Defining parameters
Level: | \( N \) | \(=\) | \( 3222 = 2 \cdot 3^{2} \cdot 179 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3222.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 24 \) | ||
Sturm bound: | \(1080\) | ||
Trace bound: | \(11\) | ||
Distinguishing \(T_p\): | \(5\), \(7\), \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3222))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 548 | 75 | 473 |
Cusp forms | 533 | 75 | 458 |
Eisenstein series | 15 | 0 | 15 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(3\) | \(179\) | Fricke | Dim |
---|---|---|---|---|
\(+\) | \(+\) | \(+\) | $+$ | \(6\) |
\(+\) | \(+\) | \(-\) | $-$ | \(9\) |
\(+\) | \(-\) | \(+\) | $-$ | \(11\) |
\(+\) | \(-\) | \(-\) | $+$ | \(12\) |
\(-\) | \(+\) | \(+\) | $-$ | \(9\) |
\(-\) | \(+\) | \(-\) | $+$ | \(6\) |
\(-\) | \(-\) | \(+\) | $+$ | \(9\) |
\(-\) | \(-\) | \(-\) | $-$ | \(13\) |
Plus space | \(+\) | \(33\) | ||
Minus space | \(-\) | \(42\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3222))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(3222))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(3222)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(179))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(358))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(537))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1074))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1611))\)\(^{\oplus 2}\)