Defining parameters
Level: | \( N \) | \(=\) | \( 354 = 2 \cdot 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 354.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 9 \) | ||
Sturm bound: | \(240\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(354))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 184 | 28 | 156 |
Cusp forms | 176 | 28 | 148 |
Eisenstein series | 8 | 0 | 8 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(3\) | \(59\) | Fricke | Dim |
---|---|---|---|---|
\(+\) | \(+\) | \(+\) | $+$ | \(3\) |
\(+\) | \(+\) | \(-\) | $-$ | \(3\) |
\(+\) | \(-\) | \(+\) | $-$ | \(2\) |
\(+\) | \(-\) | \(-\) | $+$ | \(5\) |
\(-\) | \(+\) | \(+\) | $-$ | \(3\) |
\(-\) | \(+\) | \(-\) | $+$ | \(4\) |
\(-\) | \(-\) | \(+\) | $+$ | \(6\) |
\(-\) | \(-\) | \(-\) | $-$ | \(2\) |
Plus space | \(+\) | \(18\) | ||
Minus space | \(-\) | \(10\) |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(354))\) into newform subspaces
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(354))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_0(354)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(59))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(118))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(177))\)\(^{\oplus 2}\)