Defining parameters
Level: | \( N \) | \(=\) | \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1200.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 19 \) | ||
Sturm bound: | \(480\) | ||
Trace bound: | \(13\) | ||
Distinguishing \(T_p\): | \(7\), \(11\), \(13\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1200))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 276 | 19 | 257 |
Cusp forms | 205 | 19 | 186 |
Eisenstein series | 71 | 0 | 71 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(3\) | \(5\) | Fricke | Total | Cusp | Eisenstein | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
All | New | Old | All | New | Old | All | New | Old | |||||||
\(+\) | \(+\) | \(+\) | \(+\) | \(33\) | \(1\) | \(32\) | \(25\) | \(1\) | \(24\) | \(8\) | \(0\) | \(8\) | |||
\(+\) | \(+\) | \(-\) | \(-\) | \(36\) | \(3\) | \(33\) | \(27\) | \(3\) | \(24\) | \(9\) | \(0\) | \(9\) | |||
\(+\) | \(-\) | \(+\) | \(-\) | \(36\) | \(4\) | \(32\) | \(27\) | \(4\) | \(23\) | \(9\) | \(0\) | \(9\) | |||
\(+\) | \(-\) | \(-\) | \(+\) | \(33\) | \(1\) | \(32\) | \(24\) | \(1\) | \(23\) | \(9\) | \(0\) | \(9\) | |||
\(-\) | \(+\) | \(+\) | \(-\) | \(36\) | \(2\) | \(34\) | \(27\) | \(2\) | \(25\) | \(9\) | \(0\) | \(9\) | |||
\(-\) | \(+\) | \(-\) | \(+\) | \(33\) | \(3\) | \(30\) | \(24\) | \(3\) | \(21\) | \(9\) | \(0\) | \(9\) | |||
\(-\) | \(-\) | \(+\) | \(+\) | \(33\) | \(2\) | \(31\) | \(24\) | \(2\) | \(22\) | \(9\) | \(0\) | \(9\) | |||
\(-\) | \(-\) | \(-\) | \(-\) | \(36\) | \(3\) | \(33\) | \(27\) | \(3\) | \(24\) | \(9\) | \(0\) | \(9\) | |||
Plus space | \(+\) | \(132\) | \(7\) | \(125\) | \(97\) | \(7\) | \(90\) | \(35\) | \(0\) | \(35\) | |||||
Minus space | \(-\) | \(144\) | \(12\) | \(132\) | \(108\) | \(12\) | \(96\) | \(36\) | \(0\) | \(36\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1200))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1200))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(1200)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(100))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(150))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(200))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(240))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(300))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(400))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(600))\)\(^{\oplus 2}\)