 \) | ||
Sturm bound: | \(612\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(5\), \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1734))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 342 | 45 | 297 |
Cusp forms | 271 | 45 | 226 |
Eisenstein series | 71 | 0 | 71 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(3\) | \(17\) | Fricke | Dim |
---|---|---|---|---|
\(+\) | \(+\) | \(+\) | \(+\) | \(3\) |
\(+\) | \(+\) | \(-\) | \(-\) | \(8\) |
\(+\) | \(-\) | \(+\) | \(-\) | \(6\) |
\(+\) | \(-\) | \(-\) | \(+\) | \(5\) |
\(-\) | \(+\) | \(+\) | \(-\) | \(8\) |
\(-\) | \(+\) | \(-\) | \(+\) | \(4\) |
\(-\) | \(-\) | \(+\) | \(+\) | \(2\) |
\(-\) | \(-\) | \(-\) | \(-\) | \(9\) |
Plus space | \(+\) | \(14\) | ||
Minus space | \(-\) | \(31\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1734))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1734))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(1734)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(51))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(102))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(289))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(578))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(867))\)\(^{\oplus 2}\)