Defining parameters
Level: | \( N \) | = | \( 270 = 2 \cdot 3^{3} \cdot 5 \) |
Weight: | \( k \) | = | \( 3 \) |
Nonzero newspaces: | \( 9 \) | ||
Newform subspaces: | \( 21 \) | ||
Sturm bound: | \(11664\) | ||
Trace bound: | \(4\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(270))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 4128 | 940 | 3188 |
Cusp forms | 3648 | 940 | 2708 |
Eisenstein series | 480 | 0 | 480 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(270))\)
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 \(S_{3}^{\mathrm{old}}(\Gamma_1(270))\) into lower level spaces
\( S_{3}^{\mathrm{old}}(\Gamma_1(270)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(135))\)\(^{\oplus 2}\)