Defining parameters
Level: | \( N \) | \(=\) | \( 1856 = 2^{6} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1856.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 29 \) | ||
Sturm bound: | \(480\) | ||
Trace bound: | \(17\) | ||
Distinguishing \(T_p\): | \(3\), \(5\), \(17\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1856))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 252 | 56 | 196 |
Cusp forms | 229 | 56 | 173 |
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.
\(2\) | \(29\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(11\) |
\(+\) | \(-\) | $-$ | \(17\) |
\(-\) | \(+\) | $-$ | \(17\) |
\(-\) | \(-\) | $+$ | \(11\) |
Plus space | \(+\) | \(22\) | |
Minus space | \(-\) | \(34\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1856))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1856))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(1856)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(29))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(58))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(116))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(232))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(464))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(928))\)\(^{\oplus 2}\)