Defining parameters
Level: | \( N \) | \(=\) | \( 98 = 2 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 98.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 8 \) | ||
Sturm bound: | \(56\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(98))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 50 | 10 | 40 |
Cusp forms | 34 | 10 | 24 |
Eisenstein series | 16 | 0 | 16 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(7\) | Fricke | Total | Cusp | Eisenstein | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
All | New | Old | All | New | Old | All | New | Old | ||||||
\(+\) | \(+\) | \(+\) | \(14\) | \(3\) | \(11\) | \(10\) | \(3\) | \(7\) | \(4\) | \(0\) | \(4\) | |||
\(+\) | \(-\) | \(-\) | \(11\) | \(2\) | \(9\) | \(7\) | \(2\) | \(5\) | \(4\) | \(0\) | \(4\) | |||
\(-\) | \(+\) | \(-\) | \(12\) | \(1\) | \(11\) | \(8\) | \(1\) | \(7\) | \(4\) | \(0\) | \(4\) | |||
\(-\) | \(-\) | \(+\) | \(13\) | \(4\) | \(9\) | \(9\) | \(4\) | \(5\) | \(4\) | \(0\) | \(4\) | |||
Plus space | \(+\) | \(27\) | \(7\) | \(20\) | \(19\) | \(7\) | \(12\) | \(8\) | \(0\) | \(8\) | ||||
Minus space | \(-\) | \(23\) | \(3\) | \(20\) | \(15\) | \(3\) | \(12\) | \(8\) | \(0\) | \(8\) |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(98))\) into newform subspaces
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(98))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_0(98)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 2}\)