Defining parameters
Level: | \( N \) | = | \( 130 = 2 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | = | \( 2 \) |
Character orbit: | \([\chi]\) | = | 130.j (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | = | \( 65 \) |
Character field: | \(\Q(i)\) | ||
Newforms: | \( 5 \) | ||
Sturm bound: | \(42\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(130, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 50 | 14 | 36 |
Cusp forms | 34 | 14 | 20 |
Eisenstein series | 16 | 0 | 16 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(130, [\chi])\) into irreducible Hecke orbits
Label | Dim. | \(A\) | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
\(a_2\) | \(a_3\) | \(a_5\) | \(a_7\) | ||||||
130.2.j.a | \(2\) | \(1.038\) | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(-4\) | \(-2\) | \(-8\) | \(q-iq^{2}+(-2+2i)q^{3}-q^{4}+(-1+\cdots)q^{5}+\cdots\) |
130.2.j.b | \(2\) | \(1.038\) | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(-2\) | \(-4\) | \(-4\) | \(q+iq^{2}+(-1+i)q^{3}-q^{4}+(-2+i)q^{5}+\cdots\) |
130.2.j.c | \(2\) | \(1.038\) | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(2\) | \(4\) | \(-4\) | \(q-iq^{2}+(1-i)q^{3}-q^{4}+(2-i)q^{5}+\cdots\) |
130.2.j.d | \(4\) | \(1.038\) | \(\Q(i, \sqrt{11})\) | None | \(0\) | \(2\) | \(0\) | \(12\) | \(q+\beta _{2}q^{2}+(-\beta _{1}+\beta _{2}-\beta _{3})q^{3}-q^{4}+\cdots\) |
130.2.j.e | \(4\) | \(1.038\) | \(\Q(\zeta_{12})\) | None | \(0\) | \(2\) | \(4\) | \(4\) | \(q-\zeta_{12}^{3}q^{2}+(1-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(130, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(130, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 2}\)