Defining parameters
Level: | \( N \) | \(=\) | \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1575.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 47 \) | ||
Sturm bound: | \(960\) | ||
Trace bound: | \(11\) | ||
Distinguishing \(T_p\): | \(2\), \(11\), \(13\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(1575))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 744 | 143 | 601 |
Cusp forms | 696 | 143 | 553 |
Eisenstein series | 48 | 0 | 48 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(3\) | \(5\) | \(7\) | Fricke | Total | Cusp | Eisenstein | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
All | New | Old | All | New | Old | All | New | Old | |||||||
\(+\) | \(+\) | \(+\) | \(+\) | \(96\) | \(16\) | \(80\) | \(90\) | \(16\) | \(74\) | \(6\) | \(0\) | \(6\) | |||
\(+\) | \(+\) | \(-\) | \(-\) | \(90\) | \(10\) | \(80\) | \(84\) | \(10\) | \(74\) | \(6\) | \(0\) | \(6\) | |||
\(+\) | \(-\) | \(+\) | \(-\) | \(90\) | \(14\) | \(76\) | \(84\) | \(14\) | \(70\) | \(6\) | \(0\) | \(6\) | |||
\(+\) | \(-\) | \(-\) | \(+\) | \(96\) | \(18\) | \(78\) | \(90\) | \(18\) | \(72\) | \(6\) | \(0\) | \(6\) | |||
\(-\) | \(+\) | \(+\) | \(-\) | \(90\) | \(19\) | \(71\) | \(84\) | \(19\) | \(65\) | \(6\) | \(0\) | \(6\) | |||
\(-\) | \(+\) | \(-\) | \(+\) | \(96\) | \(22\) | \(74\) | \(90\) | \(22\) | \(68\) | \(6\) | \(0\) | \(6\) | |||
\(-\) | \(-\) | \(+\) | \(+\) | \(96\) | \(23\) | \(73\) | \(90\) | \(23\) | \(67\) | \(6\) | \(0\) | \(6\) | |||
\(-\) | \(-\) | \(-\) | \(-\) | \(90\) | \(21\) | \(69\) | \(84\) | \(21\) | \(63\) | \(6\) | \(0\) | \(6\) | |||
Plus space | \(+\) | \(384\) | \(79\) | \(305\) | \(360\) | \(79\) | \(281\) | \(24\) | \(0\) | \(24\) | |||||
Minus space | \(-\) | \(360\) | \(64\) | \(296\) | \(336\) | \(64\) | \(272\) | \(24\) | \(0\) | \(24\) |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(1575))\) into newform subspaces
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(1575))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_0(1575)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(25))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(105))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(175))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(225))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(315))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(525))\)\(^{\oplus 2}\)