Defining parameters
Level: | \( N \) | \(=\) | \( 35 = 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 35.c (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 35 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(12\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(2\), \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(35, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 10 | 10 | 0 |
Cusp forms | 6 | 6 | 0 |
Eisenstein series | 4 | 4 | 0 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(35, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
35.3.c.a | $1$ | $0.954$ | \(\Q\) | \(\Q(\sqrt{-35}) \) | \(0\) | \(-1\) | \(5\) | \(-7\) | \(q-q^{3}+4q^{4}+5q^{5}-7q^{7}-8q^{9}+\cdots\) |
35.3.c.b | $1$ | $0.954$ | \(\Q\) | \(\Q(\sqrt{-35}) \) | \(0\) | \(1\) | \(-5\) | \(7\) | \(q+q^{3}+4q^{4}-5q^{5}+7q^{7}-8q^{9}+\cdots\) |
35.3.c.c | $4$ | $0.954$ | \(\Q(i, \sqrt{10})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{1}q^{2}+\beta _{3}q^{3}-5q^{4}+(\beta _{2}-\beta _{3})q^{5}+\cdots\) |