Defining parameters
Level: | \( N \) | \(=\) | \( 1323 = 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1323.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 31 \) | ||
Sturm bound: | \(336\) | ||
Trace bound: | \(13\) | ||
Distinguishing \(T_p\): | \(2\), \(5\), \(13\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1323))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 192 | 55 | 137 |
Cusp forms | 145 | 55 | 90 |
Eisenstein series | 47 | 0 | 47 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(3\) | \(7\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | \(+\) | \(12\) |
\(+\) | \(-\) | \(-\) | \(16\) |
\(-\) | \(+\) | \(-\) | \(15\) |
\(-\) | \(-\) | \(+\) | \(12\) |
Plus space | \(+\) | \(24\) | |
Minus space | \(-\) | \(31\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1323))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1323))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(1323)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(147))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(189))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(441))\)\(^{\oplus 2}\)