Defining parameters
Level: | \( N \) | \(=\) | \( 59 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 59.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 59 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(25\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{5}(59, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 21 | 21 | 0 |
Cusp forms | 19 | 19 | 0 |
Eisenstein series | 2 | 2 | 0 |
Trace form
Decomposition of \(S_{5}^{\mathrm{new}}(59, [\chi])\) into newform subspaces
Label | Dim. | \(A\) | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
\(a_2\) | \(a_3\) | \(a_5\) | \(a_7\) | ||||||
59.5.b.a | \(3\) | \(6.099\) | 3.3.1593.1 | \(\Q(\sqrt{-59}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(4\beta _{1}-3\beta _{2})q^{3}+2^{4}q^{4}+(5\beta _{1}-11\beta _{2})q^{5}+\cdots\) |
59.5.b.b | \(16\) | \(6.099\) | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) | None | \(0\) | \(-20\) | \(4\) | \(-82\) | \(q+\beta _{1}q^{2}+(-1-\beta _{4})q^{3}+(-12+\beta _{2}+\cdots)q^{4}+\cdots\) |