Defining parameters
Level: | \( N \) | \(=\) | \( 1600 = 2^{6} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 1600.m (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 40 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(240\) | ||
Trace bound: | \(19\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(1600, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 84 | 12 | 72 |
Cusp forms | 12 | 12 | 0 |
Eisenstein series | 72 | 0 | 72 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 12 | 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.m.a | $2$ | $0.799$ | \(\Q(\sqrt{-1}) \) | $D_{2}$ | \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-10}) \) | \(\Q(\sqrt{5}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q-i q^{9}-2 i q^{11}-2 q^{19}+2 q^{41}+\cdots\) |
1600.1.m.b | $2$ | $0.799$ | \(\Q(\sqrt{-1}) \) | $D_{2}$ | \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-10}) \) | \(\Q(\sqrt{5}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q-i q^{9}+2 i q^{11}+2 q^{19}+2 q^{41}+\cdots\) |
1600.1.m.c | $4$ | $0.799$ | \(\Q(i, \sqrt{6})\) | $D_{6}$ | \(\Q(\sqrt{-2}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{1}q^{3}+2\beta _{2}q^{9}-\beta _{2}q^{11}-\beta _{1}q^{17}+\cdots\) |
1600.1.m.d | $4$ | $0.799$ | \(\Q(i, \sqrt{6})\) | $D_{6}$ | \(\Q(\sqrt{-2}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{1}q^{3}+2\beta _{2}q^{9}+\beta _{2}q^{11}+\beta _{1}q^{17}+\cdots\) |