Defining parameters
Level: | \( N \) | \(=\) | \( 112 = 2^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 112.c (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 7 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(48\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(112, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 38 | 9 | 29 |
Cusp forms | 26 | 7 | 19 |
Eisenstein series | 12 | 2 | 10 |
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.c.a | $1$ | $3.052$ | \(\Q\) | \(\Q(\sqrt{-7}) \) | \(0\) | \(0\) | \(0\) | \(7\) | \(q+7q^{7}+9q^{9}+6q^{11}-18q^{23}+5^{2}q^{25}+\cdots\) |
112.3.c.b | $2$ | $3.052$ | \(\Q(\sqrt{-6}) \) | None | \(0\) | \(0\) | \(0\) | \(-10\) | \(q+\beta q^{3}+\beta q^{5}+(-5-\beta )q^{7}-15q^{9}+\cdots\) |
112.3.c.c | $4$ | $3.052$ | 4.0.2048.2 | None | \(0\) | \(0\) | \(0\) | \(-4\) | \(q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{3})q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\) |
Decomposition of \(S_{3}^{\mathrm{old}}(112, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(112, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 2}\)