Defining parameters
Level: | \( N \) | \(=\) | \( 2016 = 2^{5} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 2016.l (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 56 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(384\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(2016, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 56 | 5 | 51 |
Cusp forms | 24 | 3 | 21 |
Eisenstein series | 32 | 2 | 30 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 3 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(2016, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
2016.1.l.a | $1$ | $1.006$ | \(\Q\) | $D_{2}$ | \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-14}) \) | \(\Q(\sqrt{2}) \) | \(0\) | \(0\) | \(0\) | \(1\) | \(q+q^{7}+2q^{23}-q^{25}+q^{49}-2q^{71}+\cdots\) |
2016.1.l.b | $2$ | $1.006$ | \(\Q(\sqrt{-1}) \) | $D_{2}$ | \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-6}) \) | \(\Q(\sqrt{42}) \) | \(0\) | \(0\) | \(0\) | \(-2\) | \(q-q^{7}-iq^{11}-q^{25}-iq^{29}+q^{49}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(2016, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(2016, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 3}\)