Defining parameters
Level: | \( N \) | = | \( 1862 = 2 \cdot 7^{2} \cdot 19 \) |
Weight: | \( k \) | = | \( 4 \) |
Nonzero newspaces: | \( 32 \) | ||
Sturm bound: | \(846720\) | ||
Trace bound: | \(12\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1862))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 319680 | 101001 | 218679 |
Cusp forms | 315360 | 101001 | 214359 |
Eisenstein series | 4320 | 0 | 4320 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1862))\)
We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1862))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_1(1862)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(133))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(266))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(931))\)\(^{\oplus 2}\)