Defining parameters
Level: | \( N \) | = | \( 1984 = 2^{6} \cdot 31 \) |
Weight: | \( k \) | = | \( 1 \) |
Nonzero newspaces: | \( 6 \) | ||
Newform subspaces: | \( 10 \) | ||
Sturm bound: | \(245760\) | ||
Trace bound: | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1984))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 2330 | 690 | 1640 |
Cusp forms | 170 | 52 | 118 |
Eisenstein series | 2160 | 638 | 1522 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 32 | 12 | 0 | 8 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1984))\)
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 \(S_{1}^{\mathrm{old}}(\Gamma_1(1984))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(1984)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 7}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(124))\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(248))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(496))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(992))\)\(^{\oplus 2}\)