Defining parameters
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 28 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(96\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(5\), \(11\), \(19\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(252, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 56 | 22 | 34 |
Cusp forms | 40 | 18 | 22 |
Eisenstein series | 16 | 4 | 12 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(252, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
252.2.b.a | $2$ | $2.012$ | \(\Q(\sqrt{-7}) \) | \(\Q(\sqrt{-7}) \) | \(1\) | \(0\) | \(0\) | \(0\) | \(q+\beta q^{2}+(-2+\beta )q^{4}+(-1+2\beta )q^{7}+\cdots\) |
252.2.b.b | $4$ | $2.012$ | \(\Q(\sqrt{-2}, \sqrt{7})\) | \(\Q(\sqrt{-21}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{1}q^{2}-2q^{4}-\beta _{2}q^{5}+\beta _{3}q^{7}-2\beta _{1}q^{8}+\cdots\) |
252.2.b.c | $4$ | $2.012$ | \(\Q(i, \sqrt{7})\) | \(\Q(\sqrt{-7}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1+2\beta _{2}+\cdots)q^{7}+\cdots\) |
252.2.b.d | $4$ | $2.012$ | 4.0.2312.1 | None | \(1\) | \(0\) | \(0\) | \(-2\) | \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(-\beta _{1}-\beta _{3})q^{5}+\cdots\) |
252.2.b.e | $4$ | $2.012$ | 4.0.2312.1 | None | \(1\) | \(0\) | \(0\) | \(2\) | \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{1}+\beta _{3})q^{5}+(1+\cdots)q^{7}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(252, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(252, [\chi]) \cong \)