Defining parameters
Level: | \( N \) | \(=\) | \( 180 = 2^{2} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 180.f (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 20 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(36\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(180, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 10 | 4 | 6 |
Cusp forms | 2 | 2 | 0 |
Eisenstein series | 8 | 2 | 6 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 2 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(180, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
180.1.f.a | $2$ | $0.090$ | \(\Q(\sqrt{-1}) \) | $D_{2}$ | \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-15}) \) | \(\Q(\sqrt{15}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q-iq^{2}-q^{4}-iq^{5}+iq^{8}-q^{10}+\cdots\) |