Defining parameters
Level: | \( N \) | \(=\) | \( 1152 = 2^{7} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1152.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 20 \) | ||
Sturm bound: | \(384\) | ||
Trace bound: | \(13\) | ||
Distinguishing \(T_p\): | \(5\), \(7\), \(11\), \(13\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1152))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 224 | 20 | 204 |
Cusp forms | 161 | 20 | 141 |
Eisenstein series | 63 | 0 | 63 |
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 | ||||||
\(+\) | \(+\) | \(+\) | \(52\) | \(4\) | \(48\) | \(37\) | \(4\) | \(33\) | \(15\) | \(0\) | \(15\) | |||
\(+\) | \(-\) | \(-\) | \(56\) | \(7\) | \(49\) | \(40\) | \(7\) | \(33\) | \(16\) | \(0\) | \(16\) | |||
\(-\) | \(+\) | \(-\) | \(60\) | \(4\) | \(56\) | \(44\) | \(4\) | \(40\) | \(16\) | \(0\) | \(16\) | |||
\(-\) | \(-\) | \(+\) | \(56\) | \(5\) | \(51\) | \(40\) | \(5\) | \(35\) | \(16\) | \(0\) | \(16\) | |||
Plus space | \(+\) | \(108\) | \(9\) | \(99\) | \(77\) | \(9\) | \(68\) | \(31\) | \(0\) | \(31\) | ||||
Minus space | \(-\) | \(116\) | \(11\) | \(105\) | \(84\) | \(11\) | \(73\) | \(32\) | \(0\) | \(32\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1152))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1152))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(1152)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(128))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(192))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(288))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(384))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(576))\)\(^{\oplus 2}\)