Defining parameters
Level: | \( N \) | \(=\) | \( 735 = 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 735.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 15 \) | ||
Sturm bound: | \(224\) | ||
Trace bound: | \(4\) | ||
Distinguishing \(T_p\): | \(2\), \(13\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(735))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 128 | 28 | 100 |
Cusp forms | 97 | 28 | 69 |
Eisenstein series | 31 | 0 | 31 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(3\) | \(5\) | \(7\) | Fricke | Dim |
---|---|---|---|---|
\(+\) | \(+\) | \(+\) | \(+\) | \(2\) |
\(+\) | \(+\) | \(-\) | \(-\) | \(4\) |
\(+\) | \(-\) | \(+\) | \(-\) | \(6\) |
\(+\) | \(-\) | \(-\) | \(+\) | \(1\) |
\(-\) | \(+\) | \(+\) | \(-\) | \(5\) |
\(-\) | \(+\) | \(-\) | \(+\) | \(3\) |
\(-\) | \(-\) | \(+\) | \(+\) | \(1\) |
\(-\) | \(-\) | \(-\) | \(-\) | \(6\) |
Plus space | \(+\) | \(7\) | ||
Minus space | \(-\) | \(21\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(735))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(735))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(735)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(105))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(147))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(245))\)\(^{\oplus 2}\)