Defining parameters
Level: | \( N \) | \(=\) | \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 210.j (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 15 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(96\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(17\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(210, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 112 | 24 | 88 |
Cusp forms | 80 | 24 | 56 |
Eisenstein series | 32 | 0 | 32 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(210, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
210.2.j.a | $12$ | $1.677$ | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) | None | \(0\) | \(4\) | \(-4\) | \(0\) | \(q+\beta _{2}q^{2}+\beta _{11}q^{3}-\beta _{7}q^{4}+(-1-\beta _{1}+\cdots)q^{5}+\cdots\) |
210.2.j.b | $12$ | $1.677$ | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) | None | \(0\) | \(4\) | \(4\) | \(0\) | \(q-\beta _{1}q^{2}-\beta _{3}q^{3}+\beta _{7}q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(210, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(210, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)