Defining parameters
Level: | \( N \) | \(=\) | \( 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2070.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 42 \) | ||
Sturm bound: | \(1728\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(7\), \(11\), \(17\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(2070))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1312 | 110 | 1202 |
Cusp forms | 1280 | 110 | 1170 |
Eisenstein series | 32 | 0 | 32 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(3\) | \(5\) | \(23\) | Fricke | Total | Cusp | Eisenstein | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
All | New | Old | All | New | Old | All | New | Old | ||||||||
\(+\) | \(+\) | \(+\) | \(+\) | \(+\) | \(88\) | \(5\) | \(83\) | \(86\) | \(5\) | \(81\) | \(2\) | \(0\) | \(2\) | |||
\(+\) | \(+\) | \(+\) | \(-\) | \(-\) | \(78\) | \(6\) | \(72\) | \(76\) | \(6\) | \(70\) | \(2\) | \(0\) | \(2\) | |||
\(+\) | \(+\) | \(-\) | \(+\) | \(-\) | \(78\) | \(6\) | \(72\) | \(76\) | \(6\) | \(70\) | \(2\) | \(0\) | \(2\) | |||
\(+\) | \(+\) | \(-\) | \(-\) | \(+\) | \(84\) | \(5\) | \(79\) | \(82\) | \(5\) | \(77\) | \(2\) | \(0\) | \(2\) | |||
\(+\) | \(-\) | \(+\) | \(+\) | \(-\) | \(79\) | \(7\) | \(72\) | \(77\) | \(7\) | \(70\) | \(2\) | \(0\) | \(2\) | |||
\(+\) | \(-\) | \(+\) | \(-\) | \(+\) | \(84\) | \(9\) | \(75\) | \(82\) | \(9\) | \(73\) | \(2\) | \(0\) | \(2\) | |||
\(+\) | \(-\) | \(-\) | \(+\) | \(+\) | \(83\) | \(9\) | \(74\) | \(81\) | \(9\) | \(72\) | \(2\) | \(0\) | \(2\) | |||
\(+\) | \(-\) | \(-\) | \(-\) | \(-\) | \(82\) | \(7\) | \(75\) | \(80\) | \(7\) | \(73\) | \(2\) | \(0\) | \(2\) | |||
\(-\) | \(+\) | \(+\) | \(+\) | \(-\) | \(80\) | \(5\) | \(75\) | \(78\) | \(5\) | \(73\) | \(2\) | \(0\) | \(2\) | |||
\(-\) | \(+\) | \(+\) | \(-\) | \(+\) | \(84\) | \(6\) | \(78\) | \(82\) | \(6\) | \(76\) | \(2\) | \(0\) | \(2\) | |||
\(-\) | \(+\) | \(-\) | \(+\) | \(+\) | \(82\) | \(6\) | \(76\) | \(80\) | \(6\) | \(74\) | \(2\) | \(0\) | \(2\) | |||
\(-\) | \(+\) | \(-\) | \(-\) | \(-\) | \(82\) | \(5\) | \(77\) | \(80\) | \(5\) | \(75\) | \(2\) | \(0\) | \(2\) | |||
\(-\) | \(-\) | \(+\) | \(+\) | \(+\) | \(82\) | \(10\) | \(72\) | \(80\) | \(10\) | \(70\) | \(2\) | \(0\) | \(2\) | |||
\(-\) | \(-\) | \(+\) | \(-\) | \(-\) | \(83\) | \(7\) | \(76\) | \(81\) | \(7\) | \(74\) | \(2\) | \(0\) | \(2\) | |||
\(-\) | \(-\) | \(-\) | \(+\) | \(-\) | \(84\) | \(7\) | \(77\) | \(82\) | \(7\) | \(75\) | \(2\) | \(0\) | \(2\) | |||
\(-\) | \(-\) | \(-\) | \(-\) | \(+\) | \(79\) | \(10\) | \(69\) | \(77\) | \(10\) | \(67\) | \(2\) | \(0\) | \(2\) | |||
Plus space | \(+\) | \(666\) | \(60\) | \(606\) | \(650\) | \(60\) | \(590\) | \(16\) | \(0\) | \(16\) | ||||||
Minus space | \(-\) | \(646\) | \(50\) | \(596\) | \(630\) | \(50\) | \(580\) | \(16\) | \(0\) | \(16\) |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(2070))\) into newform subspaces
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(2070))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_0(2070)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(10))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(69))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(90))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(115))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(138))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(207))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(230))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(345))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(414))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(690))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(1035))\)\(^{\oplus 2}\)