Defining parameters
Level: | \( N \) | \(=\) | \( 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 420.w (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 420 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(192\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(420, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 208 | 208 | 0 |
Cusp forms | 176 | 176 | 0 |
Eisenstein series | 32 | 32 | 0 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(420, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
420.2.w.a | $8$ | $3.354$ | 8.0.\(\cdots\).1 | \(\Q(\sqrt{-21}) \) | \(-8\) | \(0\) | \(0\) | \(0\) | \(q+(-1+\beta _{2})q^{2}+\beta _{1}q^{3}-2\beta _{2}q^{4}+\cdots\) |
420.2.w.b | $8$ | $3.354$ | 8.0.\(\cdots\).1 | \(\Q(\sqrt{-21}) \) | \(8\) | \(0\) | \(0\) | \(0\) | \(q+(1-\beta _{2})q^{2}+\beta _{1}q^{3}-2\beta _{2}q^{4}+(-\beta _{3}+\cdots)q^{5}+\cdots\) |
420.2.w.c | $160$ | $3.354$ | None | \(0\) | \(0\) | \(0\) | \(0\) |