Defining parameters
Level: | \( N \) | \(=\) | \( 186 = 2 \cdot 3 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 186.f (of order \(5\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 31 \) |
Character field: | \(\Q(\zeta_{5})\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(64\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(186, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 144 | 16 | 128 |
Cusp forms | 112 | 16 | 96 |
Eisenstein series | 32 | 0 | 32 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(186, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
186.2.f.a | $4$ | $1.485$ | \(\Q(\zeta_{10})\) | None | \(1\) | \(-1\) | \(2\) | \(7\) | \(q+\zeta_{10}q^{2}+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{3}+\cdots\) |
186.2.f.b | $4$ | $1.485$ | \(\Q(\zeta_{10})\) | None | \(1\) | \(1\) | \(-4\) | \(-2\) | \(q+\zeta_{10}q^{2}+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{3}+\cdots\) |
186.2.f.c | $8$ | $1.485$ | 8.0.9240015625.1 | None | \(-2\) | \(2\) | \(2\) | \(-7\) | \(q-\beta _{3}q^{2}+\beta _{5}q^{3}+\beta _{4}q^{4}+(1+\beta _{2}+\cdots)q^{5}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(186, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(186, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(31, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(62, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(93, [\chi])\)\(^{\oplus 2}\)