Defining parameters
Level: | \( N \) | \(=\) | \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 720.j (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 20 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(144\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(720, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 34 | 1 | 33 |
Cusp forms | 10 | 1 | 9 |
Eisenstein series | 24 | 0 | 24 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 1 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(720, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
720.1.j.a | $1$ | $0.359$ | \(\Q\) | $D_{2}$ | \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-5}) \) | \(\Q(\sqrt{5}) \) | \(0\) | \(0\) | \(1\) | \(0\) | \(q+q^{5}+q^{25}-2q^{29}+2q^{41}-q^{49}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(720, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(720, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 2}\)