Defining parameters
Level: | \( N \) | \(=\) | \( 255 = 3 \cdot 5 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 255.j (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 17 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(72\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(255, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 80 | 24 | 56 |
Cusp forms | 64 | 24 | 40 |
Eisenstein series | 16 | 0 | 16 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(255, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
255.2.j.a | $8$ | $2.036$ | 8.0.110166016.2 | None | \(0\) | \(0\) | \(0\) | \(-4\) | \(q+\beta _{1}q^{2}+\beta _{3}q^{3}+(-1+\beta _{4}-\beta _{5}+\cdots)q^{4}+\cdots\) |
255.2.j.b | $16$ | $2.036$ | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(4\) | \(q+\beta _{1}q^{2}-\beta _{8}q^{3}+(-1+\beta _{2}-\beta _{8}+\cdots)q^{4}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(255, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(255, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(51, [\chi])\)\(^{\oplus 2}\)