Defining parameters
Level: | \( N \) | \(=\) | \( 2475 = 3^{2} \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2475.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 36 \) | ||
Sturm bound: | \(720\) | ||
Trace bound: | \(11\) | ||
Distinguishing \(T_p\): | \(2\), \(7\), \(29\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2475))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 384 | 78 | 306 |
Cusp forms | 337 | 78 | 259 |
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.
\(3\) | \(5\) | \(11\) | Fricke | Dim |
---|---|---|---|---|
\(+\) | \(+\) | \(+\) | \(+\) | \(8\) |
\(+\) | \(+\) | \(-\) | \(-\) | \(8\) |
\(+\) | \(-\) | \(+\) | \(-\) | \(7\) |
\(+\) | \(-\) | \(-\) | \(+\) | \(7\) |
\(-\) | \(+\) | \(+\) | \(-\) | \(12\) |
\(-\) | \(+\) | \(-\) | \(+\) | \(10\) |
\(-\) | \(-\) | \(+\) | \(+\) | \(11\) |
\(-\) | \(-\) | \(-\) | \(-\) | \(15\) |
Plus space | \(+\) | \(36\) | ||
Minus space | \(-\) | \(42\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2475))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2475))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(2475)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(99))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(165))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(225))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(275))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(495))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(825))\)\(^{\oplus 2}\)