Defining parameters
Level: | \( N \) | \(=\) | \( 448 = 2^{6} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 448.l (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 112 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(64\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(448, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 24 | 6 | 18 |
Cusp forms | 8 | 2 | 6 |
Eisenstein series | 16 | 4 | 12 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 2 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(448, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
448.1.l.a | $2$ | $0.224$ | \(\Q(\sqrt{-1}) \) | $D_{4}$ | \(\Q(\sqrt{-7}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-iq^{7}-iq^{9}+(1+i)q^{11}+iq^{25}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(448, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(448, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 2}\)