Defining parameters
Level: | \( N \) | \(=\) | \( 4000 = 2^{5} \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 4000.h (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 20 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(600\) | ||
Trace bound: | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(4000, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 78 | 8 | 70 |
Cusp forms | 38 | 8 | 30 |
Eisenstein series | 40 | 0 | 40 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 0 | 0 | 0 | 8 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(4000, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
4000.1.h.a | $4$ | $1.996$ | \(\Q(i, \sqrt{5})\) | $A_{5}$ | None | None | \(0\) | \(-2\) | \(0\) | \(4\) | \(q+(-1-\beta _{2})q^{3}+q^{7}+(1+\beta _{2})q^{9}+\cdots\) |
4000.1.h.b | $4$ | $1.996$ | \(\Q(i, \sqrt{5})\) | $A_{5}$ | None | None | \(0\) | \(2\) | \(0\) | \(-4\) | \(q+(1+\beta _{2})q^{3}-q^{7}+(1+\beta _{2})q^{9}+\beta _{3}q^{11}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(4000, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(4000, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(500, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(2000, [\chi])\)\(^{\oplus 2}\)