Defining parameters
Level: | \( N \) | \(=\) | \( 3 \) |
Weight: | \( k \) | \(=\) | \( 40 \) |
Character orbit: | \([\chi]\) | \(=\) | 3.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(13\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{40}(\Gamma_0(3))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 14 | 6 | 8 |
Cusp forms | 12 | 6 | 6 |
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.
\(3\) | Dim |
---|---|
\(+\) | \(3\) |
\(-\) | \(3\) |
Trace form
Decomposition of \(S_{40}^{\mathrm{new}}(\Gamma_0(3))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 3 | |||||||
3.40.a.a | $3$ | $28.902$ | \(\mathbb{Q}[x]/(x^{3} - \cdots)\) | None | \(-1107000\) | \(3486784401\) | \(93\!\cdots\!90\) | \(13\!\cdots\!04\) | $-$ | \(q+(-369000-\beta _{1})q^{2}+3^{19}q^{3}+(335300075200+\cdots)q^{4}+\cdots\) | |
3.40.a.b | $3$ | $28.902$ | \(\mathbb{Q}[x]/(x^{3} - \cdots)\) | None | \(533574\) | \(-3486784401\) | \(-53\!\cdots\!30\) | \(-15\!\cdots\!28\) | $+$ | \(q+(177858-\beta _{1})q^{2}-3^{19}q^{3}+(319147551244+\cdots)q^{4}+\cdots\) |
Decomposition of \(S_{40}^{\mathrm{old}}(\Gamma_0(3))\) into lower level spaces
\( S_{40}^{\mathrm{old}}(\Gamma_0(3)) \cong \) \(S_{40}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 2}\)