Defining parameters
Level: | \( N \) | \(=\) | \( 3600 = 2^{4} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 3600.dx (of order \(20\) and degree \(8\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 300 \) |
Character field: | \(\Q(\zeta_{20})\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(720\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(3600, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 256 | 16 | 240 |
Cusp forms | 64 | 16 | 48 |
Eisenstein series | 192 | 0 | 192 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 16 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(3600, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
3600.1.dx.a | $16$ | $1.797$ | \(\Q(\zeta_{40})\) | $D_{20}$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\zeta_{40}^{7}q^{5}+(-\zeta_{40}^{4}+\zeta_{40}^{18})q^{13}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(3600, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(3600, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(900, [\chi])\)\(^{\oplus 3}\)