Defining parameters
Level: | \( N \) | \(=\) | \( 2368 = 2^{6} \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2368.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 36 \) | ||
Sturm bound: | \(608\) | ||
Trace bound: | \(11\) | ||
Distinguishing \(T_p\): | \(3\), \(5\), \(7\), \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2368))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 316 | 72 | 244 |
Cusp forms | 293 | 72 | 221 |
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.
\(2\) | \(37\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | \(+\) | \(17\) |
\(+\) | \(-\) | \(-\) | \(19\) |
\(-\) | \(+\) | \(-\) | \(19\) |
\(-\) | \(-\) | \(+\) | \(17\) |
Plus space | \(+\) | \(34\) | |
Minus space | \(-\) | \(38\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2368))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2368))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(2368)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(37))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(74))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(148))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(296))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(592))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1184))\)\(^{\oplus 2}\)