Defining parameters
Level: | \( N \) | \(=\) | \( 121 = 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 121.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 11 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(33\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(121, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 28 | 22 | 6 |
Cusp forms | 16 | 14 | 2 |
Eisenstein series | 12 | 8 | 4 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(121, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
121.3.b.a | $2$ | $3.297$ | \(\Q(\sqrt{-2}) \) | None | \(0\) | \(-2\) | \(-14\) | \(0\) | \(q+\beta q^{2}-q^{3}+2q^{4}-7q^{5}-\beta q^{6}+\cdots\) |
121.3.b.b | $4$ | $3.297$ | \(\Q(\zeta_{10})\) | None | \(0\) | \(10\) | \(16\) | \(0\) | \(q+(\zeta_{10}-\zeta_{10}^{3})q^{2}+(2-\zeta_{10}^{2})q^{3}+\cdots\) |
121.3.b.c | $8$ | $3.297$ | 8.0.\(\cdots\).1 | None | \(0\) | \(-4\) | \(-4\) | \(0\) | \(q+\beta _{1}q^{2}+(-1+\beta _{3}+\beta _{5})q^{3}+(-3+\cdots)q^{4}+\cdots\) |
Decomposition of \(S_{3}^{\mathrm{old}}(121, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(121, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(11, [\chi])\)\(^{\oplus 2}\)