Defining parameters
Level: | \( N \) | \(=\) | \( 196 = 2^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 196.f (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 28 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(56\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(3\), \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(196, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 72 | 48 | 24 |
Cusp forms | 40 | 32 | 8 |
Eisenstein series | 32 | 16 | 16 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(196, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
196.2.f.a | $4$ | $1.565$ | \(\Q(\zeta_{12})\) | None | \(-2\) | \(0\) | \(6\) | \(0\) | \(q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(-\zeta_{12}+\cdots)q^{3}+\cdots\) |
196.2.f.b | $4$ | $1.565$ | \(\Q(\sqrt{-3}, \sqrt{-7})\) | \(\Q(\sqrt{-7}) \) | \(1\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{3}q^{2}+(1+\beta _{1}-\beta _{2})q^{4}+(3-\beta _{1}+\cdots)q^{8}+\cdots\) |
196.2.f.c | $8$ | $1.565$ | 8.0.339738624.1 | \(\Q(\sqrt{-1}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(-\beta _{2}-\beta _{5})q^{2}+2\beta _{4}q^{4}-\beta _{3}q^{5}+\cdots\) |
196.2.f.d | $16$ | $1.565$ | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) | None | \(4\) | \(0\) | \(0\) | \(0\) | \(q+(-\beta _{6}-\beta _{11})q^{2}+(2\beta _{1}+\beta _{3})q^{3}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(196, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(196, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 2}\)