Defining parameters
Level: | \( N \) | \(=\) | \( 9600 = 2^{7} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9600.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 100 \) | ||
Sturm bound: | \(3840\) | ||
Trace bound: | \(17\) | ||
Distinguishing \(T_p\): | \(7\), \(11\), \(13\), \(17\), \(29\), \(31\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(9600))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 2016 | 152 | 1864 |
Cusp forms | 1825 | 152 | 1673 |
Eisenstein series | 191 | 0 | 191 |
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 | Dim |
---|---|---|---|---|
\(+\) | \(+\) | \(+\) | \(+\) | \(17\) |
\(+\) | \(+\) | \(-\) | \(-\) | \(22\) |
\(+\) | \(-\) | \(+\) | \(-\) | \(19\) |
\(+\) | \(-\) | \(-\) | \(+\) | \(18\) |
\(-\) | \(+\) | \(+\) | \(-\) | \(19\) |
\(-\) | \(+\) | \(-\) | \(+\) | \(18\) |
\(-\) | \(-\) | \(+\) | \(+\) | \(17\) |
\(-\) | \(-\) | \(-\) | \(-\) | \(22\) |
Plus space | \(+\) | \(70\) | ||
Minus space | \(-\) | \(82\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9600))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9600))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(9600)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(100))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(128))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(150))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(160))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(192))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(200))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(240))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(300))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(320))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(384))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(400))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(480))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(600))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(640))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(800))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(960))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1200))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1600))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1920))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2400))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3200))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4800))\)\(^{\oplus 2}\)