Defining parameters
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.bj (of order \(42\) and degree \(12\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 49 \) |
Character field: | \(\Q(\zeta_{42})\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(168\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(441, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1392 | 576 | 816 |
Cusp forms | 1296 | 552 | 744 |
Eisenstein series | 96 | 24 | 72 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(441, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
441.3.bj.a | $12$ | $12.016$ | \(\Q(\zeta_{21})\) | \(\Q(\sqrt{-3}) \) | \(0\) | \(0\) | \(0\) | \(-13\) | \(q+(4\zeta_{21}^{3}+4\zeta_{21}^{10})q^{4}+(-5+5\zeta_{21}+\cdots)q^{7}+\cdots\) |
441.3.bj.b | $96$ | $12.016$ | None | \(13\) | \(0\) | \(14\) | \(-14\) | ||
441.3.bj.c | $108$ | $12.016$ | None | \(0\) | \(0\) | \(-9\) | \(7\) | ||
441.3.bj.d | $120$ | $12.016$ | None | \(0\) | \(0\) | \(3\) | \(-6\) | ||
441.3.bj.e | $216$ | $12.016$ | None | \(0\) | \(0\) | \(0\) | \(26\) |
Decomposition of \(S_{3}^{\mathrm{old}}(441, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(441, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 2}\)