Defining parameters
Level: | \( N \) | \(=\) | \( 155 = 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 155.p (of order \(12\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 155 \) |
Character field: | \(\Q(\zeta_{12})\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(32\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(2\), \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(155, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 72 | 72 | 0 |
Cusp forms | 56 | 56 | 0 |
Eisenstein series | 16 | 16 | 0 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(155, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
155.2.p.a | $4$ | $1.238$ | \(\Q(\zeta_{12})\) | None | \(-4\) | \(-6\) | \(-2\) | \(-2\) | \(q+(-1-\zeta_{12}^{3})q^{2}+(-1-\zeta_{12}-\zeta_{12}^{2}+\cdots)q^{3}+\cdots\) |
155.2.p.b | $4$ | $1.238$ | \(\Q(\zeta_{12})\) | None | \(-4\) | \(-6\) | \(4\) | \(4\) | \(q+(-1-\zeta_{12}^{3})q^{2}+(-1-\zeta_{12}-\zeta_{12}^{2}+\cdots)q^{3}+\cdots\) |
155.2.p.c | $48$ | $1.238$ | None | \(0\) | \(6\) | \(-4\) | \(-8\) |