Defining parameters
Level: | \( N \) | \(=\) | \( 3 \) |
Weight: | \( k \) | \(=\) | \( 30 \) |
Character orbit: | \([\chi]\) | \(=\) | 3.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(10\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{30}(\Gamma_0(3))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 11 | 5 | 6 |
Cusp forms | 9 | 5 | 4 |
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 |
---|---|
\(+\) | \(2\) |
\(-\) | \(3\) |
Trace form
Decomposition of \(S_{30}^{\mathrm{new}}(\Gamma_0(3))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 3 | |||||||
3.30.a.a | $2$ | $15.983$ | \(\Q(\sqrt{77089}) \) | None | \(-45036\) | \(-9565938\) | \(187613820\) | \(26\!\cdots\!48\) | $+$ | \(q+(-22518-\beta )q^{2}-3^{14}q^{3}+(106174408+\cdots)q^{4}+\cdots\) | |
3.30.a.b | $3$ | $15.983$ | \(\mathbb{Q}[x]/(x^{3} - \cdots)\) | None | \(11370\) | \(14348907\) | \(35492909586\) | \(723913582632\) | $-$ | \(q+(3790-\beta _{1})q^{2}+3^{14}q^{3}+(701653900+\cdots)q^{4}+\cdots\) |
Decomposition of \(S_{30}^{\mathrm{old}}(\Gamma_0(3))\) into lower level spaces
\( S_{30}^{\mathrm{old}}(\Gamma_0(3)) \cong \) \(S_{30}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 2}\)