Defining parameters
Level: | \( N \) | \(=\) | \( 6384 = 2^{4} \cdot 3 \cdot 7 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6384.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 58 \) | ||
Sturm bound: | \(2560\) | ||
Trace bound: | \(25\) | ||
Distinguishing \(T_p\): | \(5\), \(11\), \(13\), \(17\), \(23\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6384))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1304 | 108 | 1196 |
Cusp forms | 1257 | 108 | 1149 |
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.
\(2\) | \(3\) | \(7\) | \(19\) | Fricke | Dim |
---|---|---|---|---|---|
\(+\) | \(+\) | \(+\) | \(+\) | \(+\) | \(8\) |
\(+\) | \(+\) | \(+\) | \(-\) | \(-\) | \(6\) |
\(+\) | \(+\) | \(-\) | \(+\) | \(-\) | \(7\) |
\(+\) | \(+\) | \(-\) | \(-\) | \(+\) | \(7\) |
\(+\) | \(-\) | \(+\) | \(+\) | \(-\) | \(7\) |
\(+\) | \(-\) | \(+\) | \(-\) | \(+\) | \(7\) |
\(+\) | \(-\) | \(-\) | \(+\) | \(+\) | \(6\) |
\(+\) | \(-\) | \(-\) | \(-\) | \(-\) | \(8\) |
\(-\) | \(+\) | \(+\) | \(+\) | \(-\) | \(8\) |
\(-\) | \(+\) | \(+\) | \(-\) | \(+\) | \(6\) |
\(-\) | \(+\) | \(-\) | \(+\) | \(+\) | \(4\) |
\(-\) | \(+\) | \(-\) | \(-\) | \(-\) | \(8\) |
\(-\) | \(-\) | \(+\) | \(+\) | \(+\) | \(5\) |
\(-\) | \(-\) | \(+\) | \(-\) | \(-\) | \(9\) |
\(-\) | \(-\) | \(-\) | \(+\) | \(-\) | \(9\) |
\(-\) | \(-\) | \(-\) | \(-\) | \(+\) | \(3\) |
Plus space | \(+\) | \(46\) | |||
Minus space | \(-\) | \(62\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6384))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6384))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(6384)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(76))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(114))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(133))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(152))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(168))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(228))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(266))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(304))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(336))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(399))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(456))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(532))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(798))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(912))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1064))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1596))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2128))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3192))\)\(^{\oplus 2}\)