Defining parameters
Level: | \( N \) | \(=\) | \( 33 = 3 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 33.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(16\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(33))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 14 | 6 | 8 |
Cusp forms | 10 | 6 | 4 |
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 |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(2\) |
\(+\) | \(-\) | $-$ | \(1\) |
\(-\) | \(+\) | $-$ | \(1\) |
\(-\) | \(-\) | $+$ | \(2\) |
Plus space | \(+\) | \(4\) | |
Minus space | \(-\) | \(2\) |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(33))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 3 | 11 | |||||||
33.4.a.a | $1$ | $1.947$ | \(\Q\) | None | \(-5\) | \(3\) | \(-14\) | \(-32\) | $-$ | $+$ | \(q-5q^{2}+3q^{3}+17q^{4}-14q^{5}-15q^{6}+\cdots\) | |
33.4.a.b | $1$ | $1.947$ | \(\Q\) | None | \(-1\) | \(-3\) | \(-4\) | \(-26\) | $+$ | $-$ | \(q-q^{2}-3q^{3}-7q^{4}-4q^{5}+3q^{6}+\cdots\) | |
33.4.a.c | $2$ | $1.947$ | \(\Q(\sqrt{97}) \) | None | \(1\) | \(-6\) | \(-14\) | \(24\) | $+$ | $+$ | \(q+\beta q^{2}-3q^{3}+(2^{4}+\beta )q^{4}+(-6-2\beta )q^{5}+\cdots\) | |
33.4.a.d | $2$ | $1.947$ | \(\Q(\sqrt{33}) \) | None | \(1\) | \(6\) | \(16\) | \(2\) | $-$ | $-$ | \(q+\beta q^{2}+3q^{3}+\beta q^{4}+(10-4\beta )q^{5}+\cdots\) |
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(33))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_0(33)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 2}\)