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 | Dim |
---|---|---|---|---|---|
\(+\) | \(+\) | \(+\) | \(+\) | $+$ | \(5\) |
\(+\) | \(+\) | \(+\) | \(-\) | $-$ | \(6\) |
\(+\) | \(+\) | \(-\) | \(+\) | $-$ | \(6\) |
\(+\) | \(+\) | \(-\) | \(-\) | $+$ | \(5\) |
\(+\) | \(-\) | \(+\) | \(+\) | $-$ | \(7\) |
\(+\) | \(-\) | \(+\) | \(-\) | $+$ | \(9\) |
\(+\) | \(-\) | \(-\) | \(+\) | $+$ | \(9\) |
\(+\) | \(-\) | \(-\) | \(-\) | $-$ | \(7\) |
\(-\) | \(+\) | \(+\) | \(+\) | $-$ | \(5\) |
\(-\) | \(+\) | \(+\) | \(-\) | $+$ | \(6\) |
\(-\) | \(+\) | \(-\) | \(+\) | $+$ | \(6\) |
\(-\) | \(+\) | \(-\) | \(-\) | $-$ | \(5\) |
\(-\) | \(-\) | \(+\) | \(+\) | $+$ | \(10\) |
\(-\) | \(-\) | \(+\) | \(-\) | $-$ | \(7\) |
\(-\) | \(-\) | \(-\) | \(+\) | $-$ | \(7\) |
\(-\) | \(-\) | \(-\) | \(-\) | $+$ | \(10\) |
Plus space | \(+\) | \(60\) | |||
Minus space | \(-\) | \(50\) |
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
\( S_{4}^{\mathrm{old}}(\Gamma_0(2070)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(10))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(69))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(90))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(115))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(138))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(207))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(230))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(345))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(414))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(690))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(1035))\)\(^{\oplus 2}\)