Defining parameters
Level: | \( N \) | \(=\) | \( 220 = 2^{2} \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 220.l (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 20 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(72\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(220, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 80 | 60 | 20 |
Cusp forms | 64 | 60 | 4 |
Eisenstein series | 16 | 0 | 16 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(220, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
220.2.l.a | $2$ | $1.757$ | \(\Q(\sqrt{-1}) \) | None | \(-2\) | \(-4\) | \(-2\) | \(-2\) | \(q+(i-1)q^{2}+(-2 i-2)q^{3}-2 i q^{4}+\cdots\) |
220.2.l.b | $2$ | $1.757$ | \(\Q(\sqrt{-1}) \) | None | \(2\) | \(4\) | \(-2\) | \(2\) | \(q+(-i+1)q^{2}+(2 i+2)q^{3}-2 i q^{4}+\cdots\) |
220.2.l.c | $28$ | $1.757$ | None | \(-2\) | \(-4\) | \(2\) | \(-2\) | ||
220.2.l.d | $28$ | $1.757$ | None | \(2\) | \(4\) | \(2\) | \(2\) |
Decomposition of \(S_{2}^{\mathrm{old}}(220, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(220, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 2}\)