Defining parameters
Level: | \( N \) | \(=\) | \( 1472 = 2^{6} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1472.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 38 \) | ||
Sturm bound: | \(768\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(1472))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 588 | 132 | 456 |
Cusp forms | 564 | 132 | 432 |
Eisenstein series | 24 | 0 | 24 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(23\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | \(+\) | \(34\) |
\(+\) | \(-\) | \(-\) | \(31\) |
\(-\) | \(+\) | \(-\) | \(32\) |
\(-\) | \(-\) | \(+\) | \(35\) |
Plus space | \(+\) | \(69\) | |
Minus space | \(-\) | \(63\) |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(1472))\) into newform subspaces
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(1472))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_0(1472)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 7}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(92))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(184))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(368))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(736))\)\(^{\oplus 2}\)