Defining parameters
Level: | \( N \) | \(=\) | \( 363 = 3 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 363.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 22 \) | ||
Sturm bound: | \(176\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(2\), \(5\), \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(363))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 144 | 54 | 90 |
Cusp forms | 120 | 54 | 66 |
Eisenstein series | 24 | 0 | 24 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(3\) | \(11\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | \(+\) | \(14\) |
\(+\) | \(-\) | \(-\) | \(13\) |
\(-\) | \(+\) | \(-\) | \(10\) |
\(-\) | \(-\) | \(+\) | \(17\) |
Plus space | \(+\) | \(31\) | |
Minus space | \(-\) | \(23\) |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(363))\) into newform subspaces
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(363))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_0(363)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 2}\)