Defining parameters
Level: | \( N \) | = | \( 336 = 2^{4} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | = | \( 3 \) |
Nonzero newspaces: | \( 16 \) | ||
Newform subspaces: | \( 57 \) | ||
Sturm bound: | \(18432\) | ||
Trace bound: | \(9\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(336))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 6480 | 2528 | 3952 |
Cusp forms | 5808 | 2440 | 3368 |
Eisenstein series | 672 | 88 | 584 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(336))\)
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 available newforms together with their dimension.
Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(336))\) into lower level spaces
\( S_{3}^{\mathrm{old}}(\Gamma_1(336)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(168))\)\(^{\oplus 2}\)