Defining parameters
Level: | \( N \) | \(=\) | \( 144 = 2^{4} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 144.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 20 \) | ||
Sturm bound: | \(288\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_0(144))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 276 | 28 | 248 |
Cusp forms | 252 | 27 | 225 |
Eisenstein series | 24 | 1 | 23 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(3\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(6\) |
\(+\) | \(-\) | $-$ | \(8\) |
\(-\) | \(+\) | $-$ | \(5\) |
\(-\) | \(-\) | $+$ | \(8\) |
Plus space | \(+\) | \(14\) | |
Minus space | \(-\) | \(13\) |
Trace form
Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_0(144))\) into newform subspaces
Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_0(144))\) into lower level spaces
\( S_{12}^{\mathrm{old}}(\Gamma_0(144)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 15}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 10}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 9}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 5}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 3}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 3}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 2}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 2}\)