Defining parameters
Level: | \( N \) | \(=\) | \( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1350.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 24 \) | ||
Sturm bound: | \(540\) | ||
Trace bound: | \(17\) | ||
Distinguishing \(T_p\): | \(7\), \(11\), \(13\), \(17\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1350))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 306 | 26 | 280 |
Cusp forms | 235 | 26 | 209 |
Eisenstein series | 71 | 0 | 71 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(3\) | \(5\) | Fricke | Dim |
---|---|---|---|---|
\(+\) | \(+\) | \(+\) | \(+\) | \(3\) |
\(+\) | \(+\) | \(-\) | \(-\) | \(4\) |
\(+\) | \(-\) | \(+\) | \(-\) | \(3\) |
\(+\) | \(-\) | \(-\) | \(+\) | \(3\) |
\(-\) | \(+\) | \(+\) | \(-\) | \(4\) |
\(-\) | \(+\) | \(-\) | \(+\) | \(2\) |
\(-\) | \(-\) | \(+\) | \(+\) | \(2\) |
\(-\) | \(-\) | \(-\) | \(-\) | \(5\) |
Plus space | \(+\) | \(10\) | ||
Minus space | \(-\) | \(16\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1350))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1350))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(1350)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(54))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(90))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(135))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(150))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(225))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(270))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(450))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(675))\)\(^{\oplus 2}\)