Defining parameters
Level: | \( N \) | \(=\) | \( 448 = 2^{6} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 448.f (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 28 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(128\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(448, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 76 | 18 | 58 |
Cusp forms | 52 | 14 | 38 |
Eisenstein series | 24 | 4 | 20 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(448, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
448.2.f.a | $2$ | $3.577$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(-4\) | \(0\) | \(-4\) | \(q-2 q^{3}-2\beta q^{5}+(-\beta-2)q^{7}+q^{9}+\cdots\) |
448.2.f.b | $2$ | $3.577$ | \(\Q(\sqrt{-7}) \) | \(\Q(\sqrt{-7}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta q^{7}-3q^{9}-2\beta q^{11}-2\beta q^{23}+\cdots\) |
448.2.f.c | $2$ | $3.577$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(4\) | \(0\) | \(4\) | \(q+2 q^{3}+2\beta q^{5}+(-\beta+2)q^{7}+q^{9}+\cdots\) |
448.2.f.d | $8$ | $3.577$ | \(\Q(\zeta_{16})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta_{2} q^{3}-\beta_{5} q^{5}-\beta_{4} q^{7}+(\beta_{7}+1)q^{9}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(448, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(448, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 2}\)