Defining parameters
Level: | \( N \) | \(=\) | \( 50 = 2 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 50.f (of order \(20\) and degree \(8\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 25 \) |
Character field: | \(\Q(\zeta_{20})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(22\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(50, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 136 | 40 | 96 |
Cusp forms | 104 | 40 | 64 |
Eisenstein series | 32 | 0 | 32 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(50, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
50.3.f.a | $16$ | $1.362$ | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) | None | \(-4\) | \(2\) | \(0\) | \(-2\) | \(q+(\beta _{1}+\beta _{9})q^{2}+(-1+\beta _{2}-\beta _{3}+\beta _{7}+\cdots)q^{3}+\cdots\) |
50.3.f.b | $24$ | $1.362$ | None | \(6\) | \(2\) | \(0\) | \(-2\) |
Decomposition of \(S_{3}^{\mathrm{old}}(50, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(50, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 2}\)