Defining parameters
Level: | \( N \) | \(=\) | \( 63 = 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 63.f (of order \(3\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 9 \) |
Character field: | \(\Q(\zeta_{3})\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(32\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(63, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 52 | 36 | 16 |
Cusp forms | 44 | 36 | 8 |
Eisenstein series | 8 | 0 | 8 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(63, [\chi])\) into newform subspaces
Label | Dim. | \(A\) | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
\(a_2\) | \(a_3\) | \(a_5\) | \(a_7\) | ||||||
63.4.f.a | \(2\) | \(3.717\) | \(\Q(\sqrt{-3}) \) | None | \(1\) | \(-9\) | \(14\) | \(7\) | \(q+\zeta_{6}q^{2}+(-6+3\zeta_{6})q^{3}+(7-7\zeta_{6})q^{4}+\cdots\) |
63.4.f.b | \(16\) | \(3.717\) | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) | None | \(-3\) | \(2\) | \(-30\) | \(56\) | \(q-\beta _{1}q^{2}+(-\beta _{3}-\beta _{7})q^{3}+(5\beta _{3}-\beta _{5}+\cdots)q^{4}+\cdots\) |
63.4.f.c | \(18\) | \(3.717\) | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) | None | \(6\) | \(9\) | \(24\) | \(-63\) | \(q+(1-\beta _{2}-\beta _{3}-\beta _{5})q^{2}+(1+\beta _{8})q^{3}+\cdots\) |
Decomposition of \(S_{4}^{\mathrm{old}}(63, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(63, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 2}\)