Defining parameters
Level: | \( N \) | \(=\) | \( 3008 = 2^{6} \cdot 47 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3008.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 26 \) | ||
Sturm bound: | \(768\) | ||
Trace bound: | \(11\) | ||
Distinguishing \(T_p\): | \(3\), \(5\), \(7\), \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3008))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 396 | 92 | 304 |
Cusp forms | 373 | 92 | 281 |
Eisenstein series | 23 | 0 | 23 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(47\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(21\) |
\(+\) | \(-\) | $-$ | \(26\) |
\(-\) | \(+\) | $-$ | \(25\) |
\(-\) | \(-\) | $+$ | \(20\) |
Plus space | \(+\) | \(41\) | |
Minus space | \(-\) | \(51\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3008))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(3008))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(3008)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(47))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(94))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(188))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(376))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(752))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1504))\)\(^{\oplus 2}\)