Defining parameters
Level: | \( N \) | \(=\) | \( 800 = 2^{5} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 800.f (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 40 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(240\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(800, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 144 | 20 | 124 |
Cusp forms | 96 | 16 | 80 |
Eisenstein series | 48 | 4 | 44 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(800, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
800.2.f.a | $2$ | $6.388$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(-2\) | \(0\) | \(0\) | \(q-q^{3}-2iq^{7}-2q^{9}+5iq^{11}+6q^{13}+\cdots\) |
800.2.f.b | $2$ | $6.388$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(2\) | \(0\) | \(0\) | \(q+q^{3}+2iq^{7}-2q^{9}+5iq^{11}-6q^{13}+\cdots\) |
800.2.f.c | $4$ | $6.388$ | \(\Q(\zeta_{12})\) | None | \(0\) | \(-4\) | \(0\) | \(0\) | \(q+(-1-\zeta_{12})q^{3}+\zeta_{12}^{3}q^{7}+(1+2\zeta_{12}+\cdots)q^{9}+\cdots\) |
800.2.f.d | $4$ | $6.388$ | \(\Q(i, \sqrt{7})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{2}q^{3}+4\beta _{1}q^{7}+4q^{9}-\beta _{3}q^{11}+\cdots\) |
800.2.f.e | $4$ | $6.388$ | \(\Q(\zeta_{12})\) | None | \(0\) | \(4\) | \(0\) | \(0\) | \(q+(1+\zeta_{12})q^{3}-\zeta_{12}^{3}q^{7}+(1+2\zeta_{12}+\cdots)q^{9}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(800, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(800, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 6}\)