Defining parameters
Level: | \( N \) | \(=\) | \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 1900.j (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 380 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(300\) | ||
Trace bound: | \(19\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(1900, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 40 | 24 | 16 |
Cusp forms | 16 | 16 | 0 |
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 | 16 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(1900, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
1900.1.j.a | $8$ | $0.948$ | \(\Q(\zeta_{16})\) | $D_{8}$ | \(\Q(\sqrt{-95}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\zeta_{16}^{5}q^{2}+(-\zeta_{16}^{5}+\zeta_{16}^{7})q^{3}+\cdots\) |
1900.1.j.b | $8$ | $0.948$ | \(\Q(\zeta_{16})\) | $D_{8}$ | \(\Q(\sqrt{-95}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\zeta_{16}^{3}q^{2}+(\zeta_{16}+\zeta_{16}^{3})q^{3}+\zeta_{16}^{6}q^{4}+\cdots\) |