Defining parameters
Level: | \( N \) | \(=\) | \( 125 = 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 125.d (of order \(5\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 25 \) |
Character field: | \(\Q(\zeta_{5})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(25\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(125, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 68 | 44 | 24 |
Cusp forms | 28 | 20 | 8 |
Eisenstein series | 40 | 24 | 16 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(125, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
125.2.d.a | $4$ | $0.998$ | \(\Q(\zeta_{10})\) | None | \(2\) | \(1\) | \(0\) | \(2\) | \(q+(\zeta_{10}-\zeta_{10}^{2})q^{2}+\zeta_{10}^{3}q^{3}+(-1+\cdots)q^{4}+\cdots\) |
125.2.d.b | $16$ | $0.998$ | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{6}q^{2}+(\beta _{6}+\beta _{12}+\beta _{13}-\beta _{14}+\cdots)q^{3}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(125, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(125, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 2}\)