Defining parameters
Level: | \( N \) | \(=\) | \( 63 = 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 63.m (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 7 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(24\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(63, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 40 | 16 | 24 |
Cusp forms | 24 | 12 | 12 |
Eisenstein series | 16 | 4 | 12 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(63, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
63.3.m.a | $2$ | $1.717$ | \(\Q(\sqrt{-3}) \) | None | \(-2\) | \(0\) | \(6\) | \(-7\) | \(q-2\zeta_{6}q^{2}+(4-2\zeta_{6})q^{5}-7\zeta_{6}q^{7}+\cdots\) |
63.3.m.b | $2$ | $1.717$ | \(\Q(\sqrt{-3}) \) | \(\Q(\sqrt{-3}) \) | \(0\) | \(0\) | \(0\) | \(13\) | \(q+(4-4\zeta_{6})q^{4}+(8-3\zeta_{6})q^{7}+(-7+\cdots)q^{13}+\cdots\) |
63.3.m.c | $2$ | $1.717$ | \(\Q(\sqrt{-3}) \) | None | \(1\) | \(0\) | \(9\) | \(-7\) | \(q+\zeta_{6}q^{2}+(3-3\zeta_{6})q^{4}+(6-3\zeta_{6})q^{5}+\cdots\) |
63.3.m.d | $2$ | $1.717$ | \(\Q(\sqrt{-3}) \) | None | \(3\) | \(0\) | \(-9\) | \(13\) | \(q+3\zeta_{6}q^{2}+(-5+5\zeta_{6})q^{4}+(-6+3\zeta_{6})q^{5}+\cdots\) |
63.3.m.e | $4$ | $1.717$ | \(\Q(\sqrt{-3}, \sqrt{13})\) | None | \(0\) | \(0\) | \(0\) | \(-26\) | \(q-\beta _{2}q^{2}+(-9+9\beta _{1})q^{4}+(\beta _{2}+2\beta _{3})q^{5}+\cdots\) |
Decomposition of \(S_{3}^{\mathrm{old}}(63, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(63, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)