Defining parameters
Level: | \( N \) | = | \( 224 = 2^{5} \cdot 7 \) |
Weight: | \( k \) | = | \( 3 \) |
Nonzero newspaces: | \( 12 \) | ||
Newform subspaces: | \( 26 \) | ||
Sturm bound: | \(9216\) | ||
Trace bound: | \(13\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(224))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 3264 | 1706 | 1558 |
Cusp forms | 2880 | 1606 | 1274 |
Eisenstein series | 384 | 100 | 284 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(224))\)
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 \(S_{3}^{\mathrm{old}}(\Gamma_1(224))\) into lower level spaces
\( S_{3}^{\mathrm{old}}(\Gamma_1(224)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 2}\)