Defining parameters
Level: | \( N \) | \(=\) | \( 136 = 2^{3} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 136.e (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 136 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(54\) | ||
Trace bound: | \(9\) | ||
Distinguishing \(T_p\): | \(3\), \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(136, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 38 | 38 | 0 |
Cusp forms | 34 | 34 | 0 |
Eisenstein series | 4 | 4 | 0 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(136, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
136.3.e.a | $2$ | $3.706$ | \(\Q(\sqrt{17}) \) | \(\Q(\sqrt{-34}) \) | \(-4\) | \(0\) | \(0\) | \(0\) | \(q-2q^{2}+4q^{4}+\beta q^{5}-\beta q^{7}-8q^{8}+\cdots\) |
136.3.e.b | $2$ | $3.706$ | \(\Q(\sqrt{-2}) \) | \(\Q(\sqrt{-2}) \) | \(4\) | \(0\) | \(0\) | \(0\) | \(q+2q^{2}+\beta q^{3}+4q^{4}+2\beta q^{6}+8q^{8}+\cdots\) |
136.3.e.c | $2$ | $3.706$ | \(\Q(\sqrt{2}) \) | \(\Q(\sqrt{-34}) \) | \(4\) | \(0\) | \(0\) | \(0\) | \(q+2q^{2}+4q^{4}+\beta q^{5}-2\beta q^{7}+8q^{8}+\cdots\) |
136.3.e.d | $28$ | $3.706$ | None | \(-6\) | \(0\) | \(0\) | \(0\) |