Defining parameters
Level: | \( N \) | \(=\) | \( 616 = 2^{3} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 616.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 11 \) | ||
Sturm bound: | \(384\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(3\), \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(616))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 296 | 46 | 250 |
Cusp forms | 280 | 46 | 234 |
Eisenstein series | 16 | 0 | 16 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(7\) | \(11\) | Fricke | Dim |
---|---|---|---|---|
\(+\) | \(+\) | \(+\) | \(+\) | \(7\) |
\(+\) | \(+\) | \(-\) | \(-\) | \(4\) |
\(+\) | \(-\) | \(+\) | \(-\) | \(6\) |
\(+\) | \(-\) | \(-\) | \(+\) | \(7\) |
\(-\) | \(+\) | \(+\) | \(-\) | \(7\) |
\(-\) | \(+\) | \(-\) | \(+\) | \(5\) |
\(-\) | \(-\) | \(+\) | \(+\) | \(6\) |
\(-\) | \(-\) | \(-\) | \(-\) | \(4\) |
Plus space | \(+\) | \(25\) | ||
Minus space | \(-\) | \(21\) |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(616))\) into newform subspaces
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(616))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_0(616)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(28))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(88))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(154))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(308))\)\(^{\oplus 2}\)