Defining parameters
Level: | \( N \) | \(=\) | \( 3 \) |
Weight: | \( k \) | \(=\) | \( 68 \) |
Character orbit: | \([\chi]\) | \(=\) | 3.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(22\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{68}(\Gamma_0(3))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 23 | 11 | 12 |
Cusp forms | 21 | 11 | 10 |
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 |
---|---|
\(+\) | \(6\) |
\(-\) | \(5\) |
Trace form
Decomposition of \(S_{68}^{\mathrm{new}}(\Gamma_0(3))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 3 | |||||||
3.68.a.a | $5$ | $85.287$ | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) | None | \(-16255223088\) | \(27\!\cdots\!15\) | \(-78\!\cdots\!10\) | \(28\!\cdots\!08\) | $-$ | \(q+(-3251044618-\beta _{1})q^{2}+3^{33}q^{3}+\cdots\) | |
3.68.a.b | $6$ | $85.287$ | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) | None | \(13735355166\) | \(-33\!\cdots\!38\) | \(-18\!\cdots\!00\) | \(-28\!\cdots\!08\) | $+$ | \(q+(2289225861-\beta _{1})q^{2}-3^{33}q^{3}+\cdots\) |
Decomposition of \(S_{68}^{\mathrm{old}}(\Gamma_0(3))\) into lower level spaces
\( S_{68}^{\mathrm{old}}(\Gamma_0(3)) \cong \) \(S_{68}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 2}\)