Defining parameters
Level: | \( N \) | = | \( 120 = 2^{3} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 9 \) | ||
Newform subspaces: | \( 18 \) | ||
Sturm bound: | \(1536\) | ||
Trace bound: | \(4\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(120))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 480 | 160 | 320 |
Cusp forms | 289 | 136 | 153 |
Eisenstein series | 191 | 24 | 167 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(120))\)
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 available newforms together with their dimension.
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(120))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(120)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 2}\)