Defining parameters
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 22 \) | ||
Sturm bound: | \(180\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(2\), \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(225))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 162 | 41 | 121 |
Cusp forms | 138 | 38 | 100 |
Eisenstein series | 24 | 3 | 21 |
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 | Total | Cusp | Eisenstein | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
All | New | Old | All | New | Old | All | New | Old | ||||||
\(+\) | \(+\) | \(+\) | \(39\) | \(7\) | \(32\) | \(33\) | \(7\) | \(26\) | \(6\) | \(0\) | \(6\) | |||
\(+\) | \(-\) | \(-\) | \(41\) | \(9\) | \(32\) | \(35\) | \(9\) | \(26\) | \(6\) | \(0\) | \(6\) | |||
\(-\) | \(+\) | \(-\) | \(42\) | \(12\) | \(30\) | \(36\) | \(11\) | \(25\) | \(6\) | \(1\) | \(5\) | |||
\(-\) | \(-\) | \(+\) | \(40\) | \(13\) | \(27\) | \(34\) | \(11\) | \(23\) | \(6\) | \(2\) | \(4\) | |||
Plus space | \(+\) | \(79\) | \(20\) | \(59\) | \(67\) | \(18\) | \(49\) | \(12\) | \(2\) | \(10\) | ||||
Minus space | \(-\) | \(83\) | \(21\) | \(62\) | \(71\) | \(20\) | \(51\) | \(12\) | \(1\) | \(11\) |
Trace form
Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(225))\) into newform subspaces
Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(225))\) into lower level spaces
\( S_{6}^{\mathrm{old}}(\Gamma_0(225)) \simeq \) \(S_{6}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(25))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 2}\)