Defining parameters
Level: | \( N \) | \(=\) | \( 576 = 2^{6} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 576.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 42 \) | ||
Sturm bound: | \(576\) | ||
Trace bound: | \(11\) | ||
Distinguishing \(T_p\): | \(5\), \(7\), \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(576))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 504 | 51 | 453 |
Cusp forms | 456 | 49 | 407 |
Eisenstein series | 48 | 2 | 46 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(3\) | Fricke | Total | Cusp | Eisenstein | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
All | New | Old | All | New | Old | All | New | Old | ||||||
\(+\) | \(+\) | \(+\) | \(124\) | \(9\) | \(115\) | \(112\) | \(9\) | \(103\) | \(12\) | \(0\) | \(12\) | |||
\(+\) | \(-\) | \(-\) | \(128\) | \(16\) | \(112\) | \(116\) | \(15\) | \(101\) | \(12\) | \(1\) | \(11\) | |||
\(-\) | \(+\) | \(-\) | \(128\) | \(11\) | \(117\) | \(116\) | \(11\) | \(105\) | \(12\) | \(0\) | \(12\) | |||
\(-\) | \(-\) | \(+\) | \(124\) | \(15\) | \(109\) | \(112\) | \(14\) | \(98\) | \(12\) | \(1\) | \(11\) | |||
Plus space | \(+\) | \(248\) | \(24\) | \(224\) | \(224\) | \(23\) | \(201\) | \(24\) | \(1\) | \(23\) | ||||
Minus space | \(-\) | \(256\) | \(27\) | \(229\) | \(232\) | \(26\) | \(206\) | \(24\) | \(1\) | \(23\) |
Trace form
Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(576))\) into newform subspaces
Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(576))\) into lower level spaces
\( S_{6}^{\mathrm{old}}(\Gamma_0(576)) \simeq \) \(S_{6}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 14}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 15}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 7}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 9}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(18))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(192))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(288))\)\(^{\oplus 2}\)