Defining parameters
Level: | \( N \) | \(=\) | \( 241 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 241.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(40\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(241))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 20 | 20 | 0 |
Cusp forms | 19 | 19 | 0 |
Eisenstein series | 1 | 1 | 0 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(241\) | Dim |
---|---|
\(+\) | \(7\) |
\(-\) | \(12\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(241))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 241 | |||||||
241.2.a.a | $7$ | $1.924$ | 7.7.31056073.1 | None | \(-4\) | \(-3\) | \(-8\) | \(-7\) | $+$ | \(q+(-1+\beta _{1})q^{2}+\beta _{6}q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\) | |
241.2.a.b | $12$ | $1.924$ | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) | None | \(3\) | \(1\) | \(6\) | \(3\) | $-$ | \(q+\beta _{1}q^{2}+\beta _{8}q^{3}+(1+\beta _{2})q^{4}+(1-\beta _{9}+\cdots)q^{5}+\cdots\) |