Defining parameters
Level: | \( N \) | \(=\) | \( 5328 = 2^{4} \cdot 3^{2} \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5328.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 47 \) | ||
Sturm bound: | \(1824\) | ||
Trace bound: | \(19\) | ||
Distinguishing \(T_p\): | \(5\), \(7\), \(11\), \(13\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5328))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 936 | 90 | 846 |
Cusp forms | 889 | 90 | 799 |
Eisenstein series | 47 | 0 | 47 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(3\) | \(37\) | Fricke | Dim |
---|---|---|---|---|
\(+\) | \(+\) | \(+\) | \(+\) | \(8\) |
\(+\) | \(+\) | \(-\) | \(-\) | \(10\) |
\(+\) | \(-\) | \(+\) | \(-\) | \(14\) |
\(+\) | \(-\) | \(-\) | \(+\) | \(13\) |
\(-\) | \(+\) | \(+\) | \(-\) | \(10\) |
\(-\) | \(+\) | \(-\) | \(+\) | \(8\) |
\(-\) | \(-\) | \(+\) | \(+\) | \(13\) |
\(-\) | \(-\) | \(-\) | \(-\) | \(14\) |
Plus space | \(+\) | \(42\) | ||
Minus space | \(-\) | \(48\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5328))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5328))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(5328)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(37))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(74))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(111))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(148))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(222))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(296))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(333))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(444))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(592))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(666))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(888))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1332))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1776))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2664))\)\(^{\oplus 2}\)