Defining parameters
Level: | \( N \) | \(=\) | \( 448 = 2^{6} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 448.m (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 16 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(256\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(448, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 400 | 72 | 328 |
Cusp forms | 368 | 72 | 296 |
Eisenstein series | 32 | 0 | 32 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(448, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
448.4.m.a | $34$ | $26.433$ | None | \(0\) | \(0\) | \(0\) | \(0\) | ||
448.4.m.b | $38$ | $26.433$ | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{4}^{\mathrm{old}}(448, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(448, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 2}\)