Defining parameters
Level: | \( N \) | \(=\) | \( 5408 = 2^{5} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5408.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 47 \) | ||
Sturm bound: | \(1456\) | ||
Trace bound: | \(21\) | ||
Distinguishing \(T_p\): | \(3\), \(5\), \(7\), \(37\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5408))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 784 | 155 | 629 |
Cusp forms | 673 | 155 | 518 |
Eisenstein series | 111 | 0 | 111 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(13\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | \(+\) | \(35\) |
\(+\) | \(-\) | \(-\) | \(42\) |
\(-\) | \(+\) | \(-\) | \(42\) |
\(-\) | \(-\) | \(+\) | \(36\) |
Plus space | \(+\) | \(71\) | |
Minus space | \(-\) | \(84\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5408))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5408))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(5408)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(104))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(169))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(208))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(338))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(416))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(676))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1352))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2704))\)\(^{\oplus 2}\)