Defining parameters
Level: | \( N \) | \(=\) | \( 2500 = 2^{2} \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 2500.p (of order \(50\) and degree \(20\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 500 \) |
Character field: | \(\Q(\zeta_{50})\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(375\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(2500, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 260 | 140 | 120 |
Cusp forms | 60 | 20 | 40 |
Eisenstein series | 200 | 120 | 80 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 20 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(2500, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
2500.1.p.a | $20$ | $1.248$ | \(\Q(\zeta_{50})\) | $D_{25}$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\zeta_{50}^{3}q^{2}+\zeta_{50}^{6}q^{4}+\zeta_{50}^{9}q^{8}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(2500, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(2500, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(500, [\chi])\)\(^{\oplus 2}\)