Defining parameters
Level: | \( N \) | \(=\) | \( 200 = 2^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 200.f (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 40 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(60\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(200, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 36 | 20 | 16 |
Cusp forms | 24 | 16 | 8 |
Eisenstein series | 12 | 4 | 8 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(200, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
200.2.f.a | $2$ | $1.597$ | \(\Q(\sqrt{-1}) \) | None | \(-2\) | \(-2\) | \(0\) | \(0\) | \(q+(-1+i)q^{2}-q^{3}-2iq^{4}+(1-i)q^{6}+\cdots\) |
200.2.f.b | $2$ | $1.597$ | \(\Q(\sqrt{-1}) \) | None | \(2\) | \(2\) | \(0\) | \(0\) | \(q+(1+i)q^{2}+q^{3}+2iq^{4}+(1+i)q^{6}+\cdots\) |
200.2.f.c | $4$ | $1.597$ | \(\Q(\zeta_{12})\) | None | \(-2\) | \(4\) | \(0\) | \(0\) | \(q+(-\zeta_{12}+\zeta_{12}^{2})q^{2}+(1-\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{3}+\cdots\) |
200.2.f.d | $4$ | $1.597$ | \(\Q(i, \sqrt{7})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{1}q^{2}+(-2\beta _{1}+\beta _{3})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots\) |
200.2.f.e | $4$ | $1.597$ | \(\Q(\zeta_{12})\) | None | \(2\) | \(-4\) | \(0\) | \(0\) | \(q+(\zeta_{12}-\zeta_{12}^{2})q^{2}+(-1+\zeta_{12}-\zeta_{12}^{2}+\cdots)q^{3}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(200, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(200, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 2}\)