Defining parameters
Level: | \( N \) | \(=\) | \( 800 = 2^{5} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 800.ba (of order \(8\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 160 \) |
Character field: | \(\Q(\zeta_{8})\) | ||
Newform subspaces: | \( 8 \) | ||
Sturm bound: | \(240\) | ||
Trace bound: | \(16\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(800, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 504 | 296 | 208 |
Cusp forms | 456 | 280 | 176 |
Eisenstein series | 48 | 16 | 32 |
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.ba.a | $4$ | $6.388$ | \(\Q(\zeta_{8})\) | None | \(0\) | \(-4\) | \(0\) | \(4\) | \(q+(-\zeta_{8}+\zeta_{8}^{3})q^{2}+(-1+\zeta_{8}^{3})q^{3}+\cdots\) |
800.2.ba.b | $4$ | $6.388$ | \(\Q(\zeta_{8})\) | None | \(0\) | \(4\) | \(0\) | \(-4\) | \(q+(\zeta_{8}-\zeta_{8}^{3})q^{2}+(1-\zeta_{8}^{3})q^{3}+2q^{4}+\cdots\) |
800.2.ba.c | $8$ | $6.388$ | 8.0.18939904.2 | None | \(0\) | \(-4\) | \(0\) | \(8\) | \(q+(-\beta _{3}-\beta _{7})q^{2}+(-\beta _{2}-\beta _{4}+\beta _{5}+\cdots)q^{3}+\cdots\) |
800.2.ba.d | $8$ | $6.388$ | 8.0.18939904.2 | None | \(0\) | \(4\) | \(0\) | \(-8\) | \(q+(\beta _{4}-\beta _{5})q^{2}+(-\beta _{1}+\beta _{3}-\beta _{5}+\beta _{7})q^{3}+\cdots\) |
800.2.ba.e | $64$ | $6.388$ | None | \(0\) | \(0\) | \(0\) | \(0\) | ||
800.2.ba.f | $64$ | $6.388$ | None | \(0\) | \(0\) | \(0\) | \(0\) | ||
800.2.ba.g | $64$ | $6.388$ | None | \(0\) | \(0\) | \(0\) | \(0\) | ||
800.2.ba.h | $64$ | $6.388$ | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{2}^{\mathrm{old}}(800, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(800, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 2}\)