Defining parameters
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 41 \) | ||
Sturm bound: | \(672\) | ||
Trace bound: | \(9\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(784))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 584 | 105 | 479 |
Cusp forms | 536 | 100 | 436 |
Eisenstein series | 48 | 5 | 43 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(7\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(24\) |
\(+\) | \(-\) | $-$ | \(27\) |
\(-\) | \(+\) | $-$ | \(25\) |
\(-\) | \(-\) | $+$ | \(24\) |
Plus space | \(+\) | \(48\) | |
Minus space | \(-\) | \(52\) |
Trace form
Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(784))\) into newform subspaces
Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(784))\) into lower level spaces
\( S_{6}^{\mathrm{old}}(\Gamma_0(784)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 9}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 10}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(28))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(196))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(392))\)\(^{\oplus 2}\)