Defining parameters
Level: | \( N \) | \(=\) | \( 3240 = 2^{3} \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 3240.p (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 40 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(648\) | ||
Trace bound: | \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(3240, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 46 | 16 | 30 |
Cusp forms | 22 | 8 | 14 |
Eisenstein series | 24 | 8 | 16 |
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 \(S_{1}^{\mathrm{new}}(3240, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
3240.1.p.a | $1$ | $1.617$ | \(\Q\) | $D_{3}$ | \(\Q(\sqrt{-10}) \) | None | \(-1\) | \(0\) | \(-1\) | \(-1\) | \(q-q^{2}+q^{4}-q^{5}-q^{7}-q^{8}+q^{10}+\cdots\) |
3240.1.p.b | $1$ | $1.617$ | \(\Q\) | $D_{3}$ | \(\Q(\sqrt{-10}) \) | None | \(-1\) | \(0\) | \(-1\) | \(1\) | \(q-q^{2}+q^{4}-q^{5}+q^{7}-q^{8}+q^{10}+\cdots\) |
3240.1.p.c | $1$ | $1.617$ | \(\Q\) | $D_{3}$ | \(\Q(\sqrt{-10}) \) | None | \(1\) | \(0\) | \(1\) | \(-1\) | \(q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots\) |
3240.1.p.d | $1$ | $1.617$ | \(\Q\) | $D_{3}$ | \(\Q(\sqrt{-10}) \) | None | \(1\) | \(0\) | \(1\) | \(1\) | \(q+q^{2}+q^{4}+q^{5}+q^{7}+q^{8}+q^{10}+\cdots\) |
3240.1.p.e | $2$ | $1.617$ | \(\Q(\sqrt{3}) \) | $D_{6}$ | \(\Q(\sqrt{-10}) \) | None | \(-2\) | \(0\) | \(2\) | \(0\) | \(q-q^{2}+q^{4}+q^{5}-\beta q^{7}-q^{8}-q^{10}+\cdots\) |
3240.1.p.f | $2$ | $1.617$ | \(\Q(\sqrt{3}) \) | $D_{6}$ | \(\Q(\sqrt{-10}) \) | None | \(2\) | \(0\) | \(-2\) | \(0\) | \(q+q^{2}+q^{4}-q^{5}-\beta q^{7}+q^{8}-q^{10}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(3240, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(3240, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(1080, [\chi])\)\(^{\oplus 2}\)