Defining parameters
Level: | \( N \) | \(=\) | \( 59 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
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: | \(35\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\), \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{7}(59, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 31 | 31 | 0 |
Cusp forms | 29 | 29 | 0 |
Eisenstein series | 2 | 2 | 0 |
Trace form
Decomposition of \(S_{7}^{\mathrm{new}}(59, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
59.7.b.a | $1$ | $13.573$ | \(\Q\) | \(\Q(\sqrt{-59}) \) | \(0\) | \(-5\) | \(191\) | \(155\) | \(q-5q^{3}+2^{6}q^{4}+191q^{5}+155q^{7}+\cdots\) |
59.7.b.b | $2$ | $13.573$ | \(\Q(\sqrt{177}) \) | \(\Q(\sqrt{-59}) \) | \(0\) | \(5\) | \(-191\) | \(-155\) | \(q+(-1+7\beta )q^{3}+2^{6}q^{4}+(-85-21\beta )q^{5}+\cdots\) |
59.7.b.c | $26$ | $13.573$ | None | \(0\) | \(10\) | \(142\) | \(406\) |