Defining parameters
Level: | \( N \) | \(=\) | \( 2366 = 2 \cdot 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2366.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 38 \) | ||
Sturm bound: | \(1456\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(3\), \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(2366))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1120 | 232 | 888 |
Cusp forms | 1064 | 232 | 832 |
Eisenstein series | 56 | 0 | 56 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(7\) | \(13\) | Fricke | Dim |
---|---|---|---|---|
\(+\) | \(+\) | \(+\) | $+$ | \(30\) |
\(+\) | \(+\) | \(-\) | $-$ | \(27\) |
\(+\) | \(-\) | \(+\) | $-$ | \(25\) |
\(+\) | \(-\) | \(-\) | $+$ | \(33\) |
\(-\) | \(+\) | \(+\) | $-$ | \(29\) |
\(-\) | \(+\) | \(-\) | $+$ | \(30\) |
\(-\) | \(-\) | \(+\) | $+$ | \(34\) |
\(-\) | \(-\) | \(-\) | $-$ | \(24\) |
Plus space | \(+\) | \(127\) | ||
Minus space | \(-\) | \(105\) |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(2366))\) into newform subspaces
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(2366))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_0(2366)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(13))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(91))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(169))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(182))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(338))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(1183))\)\(^{\oplus 2}\)