Defining parameters
Level: | \( N \) | \(=\) | \( 3600 = 2^{4} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 3600.cj (of order \(10\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 100 \) |
Character field: | \(\Q(\zeta_{10})\) | ||
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 | 152 | 8 | 144 |
Cusp forms | 56 | 8 | 48 |
Eisenstein series | 96 | 0 | 96 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 8 | 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.cj.a | $8$ | $1.797$ | \(\Q(\zeta_{20})\) | $D_{10}$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\zeta_{20}^{9}q^{5}+(\zeta_{20}^{6}-\zeta_{20}^{8})q^{13}+(-\zeta_{20}+\cdots)q^{17}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(3600, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(3600, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(900, [\chi])\)\(^{\oplus 3}\)