Defining parameters
Level: | \( N \) | \(=\) | \( 6016 = 2^{7} \cdot 47 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6016.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 20 \) | ||
Sturm bound: | \(1536\) | ||
Trace bound: | \(13\) | ||
Distinguishing \(T_p\): | \(3\), \(5\), \(13\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6016))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 784 | 184 | 600 |
Cusp forms | 753 | 184 | 569 |
Eisenstein series | 31 | 0 | 31 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(47\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(43\) |
\(+\) | \(-\) | $-$ | \(51\) |
\(-\) | \(+\) | $-$ | \(49\) |
\(-\) | \(-\) | $+$ | \(41\) |
Plus space | \(+\) | \(84\) | |
Minus space | \(-\) | \(100\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6016))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6016))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(6016)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(47))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(94))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(128))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(188))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(376))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(752))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1504))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3008))\)\(^{\oplus 2}\)