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 | Total | Cusp | Eisenstein | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
All | New | Old | All | New | Old | All | New | Old | ||||||||
\(+\) | \(+\) | \(+\) | \(+\) | \(+\) | \(74\) | \(8\) | \(66\) | \(72\) | \(8\) | \(64\) | \(2\) | \(0\) | \(2\) | |||
\(+\) | \(+\) | \(+\) | \(-\) | \(-\) | \(86\) | \(6\) | \(80\) | \(83\) | \(6\) | \(77\) | \(3\) | \(0\) | \(3\) | |||
\(+\) | \(+\) | \(-\) | \(+\) | \(-\) | \(88\) | \(7\) | \(81\) | \(85\) | \(7\) | \(78\) | \(3\) | \(0\) | \(3\) | |||
\(+\) | \(+\) | \(-\) | \(-\) | \(+\) | \(76\) | \(7\) | \(69\) | \(73\) | \(7\) | \(66\) | \(3\) | \(0\) | \(3\) | |||
\(+\) | \(-\) | \(+\) | \(+\) | \(-\) | \(89\) | \(7\) | \(82\) | \(86\) | \(7\) | \(79\) | \(3\) | \(0\) | \(3\) | |||
\(+\) | \(-\) | \(+\) | \(-\) | \(+\) | \(77\) | \(7\) | \(70\) | \(74\) | \(7\) | \(67\) | \(3\) | \(0\) | \(3\) | |||
\(+\) | \(-\) | \(-\) | \(+\) | \(+\) | \(75\) | \(6\) | \(69\) | \(72\) | \(6\) | \(66\) | \(3\) | \(0\) | \(3\) | |||
\(+\) | \(-\) | \(-\) | \(-\) | \(-\) | \(87\) | \(8\) | \(79\) | \(84\) | \(8\) | \(76\) | \(3\) | \(0\) | \(3\) | |||
\(-\) | \(+\) | \(+\) | \(+\) | \(-\) | \(81\) | \(8\) | \(73\) | \(78\) | \(8\) | \(70\) | \(3\) | \(0\) | \(3\) | |||
\(-\) | \(+\) | \(+\) | \(-\) | \(+\) | \(85\) | \(6\) | \(79\) | \(82\) | \(6\) | \(76\) | \(3\) | \(0\) | \(3\) | |||
\(-\) | \(+\) | \(-\) | \(+\) | \(+\) | \(83\) | \(4\) | \(79\) | \(80\) | \(4\) | \(76\) | \(3\) | \(0\) | \(3\) | |||
\(-\) | \(+\) | \(-\) | \(-\) | \(-\) | \(79\) | \(8\) | \(71\) | \(76\) | \(8\) | \(68\) | \(3\) | \(0\) | \(3\) | |||
\(-\) | \(-\) | \(+\) | \(+\) | \(+\) | \(82\) | \(5\) | \(77\) | \(79\) | \(5\) | \(74\) | \(3\) | \(0\) | \(3\) | |||
\(-\) | \(-\) | \(+\) | \(-\) | \(-\) | \(78\) | \(9\) | \(69\) | \(75\) | \(9\) | \(66\) | \(3\) | \(0\) | \(3\) | |||
\(-\) | \(-\) | \(-\) | \(+\) | \(-\) | \(80\) | \(9\) | \(71\) | \(77\) | \(9\) | \(68\) | \(3\) | \(0\) | \(3\) | |||
\(-\) | \(-\) | \(-\) | \(-\) | \(+\) | \(84\) | \(3\) | \(81\) | \(81\) | \(3\) | \(78\) | \(3\) | \(0\) | \(3\) | |||
Plus space | \(+\) | \(636\) | \(46\) | \(590\) | \(613\) | \(46\) | \(567\) | \(23\) | \(0\) | \(23\) | ||||||
Minus space | \(-\) | \(668\) | \(62\) | \(606\) | \(644\) | \(62\) | \(582\) | \(24\) | \(0\) | \(24\) |
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
\( S_{2}^{\mathrm{old}}(\Gamma_0(6384)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(76))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(114))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(133))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(152))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(168))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(228))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(266))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(304))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(336))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(399))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(456))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(532))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(798))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(912))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1064))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1596))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2128))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3192))\)\(^{\oplus 2}\)