Defining parameters
Level: | \( N \) | \(=\) | \( 196 = 2^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 196.d (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 28 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(56\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(196, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 36 | 24 | 12 |
Cusp forms | 20 | 16 | 4 |
Eisenstein series | 16 | 8 | 8 |
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.d.a | $4$ | $1.565$ | 4.0.2048.2 | \(\Q(\sqrt{-1}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{2}q^{2}+2q^{4}+\beta _{1}q^{5}-2\beta _{2}q^{8}+\cdots\) |
196.2.d.b | $4$ | $1.565$ | \(\Q(\zeta_{12})\) | None | \(4\) | \(0\) | \(0\) | \(0\) | \(q+(1+\zeta_{12})q^{2}+\zeta_{12}^{3}q^{3}+2\zeta_{12}q^{4}+\cdots\) |
196.2.d.c | $8$ | $1.565$ | 8.0.\(\cdots\).10 | None | \(-4\) | \(0\) | \(0\) | \(0\) | \(q+(-1+\beta _{5})q^{2}+(-2\beta _{1}-\beta _{7})q^{3}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(196, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(196, [\chi]) \cong \)