Defining parameters
Level: | \( N \) | \(=\) | \( 59 \) |
Weight: | \( k \) | \(=\) | \( 19 \) |
Character orbit: | \([\chi]\) | \(=\) | 59.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 59 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(95\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\), \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{19}(59, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 91 | 91 | 0 |
Cusp forms | 89 | 89 | 0 |
Eisenstein series | 2 | 2 | 0 |
Trace form
Decomposition of \(S_{19}^{\mathrm{new}}(59, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
59.19.b.a | $1$ | $121.178$ | \(\Q\) | \(\Q(\sqrt{-59}) \) | \(0\) | \(10810\) | \(-1985254\) | \(-50982910\) | \(q+10810q^{3}+2^{18}q^{4}-1985254q^{5}+\cdots\) |
59.19.b.b | $2$ | $121.178$ | \(\Q(\sqrt{177}) \) | \(\Q(\sqrt{-59}) \) | \(0\) | \(-10810\) | \(1985254\) | \(50982910\) | \(q+(-5405-616\beta )q^{3}+2^{18}q^{4}+(992627+\cdots)q^{5}+\cdots\) |
59.19.b.c | $86$ | $121.178$ | None | \(0\) | \(-47870\) | \(-1461458\) | \(42126406\) |