Defining parameters
Level: | \( N \) | \(=\) | \( 33 = 3 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 33.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(24\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(33))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 22 | 8 | 14 |
Cusp forms | 18 | 8 | 10 |
Eisenstein series | 4 | 0 | 4 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(3\) | \(11\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(2\) |
\(+\) | \(-\) | $-$ | \(3\) |
\(-\) | \(+\) | $-$ | \(2\) |
\(-\) | \(-\) | $+$ | \(1\) |
Plus space | \(+\) | \(3\) | |
Minus space | \(-\) | \(5\) |
Trace form
Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(33))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 3 | 11 | |||||||
33.6.a.a | $1$ | $5.293$ | \(\Q\) | None | \(-2\) | \(-9\) | \(46\) | \(148\) | $+$ | $-$ | \(q-2q^{2}-9q^{3}-28q^{4}+46q^{5}+18q^{6}+\cdots\) | |
33.6.a.b | $1$ | $5.293$ | \(\Q\) | None | \(1\) | \(9\) | \(-92\) | \(-26\) | $-$ | $-$ | \(q+q^{2}+9q^{3}-31q^{4}-92q^{5}+9q^{6}+\cdots\) | |
33.6.a.c | $2$ | $5.293$ | \(\Q(\sqrt{177}) \) | None | \(-5\) | \(-18\) | \(58\) | \(-286\) | $+$ | $+$ | \(q+(-2-\beta )q^{2}-9q^{3}+(2^{4}+5\beta )q^{4}+\cdots\) | |
33.6.a.d | $2$ | $5.293$ | \(\Q(\sqrt{313}) \) | None | \(1\) | \(-18\) | \(-38\) | \(-18\) | $+$ | $-$ | \(q+\beta q^{2}-9q^{3}+(46+\beta )q^{4}+(-24+\cdots)q^{5}+\cdots\) | |
33.6.a.e | $2$ | $5.293$ | \(\Q(\sqrt{33}) \) | None | \(13\) | \(18\) | \(58\) | \(146\) | $-$ | $+$ | \(q+(7-\beta )q^{2}+9q^{3}+(5^{2}-13\beta )q^{4}+\cdots\) |
Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(33))\) into lower level spaces
\( S_{6}^{\mathrm{old}}(\Gamma_0(33)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 2}\)