Defining parameters
Level: | \( N \) | \(=\) | \( 440 = 2^{3} \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 440.bh (of order \(10\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 440 \) |
Character field: | \(\Q(\zeta_{10})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(72\) | ||
Trace bound: | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(440, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 24 | 24 | 0 |
Cusp forms | 8 | 8 | 0 |
Eisenstein series | 16 | 16 | 0 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 8 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(440, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
440.1.bh.a | $4$ | $0.220$ | \(\Q(\zeta_{10})\) | $D_{5}$ | \(\Q(\sqrt{-10}) \) | None | \(-1\) | \(0\) | \(-1\) | \(3\) | \(q-\zeta_{10}q^{2}+\zeta_{10}^{2}q^{4}+\zeta_{10}^{4}q^{5}+(1+\cdots)q^{7}+\cdots\) |
440.1.bh.b | $4$ | $0.220$ | \(\Q(\zeta_{10})\) | $D_{5}$ | \(\Q(\sqrt{-10}) \) | None | \(1\) | \(0\) | \(1\) | \(-3\) | \(q+\zeta_{10}q^{2}+\zeta_{10}^{2}q^{4}-\zeta_{10}^{4}q^{5}+(-1+\cdots)q^{7}+\cdots\) |