Defining parameters
Level: | \( N \) | \(=\) | \( 1 \) |
Weight: | \( k \) | \(=\) | \( 88 \) |
Character orbit: | \([\chi]\) | \(=\) | 1.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(7\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{88}(\Gamma_0(1))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 8 | 8 | 0 |
Cusp forms | 7 | 7 | 0 |
Eisenstein series | 1 | 1 | 0 |
Trace form
Decomposition of \(S_{88}^{\mathrm{new}}(\Gamma_0(1))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | Fricke sign | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | |||||||
1.88.a.a | $7$ | $47.933$ | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) | None | \(18\!\cdots\!36\) | \(-75\!\cdots\!48\) | \(33\!\cdots\!50\) | \(45\!\cdots\!56\) | $+$ | \(q+(2599574577562+\beta _{1})q^{2}+\cdots\) |