Defining parameters
Level: | \( N \) | \(=\) | \( 800 = 2^{5} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 800.bq (of order \(20\) and degree \(8\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 100 \) |
Character field: | \(\Q(\zeta_{20})\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(240\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(800, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1024 | 240 | 784 |
Cusp forms | 896 | 240 | 656 |
Eisenstein series | 128 | 0 | 128 |
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.bq.a | $56$ | $6.388$ | None | \(0\) | \(0\) | \(-2\) | \(-4\) | ||
800.2.bq.b | $56$ | $6.388$ | None | \(0\) | \(0\) | \(-2\) | \(4\) | ||
800.2.bq.c | $64$ | $6.388$ | None | \(0\) | \(0\) | \(2\) | \(-4\) | ||
800.2.bq.d | $64$ | $6.388$ | None | \(0\) | \(0\) | \(2\) | \(4\) |
Decomposition of \(S_{2}^{\mathrm{old}}(800, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(800, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(400, [\chi])\)\(^{\oplus 2}\)