Defining parameters
Level: | \( N \) | \(=\) | \( 2112 = 2^{6} \cdot 3 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2112.h (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 88 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(768\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(5\), \(59\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(2112, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 408 | 48 | 360 |
Cusp forms | 360 | 48 | 312 |
Eisenstein series | 48 | 0 | 48 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(2112, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
2112.2.h.a | $8$ | $16.864$ | \(\Q(\zeta_{20})\) | None | \(0\) | \(-8\) | \(0\) | \(0\) | \(q-q^{3}+(-\zeta_{20}+\zeta_{20}^{2})q^{5}+\zeta_{20}^{5}q^{7}+\cdots\) |
2112.2.h.b | $8$ | $16.864$ | \(\Q(\zeta_{20})\) | None | \(0\) | \(8\) | \(0\) | \(0\) | \(q+q^{3}+(-\zeta_{20}+\zeta_{20}^{2})q^{5}-\zeta_{20}^{5}q^{7}+\cdots\) |
2112.2.h.c | $16$ | $16.864$ | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) | None | \(0\) | \(-16\) | \(0\) | \(0\) | \(q-q^{3}+\beta _{11}q^{5}+\beta _{2}q^{7}+q^{9}-\beta _{12}q^{11}+\cdots\) |
2112.2.h.d | $16$ | $16.864$ | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) | None | \(0\) | \(16\) | \(0\) | \(0\) | \(q+q^{3}+\beta _{11}q^{5}+\beta _{2}q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(2112, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(2112, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(88, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(176, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(264, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(352, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(528, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(704, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1056, [\chi])\)\(^{\oplus 2}\)