Defining parameters
Level: | \( N \) | \(=\) | \( 336 = 2^{4} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 336.h (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 12 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(128\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(336, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 76 | 12 | 64 |
Cusp forms | 52 | 12 | 40 |
Eisenstein series | 24 | 0 | 24 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(336, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
336.2.h.a | $4$ | $2.683$ | \(\Q(\zeta_{8})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(\zeta_{8}-\zeta_{8}^{3})q^{3}-\zeta_{8}^{2}q^{5}-\zeta_{8}q^{7}+\cdots\) |
336.2.h.b | $8$ | $2.683$ | 8.0.56070144.2 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{6}q^{3}+(\beta _{3}+\beta _{5})q^{5}+\beta _{4}q^{7}+(2+\cdots)q^{9}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(336, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(336, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 3}\)