Defining parameters
Level: | \( N \) | \(=\) | \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 504.i (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 168 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(384\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(504, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 296 | 96 | 200 |
Cusp forms | 280 | 96 | 184 |
Eisenstein series | 16 | 0 | 16 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(504, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
504.4.i.a | $8$ | $29.737$ | 8.0.157351936.1 | \(\Q(\sqrt{-7}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{5}q^{2}+(\beta _{1}+2\beta _{3})q^{4}-7\beta _{3}q^{7}+\cdots\) |
504.4.i.b | $88$ | $29.737$ | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{4}^{\mathrm{old}}(504, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(504, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 2}\)