Defining parameters
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.p (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 21 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(112\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(441, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 144 | 28 | 116 |
Cusp forms | 80 | 28 | 52 |
Eisenstein series | 64 | 0 | 64 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(441, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
441.2.p.a | $4$ | $3.521$ | \(\Q(\sqrt{-2}, \sqrt{-3})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{1}q^{2}+(\beta _{1}-2\beta _{3})q^{5}-2\beta _{3}q^{8}+\cdots\) |
441.2.p.b | $8$ | $3.521$ | 8.0.\(\cdots\).5 | \(\Q(\sqrt{-7}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{1}q^{2}+(2+\beta _{3}-2\beta _{4}+\beta _{6})q^{4}+\cdots\) |
441.2.p.c | $16$ | $3.521$ | \(\Q(\zeta_{48})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(\zeta_{48}-\zeta_{48}^{3}+\zeta_{48}^{5})q^{2}+(1-\zeta_{48}^{2}+\cdots)q^{4}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(441, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(441, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 2}\)