Defining parameters
Level: | \( N \) | \(=\) | \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 210.m (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 35 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(96\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(13\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(210, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 112 | 16 | 96 |
Cusp forms | 80 | 16 | 64 |
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.m.a | $8$ | $1.677$ | 8.0.1698758656.6 | None | \(0\) | \(0\) | \(0\) | \(4\) | \(q+\beta _{3}q^{2}+\beta _{3}q^{3}-\beta _{5}q^{4}+(\beta _{1}+\beta _{4}+\cdots)q^{5}+\cdots\) |
210.2.m.b | $8$ | $1.677$ | 8.0.1698758656.6 | None | \(0\) | \(0\) | \(0\) | \(8\) | \(q+\beta _{3}q^{2}-\beta _{3}q^{3}-\beta _{5}q^{4}+(-\beta _{1}-\beta _{4}+\cdots)q^{5}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(210, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(210, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)