Defining parameters
Level: | \( N \) | \(=\) | \( 448 = 2^{6} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 448.m (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 16 \) |
Character field: | \(\Q(i)\) | ||
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 | 144 | 24 | 120 |
Cusp forms | 112 | 24 | 88 |
Eisenstein series | 32 | 0 | 32 |
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.m.a | $2$ | $3.577$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(4\) | \(0\) | \(q+(2+2i)q^{5}+iq^{7}+3iq^{9}+(-1+\cdots)q^{11}+\cdots\) |
448.2.m.b | $2$ | $3.577$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(4\) | \(-4\) | \(0\) | \(q+(2-2i)q^{3}+(-2-2i)q^{5}-iq^{7}+\cdots\) |
448.2.m.c | $8$ | $3.577$ | 8.0.214798336.3 | None | \(0\) | \(0\) | \(-4\) | \(0\) | \(q-\beta _{4}q^{3}+\beta _{1}q^{5}+\beta _{5}q^{7}+(-\beta _{5}-\beta _{7})q^{9}+\cdots\) |
448.2.m.d | $12$ | $3.577$ | 12.0.\(\cdots\).1 | None | \(0\) | \(-4\) | \(4\) | \(0\) | \(q+\beta _{6}q^{3}+(1+\beta _{2}+\beta _{3}+\beta _{5})q^{5}-\beta _{3}q^{7}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(448, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(448, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 2}\)