Defining parameters
Level: | \( N \) | = | \( 400 = 2^{4} \cdot 5^{2} \) |
Weight: | \( k \) | = | \( 3 \) |
Nonzero newspaces: | \( 14 \) | ||
Newform subspaces: | \( 60 \) | ||
Sturm bound: | \(28800\) | ||
Trace bound: | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(400))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 9992 | 5069 | 4923 |
Cusp forms | 9208 | 4885 | 4323 |
Eisenstein series | 784 | 184 | 600 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(400))\)
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 \(S_{3}^{\mathrm{old}}(\Gamma_1(400))\) into lower level spaces
\( S_{3}^{\mathrm{old}}(\Gamma_1(400)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(200))\)\(^{\oplus 2}\)