Defining parameters
Level: | \( N \) | \(=\) | \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1200.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 47 \) | ||
Sturm bound: | \(960\) | ||
Trace bound: | \(11\) | ||
Distinguishing \(T_p\): | \(7\), \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(1200))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 756 | 57 | 699 |
Cusp forms | 684 | 57 | 627 |
Eisenstein series | 72 | 0 | 72 |
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 | |||||||
\(+\) | \(+\) | \(+\) | \(+\) | \(96\) | \(8\) | \(88\) | \(87\) | \(8\) | \(79\) | \(9\) | \(0\) | \(9\) | |||
\(+\) | \(+\) | \(-\) | \(-\) | \(93\) | \(7\) | \(86\) | \(84\) | \(7\) | \(77\) | \(9\) | \(0\) | \(9\) | |||
\(+\) | \(-\) | \(+\) | \(-\) | \(93\) | \(5\) | \(88\) | \(84\) | \(5\) | \(79\) | \(9\) | \(0\) | \(9\) | |||
\(+\) | \(-\) | \(-\) | \(+\) | \(96\) | \(9\) | \(87\) | \(87\) | \(9\) | \(78\) | \(9\) | \(0\) | \(9\) | |||
\(-\) | \(+\) | \(+\) | \(-\) | \(93\) | \(7\) | \(86\) | \(84\) | \(7\) | \(77\) | \(9\) | \(0\) | \(9\) | |||
\(-\) | \(+\) | \(-\) | \(+\) | \(96\) | \(7\) | \(89\) | \(87\) | \(7\) | \(80\) | \(9\) | \(0\) | \(9\) | |||
\(-\) | \(-\) | \(+\) | \(+\) | \(96\) | \(7\) | \(89\) | \(87\) | \(7\) | \(80\) | \(9\) | \(0\) | \(9\) | |||
\(-\) | \(-\) | \(-\) | \(-\) | \(93\) | \(7\) | \(86\) | \(84\) | \(7\) | \(77\) | \(9\) | \(0\) | \(9\) | |||
Plus space | \(+\) | \(384\) | \(31\) | \(353\) | \(348\) | \(31\) | \(317\) | \(36\) | \(0\) | \(36\) | |||||
Minus space | \(-\) | \(372\) | \(26\) | \(346\) | \(336\) | \(26\) | \(310\) | \(36\) | \(0\) | \(36\) |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(1200))\) into newform subspaces
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(1200))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_0(1200)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 20}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(10))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(12))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(25))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(60))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(100))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(150))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(200))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(240))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(300))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(400))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(600))\)\(^{\oplus 2}\)