Defining parameters
Level: | \( N \) | \(=\) | \( 3840 = 2^{8} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 3840.c (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 15 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 8 \) | ||
Sturm bound: | \(768\) | ||
Trace bound: | \(15\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(3840, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 88 | 20 | 68 |
Cusp forms | 40 | 12 | 28 |
Eisenstein series | 48 | 8 | 40 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 12 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(3840, [\chi])\) into newform subspaces
Decomposition of \(S_{1}^{\mathrm{old}}(3840, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(3840, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(960, [\chi])\)\(^{\oplus 3}\)