Defining parameters
Level: | \( N \) | \(=\) | \( 2178 = 2 \cdot 3^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2178.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 59 \) | ||
Sturm bound: | \(1584\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(5\), \(7\), \(17\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(2178))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1236 | 136 | 1100 |
Cusp forms | 1140 | 136 | 1004 |
Eisenstein series | 96 | 0 | 96 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(3\) | \(11\) | Fricke | Dim |
---|---|---|---|---|
\(+\) | \(+\) | \(+\) | $+$ | \(12\) |
\(+\) | \(+\) | \(-\) | $-$ | \(15\) |
\(+\) | \(-\) | \(+\) | $-$ | \(20\) |
\(+\) | \(-\) | \(-\) | $+$ | \(21\) |
\(-\) | \(+\) | \(+\) | $-$ | \(12\) |
\(-\) | \(+\) | \(-\) | $+$ | \(15\) |
\(-\) | \(-\) | \(+\) | $+$ | \(22\) |
\(-\) | \(-\) | \(-\) | $-$ | \(19\) |
Plus space | \(+\) | \(70\) | ||
Minus space | \(-\) | \(66\) |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(2178))\) into newform subspaces
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(2178))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_0(2178)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(18))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(99))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(198))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(242))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(363))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(726))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(1089))\)\(^{\oplus 2}\)