Defining parameters
Level: | \( N \) | \(=\) | \( 6075 = 3^{5} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6075.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 70 \) | ||
Sturm bound: | \(1620\) | ||
Trace bound: | \(13\) | ||
Distinguishing \(T_p\): | \(2\), \(7\), \(11\), \(13\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6075))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 864 | 228 | 636 |
Cusp forms | 757 | 228 | 529 |
Eisenstein series | 107 | 0 | 107 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(3\) | \(5\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(48\) |
\(+\) | \(-\) | $-$ | \(64\) |
\(-\) | \(+\) | $-$ | \(60\) |
\(-\) | \(-\) | $+$ | \(56\) |
Plus space | \(+\) | \(104\) | |
Minus space | \(-\) | \(124\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6075))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6075))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(6075)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(81))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(135))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(225))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(243))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(405))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(675))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1215))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2025))\)\(^{\oplus 2}\)