Defining parameters
Level: | \( N \) | \(=\) | \( 9744 = 2^{4} \cdot 3 \cdot 7 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9744.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 61 \) | ||
Sturm bound: | \(3840\) | ||
Trace bound: | \(13\) | ||
Distinguishing \(T_p\): | \(5\), \(11\), \(13\), \(17\), \(23\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(9744))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1944 | 168 | 1776 |
Cusp forms | 1897 | 168 | 1729 |
Eisenstein series | 47 | 0 | 47 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(3\) | \(7\) | \(29\) | Fricke | Dim |
---|---|---|---|---|---|
\(+\) | \(+\) | \(+\) | \(+\) | $+$ | \(10\) |
\(+\) | \(+\) | \(+\) | \(-\) | $-$ | \(12\) |
\(+\) | \(+\) | \(-\) | \(+\) | $-$ | \(11\) |
\(+\) | \(+\) | \(-\) | \(-\) | $+$ | \(9\) |
\(+\) | \(-\) | \(+\) | \(+\) | $-$ | \(11\) |
\(+\) | \(-\) | \(+\) | \(-\) | $+$ | \(9\) |
\(+\) | \(-\) | \(-\) | \(+\) | $+$ | \(10\) |
\(+\) | \(-\) | \(-\) | \(-\) | $-$ | \(12\) |
\(-\) | \(+\) | \(+\) | \(+\) | $-$ | \(11\) |
\(-\) | \(+\) | \(+\) | \(-\) | $+$ | \(9\) |
\(-\) | \(+\) | \(-\) | \(+\) | $+$ | \(10\) |
\(-\) | \(+\) | \(-\) | \(-\) | $-$ | \(12\) |
\(-\) | \(-\) | \(+\) | \(+\) | $+$ | \(10\) |
\(-\) | \(-\) | \(+\) | \(-\) | $-$ | \(12\) |
\(-\) | \(-\) | \(-\) | \(+\) | $-$ | \(11\) |
\(-\) | \(-\) | \(-\) | \(-\) | $+$ | \(9\) |
Plus space | \(+\) | \(76\) | |||
Minus space | \(-\) | \(92\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9744))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9744))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(9744)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(28))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(29))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(58))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(87))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(116))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(168))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(174))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(203))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(232))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(336))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(348))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(406))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(464))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(609))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(696))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(812))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1218))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1392))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1624))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2436))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3248))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4872))\)\(^{\oplus 2}\)