Defining parameters
Level: | \( N \) | \(=\) | \( 160 = 2^{5} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 160.e (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 40 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(72\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(3\), \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(160, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 56 | 14 | 42 |
Cusp forms | 40 | 10 | 30 |
Eisenstein series | 16 | 4 | 12 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(160, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
160.3.e.a | $1$ | $4.360$ | \(\Q\) | \(\Q(\sqrt{-10}) \) | \(0\) | \(0\) | \(-5\) | \(6\) | \(q-5q^{5}+6q^{7}+9q^{9}+18q^{11}+6q^{13}+\cdots\) |
160.3.e.b | $1$ | $4.360$ | \(\Q\) | \(\Q(\sqrt{-10}) \) | \(0\) | \(0\) | \(5\) | \(-6\) | \(q+5q^{5}-6q^{7}+9q^{9}+18q^{11}-6q^{13}+\cdots\) |
160.3.e.c | $8$ | $4.360$ | 8.0.\(\cdots\).2 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{2}q^{3}+\beta _{3}q^{5}+(-\beta _{1}+\beta _{3}-\beta _{4}+\cdots)q^{7}+\cdots\) |
Decomposition of \(S_{3}^{\mathrm{old}}(160, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(160, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 3}\)