Defining parameters
Level: | \( N \) | \(=\) | \( 11 \) |
Weight: | \( k \) | \(=\) | \( 18 \) |
Character orbit: | \([\chi]\) | \(=\) | 11.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(18\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{18}(\Gamma_0(11))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 18 | 14 | 4 |
Cusp forms | 16 | 14 | 2 |
Eisenstein series | 2 | 0 | 2 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(11\) | Dim |
---|---|
\(+\) | \(6\) |
\(-\) | \(8\) |
Trace form
Decomposition of \(S_{18}^{\mathrm{new}}(\Gamma_0(11))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 11 | |||||||
11.18.a.a | $6$ | $20.154$ | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) | None | \(0\) | \(11865\) | \(347991\) | \(-31314630\) | $+$ | \(q-\beta _{1}q^{2}+(1977+14\beta _{1}-\beta _{2})q^{3}+\cdots\) | |
11.18.a.b | $8$ | $20.154$ | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) | None | \(256\) | \(3058\) | \(1795234\) | \(-896364\) | $-$ | \(q+(2^{5}-\beta _{1})q^{2}+(382-9\beta _{1}+\beta _{2})q^{3}+\cdots\) |
Decomposition of \(S_{18}^{\mathrm{old}}(\Gamma_0(11))\) into lower level spaces
\( S_{18}^{\mathrm{old}}(\Gamma_0(11)) \cong \) \(S_{18}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 2}\)