Defining parameters
Level: | \( N \) | \(=\) | \( 800 = 2^{5} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 800.f (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 40 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(480\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(800, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 384 | 56 | 328 |
Cusp forms | 336 | 52 | 284 |
Eisenstein series | 48 | 4 | 44 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(800, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
800.4.f.a | $4$ | $47.202$ | \(\Q(i, \sqrt{7})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{2}q^{3}-4\beta _{1}q^{7}+q^{9}-3\beta _{3}q^{11}+\cdots\) |
800.4.f.b | $12$ | $47.202$ | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) | None | \(0\) | \(-12\) | \(0\) | \(0\) | \(q+(-1+\beta _{4})q^{3}+(-\beta _{2}-\beta _{6})q^{7}+(9+\cdots)q^{9}+\cdots\) |
800.4.f.c | $12$ | $47.202$ | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) | None | \(0\) | \(12\) | \(0\) | \(0\) | \(q+(1-\beta _{4})q^{3}+(\beta _{2}+\beta _{6})q^{7}+(9-2\beta _{4}+\cdots)q^{9}+\cdots\) |
800.4.f.d | $24$ | $47.202$ | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{4}^{\mathrm{old}}(800, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(800, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 6}\)