Defining parameters
Level: | \( N \) | \(=\) | \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 210.d (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 105 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(96\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(23\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(210, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 56 | 16 | 40 |
Cusp forms | 40 | 16 | 24 |
Eisenstein series | 16 | 0 | 16 |
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.d.a | $8$ | $1.677$ | 8.0.\(\cdots\).11 | None | \(-8\) | \(0\) | \(0\) | \(0\) | \(q-q^{2}-\beta _{7}q^{3}+q^{4}+(\beta _{1}+\beta _{2}+\beta _{3}+\cdots)q^{5}+\cdots\) |
210.2.d.b | $8$ | $1.677$ | 8.0.\(\cdots\).11 | None | \(8\) | \(0\) | \(0\) | \(0\) | \(q+q^{2}+\beta _{1}q^{3}+q^{4}+(-\beta _{1}-\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(210, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(210, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)