Defining parameters
Level: | \( N \) | \(=\) | \( 500 = 2^{2} \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 500.h (of order \(10\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 100 \) |
Character field: | \(\Q(\zeta_{10})\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(75\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(500, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 48 | 32 | 16 |
Cusp forms | 8 | 8 | 0 |
Eisenstein series | 40 | 24 | 16 |
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 \(S_{1}^{\mathrm{new}}(500, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
500.1.h.a | $8$ | $0.250$ | \(\Q(\zeta_{20})\) | $D_{5}$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\zeta_{20}q^{2}+\zeta_{20}^{2}q^{4}-\zeta_{20}^{3}q^{8}-\zeta_{20}^{4}q^{9}+\cdots\) |