Defining parameters
Level: | \( N \) | = | \( 280 = 2^{3} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 18 \) | ||
Newform subspaces: | \( 44 \) | ||
Sturm bound: | \(9216\) | ||
Trace bound: | \(10\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(280))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 2592 | 1198 | 1394 |
Cusp forms | 2017 | 1078 | 939 |
Eisenstein series | 575 | 120 | 455 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(280))\)
We only show spaces with even 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 \(S_{2}^{\mathrm{old}}(\Gamma_1(280))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(280)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(140))\)\(^{\oplus 2}\)