Defining parameters
Level: | \( N \) | \(=\) | \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1575.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 26 \) | ||
Sturm bound: | \(480\) | ||
Trace bound: | \(13\) | ||
Distinguishing \(T_p\): | \(2\), \(11\), \(13\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1575))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 264 | 47 | 217 |
Cusp forms | 217 | 47 | 170 |
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.
\(3\) | \(5\) | \(7\) | Fricke | Dim |
---|---|---|---|---|
\(+\) | \(+\) | \(+\) | \(+\) | \(2\) |
\(+\) | \(+\) | \(-\) | \(-\) | \(8\) |
\(+\) | \(-\) | \(+\) | \(-\) | \(6\) |
\(+\) | \(-\) | \(-\) | \(+\) | \(2\) |
\(-\) | \(+\) | \(+\) | \(-\) | \(8\) |
\(-\) | \(+\) | \(-\) | \(+\) | \(5\) |
\(-\) | \(-\) | \(+\) | \(+\) | \(7\) |
\(-\) | \(-\) | \(-\) | \(-\) | \(9\) |
Plus space | \(+\) | \(16\) | ||
Minus space | \(-\) | \(31\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1575))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1575))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(1575)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(105))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(175))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(225))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(315))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(525))\)\(^{\oplus 2}\)