Defining parameters
Level: | \( N \) | \(=\) | \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 210.g (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 5 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(192\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(210, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 152 | 20 | 132 |
Cusp forms | 136 | 20 | 116 |
Eisenstein series | 16 | 0 | 16 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(210, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
210.4.g.a | $4$ | $12.390$ | \(\Q(i, \sqrt{6})\) | None | \(0\) | \(0\) | \(-4\) | \(0\) | \(q+2\beta _{1}q^{2}+3\beta _{1}q^{3}-4q^{4}+(-1-2\beta _{1}+\cdots)q^{5}+\cdots\) |
210.4.g.b | $4$ | $12.390$ | \(\Q(i, \sqrt{21})\) | None | \(0\) | \(0\) | \(16\) | \(0\) | \(q+2\beta _{1}q^{2}-3\beta _{1}q^{3}-4q^{4}+(4-2\beta _{1}+\cdots)q^{5}+\cdots\) |
210.4.g.c | $6$ | $12.390$ | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) | None | \(0\) | \(0\) | \(-2\) | \(0\) | \(q+2\beta _{1}q^{2}-3\beta _{1}q^{3}-4q^{4}-\beta _{3}q^{5}+\cdots\) |
210.4.g.d | $6$ | $12.390$ | 6.0.\(\cdots\).2 | None | \(0\) | \(0\) | \(14\) | \(0\) | \(q+2\beta _{1}q^{2}+3\beta _{1}q^{3}-4q^{4}+(2-3\beta _{1}+\cdots)q^{5}+\cdots\) |
Decomposition of \(S_{4}^{\mathrm{old}}(210, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(210, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 2}\)