Defining parameters
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.g (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 105 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(32\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(2\), \(13\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(105, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 20 | 20 | 0 |
Cusp forms | 12 | 12 | 0 |
Eisenstein series | 8 | 8 | 0 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(105, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
105.2.g.a | $4$ | $0.838$ | \(\Q(\sqrt{-2}, \sqrt{3})\) | None | \(0\) | \(-4\) | \(0\) | \(4\) | \(q-\beta _{2}q^{2}+(-1-\beta _{1})q^{3}+q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\) |
105.2.g.b | $4$ | $0.838$ | \(\Q(\sqrt{-5}, \sqrt{7})\) | \(\Q(\sqrt{-35}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{3}q^{3}-2q^{4}+(\beta _{1}+\beta _{3})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\) |
105.2.g.c | $4$ | $0.838$ | \(\Q(\sqrt{-2}, \sqrt{3})\) | None | \(0\) | \(4\) | \(0\) | \(-4\) | \(q-\beta _{2}q^{2}+(1-\beta _{1})q^{3}+q^{4}+(\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\) |