Defining parameters
Level: | \( N \) | \(=\) | \( 112 = 2^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 112.r (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 28 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(48\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(112, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 76 | 16 | 60 |
Cusp forms | 52 | 16 | 36 |
Eisenstein series | 24 | 0 | 24 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(112, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
112.3.r.a | $4$ | $3.052$ | \(\Q(\sqrt{-3}, \sqrt{-7})\) | None | \(0\) | \(0\) | \(2\) | \(0\) | \(q+\beta _{1}q^{3}+\beta _{2}q^{5}+(3\beta _{1}-\beta _{3})q^{7}-2\beta _{2}q^{9}+\cdots\) |
112.3.r.b | $6$ | $3.052$ | 6.0.259470000.1 | None | \(0\) | \(-3\) | \(-1\) | \(-14\) | \(q+(-1-\beta _{5})q^{3}+(\beta _{1}-\beta _{3})q^{5}+(-1+\cdots)q^{7}+\cdots\) |
112.3.r.c | $6$ | $3.052$ | 6.0.259470000.1 | None | \(0\) | \(3\) | \(-1\) | \(14\) | \(q+(1+\beta _{5})q^{3}+(\beta _{1}-\beta _{3})q^{5}+(1+\beta _{2}+\cdots)q^{7}+\cdots\) |
Decomposition of \(S_{3}^{\mathrm{old}}(112, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(112, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 3}\)