Defining parameters
Level: | \( N \) | \(=\) | \( 182 = 2 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 182.h (of order \(3\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 91 \) |
Character field: | \(\Q(\zeta_{3})\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(56\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(3\), \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(182, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 64 | 20 | 44 |
Cusp forms | 48 | 20 | 28 |
Eisenstein series | 16 | 0 | 16 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(182, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
182.2.h.a | $2$ | $1.453$ | \(\Q(\sqrt{-3}) \) | None | \(1\) | \(2\) | \(-1\) | \(1\) | \(q+\zeta_{6}q^{2}+q^{3}+(-1+\zeta_{6})q^{4}+(-1+\cdots)q^{5}+\cdots\) |
182.2.h.b | $2$ | $1.453$ | \(\Q(\sqrt{-3}) \) | None | \(1\) | \(2\) | \(3\) | \(5\) | \(q+\zeta_{6}q^{2}+q^{3}+(-1+\zeta_{6})q^{4}+(3-3\zeta_{6})q^{5}+\cdots\) |
182.2.h.c | $6$ | $1.453$ | 6.0.4740147.1 | None | \(3\) | \(-2\) | \(0\) | \(-12\) | \(q+\beta _{1}q^{2}+\beta _{2}q^{3}+(-1+\beta _{1})q^{4}+(\beta _{4}+\cdots)q^{5}+\cdots\) |
182.2.h.d | $10$ | $1.453$ | 10.0.\(\cdots\).1 | None | \(-5\) | \(2\) | \(-2\) | \(0\) | \(q+\beta _{2}q^{2}+(-\beta _{4}+\beta _{5})q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(182, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(182, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 2}\)