Defining parameters
Level: | \( N \) | \(=\) | \( 1215 = 3^{5} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 1215.d (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 15 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(162\) | ||
Trace bound: | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(1215, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 30 | 6 | 24 |
Cusp forms | 12 | 6 | 6 |
Eisenstein series | 18 | 0 | 18 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 6 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(1215, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
1215.1.d.a | $3$ | $0.606$ | \(\Q(\zeta_{18})^+\) | $D_{9}$ | \(\Q(\sqrt{-15}) \) | None | \(0\) | \(0\) | \(-3\) | \(0\) | \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+(1+\beta _{1}+\cdots)q^{8}+\cdots\) |
1215.1.d.b | $3$ | $0.606$ | \(\Q(\zeta_{18})^+\) | $D_{9}$ | \(\Q(\sqrt{-15}) \) | None | \(0\) | \(0\) | \(3\) | \(0\) | \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}+(-1-\beta _{1}+\cdots)q^{8}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(1215, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(1215, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(405, [\chi])\)\(^{\oplus 2}\)