Defining parameters
Level: | \( N \) | \(=\) | \( 1815 = 3 \cdot 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1815.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 41 \) | ||
Sturm bound: | \(1056\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(2\), \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(1815))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 816 | 218 | 598 |
Cusp forms | 768 | 218 | 550 |
Eisenstein series | 48 | 0 | 48 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(3\) | \(5\) | \(11\) | Fricke | Dim |
---|---|---|---|---|
\(+\) | \(+\) | \(+\) | $+$ | \(28\) |
\(+\) | \(+\) | \(-\) | $-$ | \(27\) |
\(+\) | \(-\) | \(+\) | $-$ | \(22\) |
\(+\) | \(-\) | \(-\) | $+$ | \(32\) |
\(-\) | \(+\) | \(+\) | $-$ | \(26\) |
\(-\) | \(+\) | \(-\) | $+$ | \(28\) |
\(-\) | \(-\) | \(+\) | $+$ | \(32\) |
\(-\) | \(-\) | \(-\) | $-$ | \(23\) |
Plus space | \(+\) | \(120\) | ||
Minus space | \(-\) | \(98\) |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(1815))\) into newform subspaces
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(1815))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_0(1815)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(165))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(363))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(605))\)\(^{\oplus 2}\)