Defining parameters
Level: | \( N \) | = | \( 134 = 2 \cdot 67 \) |
Weight: | \( k \) | = | \( 2 \) |
Character orbit: | \([\chi]\) | = | 134.c (of order \(3\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | = | \( 67 \) |
Character field: | \(\Q(\zeta_{3})\) | ||
Newforms: | \( 3 \) | ||
Sturm bound: | \(34\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(134, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 38 | 10 | 28 |
Cusp forms | 30 | 10 | 20 |
Eisenstein series | 8 | 0 | 8 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(134, [\chi])\) into irreducible Hecke orbits
Label | Dim. | \(A\) | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
\(a_2\) | \(a_3\) | \(a_5\) | \(a_7\) | ||||||
134.2.c.a | \(2\) | \(1.070\) | \(\Q(\sqrt{-3}) \) | None | \(-1\) | \(-2\) | \(4\) | \(4\) | \(q+(-1+\zeta_{6})q^{2}-q^{3}-\zeta_{6}q^{4}+2q^{5}+\cdots\) |
134.2.c.b | \(4\) | \(1.070\) | \(\Q(\sqrt{-3}, \sqrt{-7})\) | None | \(-2\) | \(2\) | \(-4\) | \(-1\) | \(q+\beta _{1}q^{2}+(1-\beta _{2})q^{3}+(-1-\beta _{1})q^{4}+\cdots\) |
134.2.c.c | \(4\) | \(1.070\) | \(\Q(\sqrt{-3}, \sqrt{5})\) | None | \(2\) | \(6\) | \(0\) | \(-1\) | \(q+(1+\beta _{3})q^{2}+(1-\beta _{2})q^{3}+\beta _{3}q^{4}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(134, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(134, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(67, [\chi])\)\(^{\oplus 2}\)