Defining parameters
Level: | \( N \) | = | \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | = | \( 1 \) |
Nonzero newspaces: | \( 11 \) | ||
Newform subspaces: | \( 24 \) | ||
Sturm bound: | \(172800\) | ||
Trace bound: | \(19\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1800))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 3098 | 477 | 2621 |
Cusp forms | 410 | 108 | 302 |
Eisenstein series | 2688 | 369 | 2319 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 84 | 0 | 8 | 16 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1800))\)
We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(1800))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(1800)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(180))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(200))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(225))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(300))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(360))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(600))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(900))\)\(^{\oplus 2}\)