Defining parameters
Level: | \( N \) | \(=\) | \( 4008 = 2^{3} \cdot 3 \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4008.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 13 \) | ||
Sturm bound: | \(1344\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(5\), \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4008))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 680 | 82 | 598 |
Cusp forms | 665 | 82 | 583 |
Eisenstein series | 15 | 0 | 15 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(3\) | \(167\) | Fricke | Dim |
---|---|---|---|---|
\(+\) | \(+\) | \(+\) | $+$ | \(10\) |
\(+\) | \(+\) | \(-\) | $-$ | \(11\) |
\(+\) | \(-\) | \(+\) | $-$ | \(14\) |
\(+\) | \(-\) | \(-\) | $+$ | \(7\) |
\(-\) | \(+\) | \(+\) | $-$ | \(8\) |
\(-\) | \(+\) | \(-\) | $+$ | \(11\) |
\(-\) | \(-\) | \(+\) | $+$ | \(9\) |
\(-\) | \(-\) | \(-\) | $-$ | \(12\) |
Plus space | \(+\) | \(37\) | ||
Minus space | \(-\) | \(45\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4008))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4008))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(4008)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(167))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(334))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(501))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(668))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1002))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1336))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2004))\)\(^{\oplus 2}\)