Defining parameters
Level: | \( N \) | \(=\) | \( 672 = 2^{5} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 672.h (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 12 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(256\) | ||
Trace bound: | \(13\) | ||
Distinguishing \(T_p\): | \(5\), \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(672, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 144 | 24 | 120 |
Cusp forms | 112 | 24 | 88 |
Eisenstein series | 32 | 0 | 32 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(672, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
672.2.h.a | $4$ | $5.366$ | \(\Q(\zeta_{8})\) | None | \(0\) | \(-4\) | \(0\) | \(0\) | \(q+(-1-\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+(\zeta_{8}+2\zeta_{8}^{2}+\cdots)q^{5}+\cdots\) |
672.2.h.b | $4$ | $5.366$ | \(\Q(\zeta_{8})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(\zeta_{8}-\zeta_{8}^{3})q^{3}-3\zeta_{8}^{2}q^{5}-\zeta_{8}q^{7}+\cdots\) |
672.2.h.c | $4$ | $5.366$ | \(\Q(\zeta_{8})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(\zeta_{8}-\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{5}-\zeta_{8}q^{7}+\cdots\) |
672.2.h.d | $4$ | $5.366$ | \(\Q(\zeta_{8})\) | None | \(0\) | \(4\) | \(0\) | \(0\) | \(q+(1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+(-\zeta_{8}+2\zeta_{8}^{2}+\cdots)q^{5}+\cdots\) |
672.2.h.e | $8$ | $5.366$ | 8.0.40960000.1 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{2}q^{3}-\beta _{4}q^{5}+\beta _{1}q^{7}+(-2+\beta _{6}+\cdots)q^{9}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(672, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(672, [\chi]) \cong \)