Defining parameters
Level: | \( N \) | \(=\) | \( 1600 = 2^{6} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 1600.p (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 5 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(240\) | ||
Trace bound: | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(1600, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 102 | 10 | 92 |
Cusp forms | 30 | 6 | 24 |
Eisenstein series | 72 | 4 | 68 |
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 \(S_{1}^{\mathrm{new}}(1600, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
1600.1.p.a | $2$ | $0.799$ | \(\Q(\sqrt{-1}) \) | $D_{4}$ | \(\Q(\sqrt{-5}) \) | None | \(0\) | \(-2\) | \(0\) | \(-2\) | \(q+(-1+i)q^{3}+(-1-i)q^{7}-iq^{9}+\cdots\) |
1600.1.p.b | $2$ | $0.799$ | \(\Q(\sqrt{-1}) \) | $D_{4}$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+iq^{9}+(-1+i)q^{13}+(1+i)q^{17}+\cdots\) |
1600.1.p.c | $2$ | $0.799$ | \(\Q(\sqrt{-1}) \) | $D_{4}$ | \(\Q(\sqrt{-5}) \) | None | \(0\) | \(2\) | \(0\) | \(2\) | \(q+(1-i)q^{3}+(1+i)q^{7}-iq^{9}+q^{21}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(1600, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(1600, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(800, [\chi])\)\(^{\oplus 2}\)