Defining parameters
Level: | \( N \) | \(=\) | \( 4598 = 2 \cdot 11^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4598.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 56 \) | ||
Sturm bound: | \(1320\) | ||
Trace bound: | \(13\) | ||
Distinguishing \(T_p\): | \(3\), \(5\), \(7\), \(13\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4598))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 684 | 163 | 521 |
Cusp forms | 637 | 163 | 474 |
Eisenstein series | 47 | 0 | 47 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(11\) | \(19\) | Fricke | Dim |
---|---|---|---|---|
\(+\) | \(+\) | \(+\) | \(+\) | \(16\) |
\(+\) | \(+\) | \(-\) | \(-\) | \(23\) |
\(+\) | \(-\) | \(+\) | \(-\) | \(24\) |
\(+\) | \(-\) | \(-\) | \(+\) | \(19\) |
\(-\) | \(+\) | \(+\) | \(-\) | \(25\) |
\(-\) | \(+\) | \(-\) | \(+\) | \(14\) |
\(-\) | \(-\) | \(+\) | \(+\) | \(16\) |
\(-\) | \(-\) | \(-\) | \(-\) | \(26\) |
Plus space | \(+\) | \(65\) | ||
Minus space | \(-\) | \(98\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4598))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4598))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(4598)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(209))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(242))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(418))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2299))\)\(^{\oplus 2}\)