Defining parameters
Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1728.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 30 \) | ||
Sturm bound: | \(576\) | ||
Trace bound: | \(11\) | ||
Distinguishing \(T_p\): | \(5\), \(7\), \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1728))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 324 | 32 | 292 |
Cusp forms | 253 | 32 | 221 |
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.
\(2\) | \(3\) | Fricke | Total | Cusp | Eisenstein | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
All | New | Old | All | New | Old | All | New | Old | ||||||
\(+\) | \(+\) | \(+\) | \(78\) | \(7\) | \(71\) | \(61\) | \(7\) | \(54\) | \(17\) | \(0\) | \(17\) | |||
\(+\) | \(-\) | \(-\) | \(84\) | \(9\) | \(75\) | \(66\) | \(9\) | \(57\) | \(18\) | \(0\) | \(18\) | |||
\(-\) | \(+\) | \(-\) | \(84\) | \(9\) | \(75\) | \(66\) | \(9\) | \(57\) | \(18\) | \(0\) | \(18\) | |||
\(-\) | \(-\) | \(+\) | \(78\) | \(7\) | \(71\) | \(60\) | \(7\) | \(53\) | \(18\) | \(0\) | \(18\) | |||
Plus space | \(+\) | \(156\) | \(14\) | \(142\) | \(121\) | \(14\) | \(107\) | \(35\) | \(0\) | \(35\) | ||||
Minus space | \(-\) | \(168\) | \(18\) | \(150\) | \(132\) | \(18\) | \(114\) | \(36\) | \(0\) | \(36\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1728))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1728))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(1728)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(54))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(108))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(192))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(216))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(288))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(432))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(576))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(864))\)\(^{\oplus 2}\)