Defining parameters
Level: | \( N \) | \(=\) | \( 8010 = 2 \cdot 3^{2} \cdot 5 \cdot 89 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8010.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 44 \) | ||
Sturm bound: | \(3240\) | ||
Trace bound: | \(11\) | ||
Distinguishing \(T_p\): | \(7\), \(11\), \(13\), \(17\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8010))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1636 | 144 | 1492 |
Cusp forms | 1605 | 144 | 1461 |
Eisenstein series | 31 | 0 | 31 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(3\) | \(5\) | \(89\) | Fricke | Dim |
---|---|---|---|---|---|
\(+\) | \(+\) | \(+\) | \(+\) | $+$ | \(10\) |
\(+\) | \(+\) | \(+\) | \(-\) | $-$ | \(4\) |
\(+\) | \(+\) | \(-\) | \(+\) | $-$ | \(8\) |
\(+\) | \(+\) | \(-\) | \(-\) | $+$ | \(6\) |
\(+\) | \(-\) | \(+\) | \(+\) | $-$ | \(11\) |
\(+\) | \(-\) | \(+\) | \(-\) | $+$ | \(11\) |
\(+\) | \(-\) | \(-\) | \(+\) | $+$ | \(9\) |
\(+\) | \(-\) | \(-\) | \(-\) | $-$ | \(13\) |
\(-\) | \(+\) | \(+\) | \(+\) | $-$ | \(6\) |
\(-\) | \(+\) | \(+\) | \(-\) | $+$ | \(8\) |
\(-\) | \(+\) | \(-\) | \(+\) | $+$ | \(4\) |
\(-\) | \(+\) | \(-\) | \(-\) | $-$ | \(10\) |
\(-\) | \(-\) | \(+\) | \(+\) | $+$ | \(10\) |
\(-\) | \(-\) | \(+\) | \(-\) | $-$ | \(12\) |
\(-\) | \(-\) | \(-\) | \(+\) | $-$ | \(14\) |
\(-\) | \(-\) | \(-\) | \(-\) | $+$ | \(8\) |
Plus space | \(+\) | \(66\) | |||
Minus space | \(-\) | \(78\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8010))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8010))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(8010)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(89))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(90))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(178))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(267))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(445))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(534))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(801))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(890))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1335))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1602))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2670))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4005))\)\(^{\oplus 2}\)