Defining parameters
| Level: | \( N \) | \(=\) | \( 30 = 2 \cdot 3 \cdot 5 \) |
| Weight: | \( k \) | \(=\) | \( 11 \) |
| Character orbit: | \([\chi]\) | \(=\) | 30.b (of order \(2\) and degree \(1\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 15 \) |
| Character field: | \(\Q\) | ||
| Newform subspaces: | \( 1 \) | ||
| Sturm bound: | \(66\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{11}(30, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 64 | 20 | 44 |
| Cusp forms | 56 | 20 | 36 |
| Eisenstein series | 8 | 0 | 8 |
Trace form
Decomposition of \(S_{11}^{\mathrm{new}}(30, [\chi])\) into newform subspaces
| Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|
| $a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
| 30.11.b.a | $20$ | $19.061$ | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{2}q^{2}+(-\beta _{2}-\beta _{3})q^{3}+2^{9}q^{4}+\cdots\) |
Decomposition of \(S_{11}^{\mathrm{old}}(30, [\chi])\) into lower level spaces
\( S_{11}^{\mathrm{old}}(30, [\chi]) \simeq \) \(S_{11}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 2}\)