Defining parameters
Level: | \( N \) | \(=\) | \( 858 = 2 \cdot 3 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 858.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 17 \) | ||
Sturm bound: | \(336\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(5\), \(7\), \(17\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(858))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 176 | 21 | 155 |
Cusp forms | 161 | 21 | 140 |
Eisenstein series | 15 | 0 | 15 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(3\) | \(11\) | \(13\) | Fricke | Dim |
---|---|---|---|---|---|
\(+\) | \(+\) | \(+\) | \(+\) | $+$ | \(2\) |
\(+\) | \(+\) | \(-\) | \(+\) | $-$ | \(1\) |
\(+\) | \(+\) | \(-\) | \(-\) | $+$ | \(2\) |
\(+\) | \(-\) | \(+\) | \(+\) | $-$ | \(2\) |
\(+\) | \(-\) | \(+\) | \(-\) | $+$ | \(1\) |
\(+\) | \(-\) | \(-\) | \(-\) | $-$ | \(2\) |
\(-\) | \(+\) | \(+\) | \(+\) | $-$ | \(1\) |
\(-\) | \(+\) | \(+\) | \(-\) | $+$ | \(1\) |
\(-\) | \(+\) | \(-\) | \(+\) | $+$ | \(1\) |
\(-\) | \(+\) | \(-\) | \(-\) | $-$ | \(2\) |
\(-\) | \(-\) | \(+\) | \(-\) | $-$ | \(3\) |
\(-\) | \(-\) | \(-\) | \(+\) | $-$ | \(3\) |
Plus space | \(+\) | \(7\) | |||
Minus space | \(-\) | \(14\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(858))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(858))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(858)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(78))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(143))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(286))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(429))\)\(^{\oplus 2}\)