Defining parameters
Level: | \( N \) | = | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | = | \( 3 \) |
Nonzero newspaces: | \( 10 \) | ||
Newform subspaces: | \( 26 \) | ||
Sturm bound: | \(24576\) | ||
Trace bound: | \(25\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(384))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 8512 | 3504 | 5008 |
Cusp forms | 7872 | 3408 | 4464 |
Eisenstein series | 640 | 96 | 544 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(384))\)
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 \(S_{3}^{\mathrm{old}}(\Gamma_1(384))\) into lower level spaces
\( S_{3}^{\mathrm{old}}(\Gamma_1(384)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(128))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(192))\)\(^{\oplus 2}\)