Defining parameters
Level: | \( N \) | \(=\) | \( 196 = 2^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 196.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 7 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(84\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(196, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 68 | 6 | 62 |
Cusp forms | 44 | 6 | 38 |
Eisenstein series | 24 | 0 | 24 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(196, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
196.3.b.a | $2$ | $5.341$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\zeta_{6}q^{3}+\zeta_{6}q^{5}+6q^{9}+15q^{11}+\cdots\) |
196.3.b.b | $4$ | $5.341$ | 4.0.2048.2 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{2}q^{3}+(\beta _{1}+2\beta _{2})q^{5}+(-1-\beta _{3})q^{9}+\cdots\) |
Decomposition of \(S_{3}^{\mathrm{old}}(196, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(196, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 2}\)