Defining parameters
Level: | \( N \) | \(=\) | \( 63 = 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 63.h (of order \(3\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 63 \) |
Character field: | \(\Q(\zeta_{3})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(16\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(63, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 20 | 20 | 0 |
Cusp forms | 12 | 12 | 0 |
Eisenstein series | 8 | 8 | 0 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(63, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
63.2.h.a | $2$ | $0.503$ | \(\Q(\sqrt{-3}) \) | None | \(2\) | \(0\) | \(1\) | \(4\) | \(q+q^{2}+(1-2\zeta_{6})q^{3}-q^{4}+\zeta_{6}q^{5}+\cdots\) |
63.2.h.b | $10$ | $0.503$ | 10.0.\(\cdots\).1 | None | \(-4\) | \(-1\) | \(4\) | \(-4\) | \(q+(-\beta _{1}+\beta _{5})q^{2}-\beta _{8}q^{3}+(1-\beta _{4}+\cdots)q^{4}+\cdots\) |