Defining parameters
Level: | \( N \) | \(=\) | \( 224 = 2^{5} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 224.r (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 28 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(96\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(224, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 144 | 32 | 112 |
Cusp forms | 112 | 32 | 80 |
Eisenstein series | 32 | 0 | 32 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(224, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
224.3.r.a | $4$ | $6.104$ | \(\Q(\zeta_{12})\) | None | \(0\) | \(0\) | \(-18\) | \(0\) | \(q+5\zeta_{12}q^{3}-9\zeta_{12}^{2}q^{5}+(8\zeta_{12}-3\zeta_{12}^{3})q^{7}+\cdots\) |
224.3.r.b | $4$ | $6.104$ | \(\Q(\zeta_{12})\) | None | \(0\) | \(0\) | \(-2\) | \(0\) | \(q+\zeta_{12}q^{3}-\zeta_{12}^{2}q^{5}-7\zeta_{12}^{3}q^{7}+\cdots\) |
224.3.r.c | $12$ | $6.104$ | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) | None | \(0\) | \(0\) | \(2\) | \(0\) | \(q-\beta _{1}q^{3}+(\beta _{5}+\beta _{11})q^{5}+(\beta _{3}-\beta _{6}+\cdots)q^{7}+\cdots\) |
224.3.r.d | $12$ | $6.104$ | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) | None | \(0\) | \(0\) | \(18\) | \(0\) | \(q+(\beta _{7}+\beta _{9}-\beta _{10})q^{3}+(-3\beta _{1}+\beta _{4}+\cdots)q^{5}+\cdots\) |
Decomposition of \(S_{3}^{\mathrm{old}}(224, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(224, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 2}\)