Defining parameters
Level: | \( N \) | \(=\) | \( 52 = 2^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 52.l (of order \(12\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 52 \) |
Character field: | \(\Q(\zeta_{12})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(42\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{6}(52, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 148 | 148 | 0 |
Cusp forms | 132 | 132 | 0 |
Eisenstein series | 16 | 16 | 0 |
Trace form
Decomposition of \(S_{6}^{\mathrm{new}}(52, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
52.6.l.a | $4$ | $8.340$ | \(\Q(\zeta_{12})\) | \(\Q(\sqrt{-1}) \) | \(8\) | \(0\) | \(6\) | \(0\) | \(q+(4\zeta_{12}+4\zeta_{12}^{2}-4\zeta_{12}^{3})q^{2}+2^{5}\zeta_{12}q^{4}+\cdots\) |
52.6.l.b | $128$ | $8.340$ | None | \(-12\) | \(0\) | \(-52\) | \(0\) |