Defining parameters
Level: | \( N \) | \(=\) | \( 4010 = 2 \cdot 5 \cdot 401 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4010.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 15 \) | ||
Sturm bound: | \(1206\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(3\), \(7\), \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4010))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 606 | 135 | 471 |
Cusp forms | 599 | 135 | 464 |
Eisenstein series | 7 | 0 | 7 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(5\) | \(401\) | Fricke | Dim |
---|---|---|---|---|
\(+\) | \(+\) | \(+\) | $+$ | \(16\) |
\(+\) | \(+\) | \(-\) | $-$ | \(18\) |
\(+\) | \(-\) | \(+\) | $-$ | \(21\) |
\(+\) | \(-\) | \(-\) | $+$ | \(13\) |
\(-\) | \(+\) | \(+\) | $-$ | \(22\) |
\(-\) | \(+\) | \(-\) | $+$ | \(12\) |
\(-\) | \(-\) | \(+\) | $+$ | \(9\) |
\(-\) | \(-\) | \(-\) | $-$ | \(24\) |
Plus space | \(+\) | \(50\) | ||
Minus space | \(-\) | \(85\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4010))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4010))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(4010)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(401))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(802))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2005))\)\(^{\oplus 2}\)