Defining parameters
Level: | \( N \) | \(=\) | \( 832 = 2^{6} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 832.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 16 \) | ||
Sturm bound: | \(224\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(3\), \(5\), \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(832))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 124 | 24 | 100 |
Cusp forms | 101 | 24 | 77 |
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.
\(2\) | \(13\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | \(+\) | \(5\) |
\(+\) | \(-\) | \(-\) | \(7\) |
\(-\) | \(+\) | \(-\) | \(7\) |
\(-\) | \(-\) | \(+\) | \(5\) |
Plus space | \(+\) | \(10\) | |
Minus space | \(-\) | \(14\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(832))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(832))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(832)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(104))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(208))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(416))\)\(^{\oplus 2}\)