Defining parameters
Level: | \( N \) | \(=\) | \( 448 = 2^{6} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 448.p (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 28 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(128\) | ||
Trace bound: | \(9\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(448, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 152 | 36 | 116 |
Cusp forms | 104 | 28 | 76 |
Eisenstein series | 48 | 8 | 40 |
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.p.a | $2$ | $3.577$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(-1\) | \(-3\) | \(-4\) | \(q+(-1+\zeta_{6})q^{3}+(-2+\zeta_{6})q^{5}+(-1+\cdots)q^{7}+\cdots\) |
448.2.p.b | $2$ | $3.577$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(1\) | \(-3\) | \(4\) | \(q+(1-\zeta_{6})q^{3}+(-2+\zeta_{6})q^{5}+(1+2\zeta_{6})q^{7}+\cdots\) |
448.2.p.c | $4$ | $3.577$ | \(\Q(\sqrt{-3}, \sqrt{7})\) | None | \(0\) | \(0\) | \(6\) | \(0\) | \(q+\beta _{1}q^{3}+(2+\beta _{2})q^{5}+\beta _{3}q^{7}+4\beta _{2}q^{9}+\cdots\) |
448.2.p.d | $4$ | $3.577$ | \(\Q(\zeta_{12})\) | None | \(0\) | \(0\) | \(6\) | \(0\) | \(q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+(1+\zeta_{12}^{2})q^{5}+\cdots\) |
448.2.p.e | $16$ | $3.577$ | 16.0.\(\cdots\).2 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{14}q^{3}+\beta _{13}q^{5}+\beta _{9}q^{7}+(-\beta _{3}+\cdots)q^{9}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(448, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(448, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 2}\)