Defining parameters
Level: | \( N \) | \(=\) | \( 4608 = 2^{9} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4608.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 29 \) | ||
Sturm bound: | \(1536\) | ||
Trace bound: | \(25\) | ||
Distinguishing \(T_p\): | \(5\), \(7\), \(11\), \(17\), \(23\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4608))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 832 | 80 | 752 |
Cusp forms | 705 | 80 | 625 |
Eisenstein series | 127 | 0 | 127 |
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 | Dim |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(16\) |
\(+\) | \(-\) | $-$ | \(26\) |
\(-\) | \(+\) | $-$ | \(16\) |
\(-\) | \(-\) | $+$ | \(22\) |
Plus space | \(+\) | \(38\) | |
Minus space | \(-\) | \(42\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4608))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4608))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(4608)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(128))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(192))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(256))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(288))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(384))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(512))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(576))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(768))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1152))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1536))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2304))\)\(^{\oplus 2}\)