Defining parameters
Level: | \( N \) | = | \( 224 = 2^{5} \cdot 7 \) |
Weight: | \( k \) | = | \( 1 \) |
Nonzero newspaces: | \( 3 \) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(3072\) | ||
Trace bound: | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(224))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 208 | 59 | 149 |
Cusp forms | 16 | 9 | 7 |
Eisenstein series | 192 | 50 | 142 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 5 | 4 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(224))\)
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.
Label | \(\chi\) | Newforms | Dimension | \(\chi\) degree |
---|---|---|---|---|
224.1.c | \(\chi_{224}(97, \cdot)\) | None | 0 | 1 |
224.1.d | \(\chi_{224}(127, \cdot)\) | None | 0 | 1 |
224.1.g | \(\chi_{224}(15, \cdot)\) | None | 0 | 1 |
224.1.h | \(\chi_{224}(209, \cdot)\) | 224.1.h.a | 1 | 1 |
224.1.k | \(\chi_{224}(71, \cdot)\) | None | 0 | 2 |
224.1.l | \(\chi_{224}(41, \cdot)\) | None | 0 | 2 |
224.1.n | \(\chi_{224}(17, \cdot)\) | None | 0 | 2 |
224.1.o | \(\chi_{224}(79, \cdot)\) | None | 0 | 2 |
224.1.r | \(\chi_{224}(95, \cdot)\) | 224.1.r.a | 4 | 2 |
224.1.s | \(\chi_{224}(33, \cdot)\) | None | 0 | 2 |
224.1.v | \(\chi_{224}(13, \cdot)\) | 224.1.v.a | 4 | 4 |
224.1.w | \(\chi_{224}(43, \cdot)\) | None | 0 | 4 |
224.1.y | \(\chi_{224}(23, \cdot)\) | None | 0 | 4 |
224.1.bb | \(\chi_{224}(73, \cdot)\) | None | 0 | 4 |
224.1.bc | \(\chi_{224}(5, \cdot)\) | None | 0 | 8 |
224.1.bf | \(\chi_{224}(11, \cdot)\) | None | 0 | 8 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(224))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(224)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 2}\)