Defining parameters
Level: | \( N \) | \(=\) | \( 215 = 5 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 215.l (of order \(12\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 215 \) |
Character field: | \(\Q(\zeta_{12})\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(44\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(215, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 96 | 96 | 0 |
Cusp forms | 80 | 80 | 0 |
Eisenstein series | 16 | 16 | 0 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(215, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
215.2.l.a | $4$ | $1.717$ | \(\Q(\zeta_{12})\) | None | \(-2\) | \(2\) | \(2\) | \(-2\) | \(q+(\zeta_{12}-\zeta_{12}^{2})q^{2}+(\zeta_{12}^{2}-\zeta_{12}^{3})q^{3}+\cdots\) |
215.2.l.b | $4$ | $1.717$ | \(\Q(\zeta_{12})\) | None | \(2\) | \(4\) | \(-2\) | \(2\) | \(q+(1+\zeta_{12}-\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(1+\cdots)q^{3}+\cdots\) |
215.2.l.c | $72$ | $1.717$ | None | \(0\) | \(-12\) | \(-6\) | \(-12\) |