Defining parameters
Level: | \( N \) | \(=\) | \( 21 = 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 21.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(10\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(21))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 10 | 4 | 6 |
Cusp forms | 6 | 4 | 2 |
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.
\(3\) | \(7\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(1\) |
\(+\) | \(-\) | $-$ | \(1\) |
\(-\) | \(-\) | $+$ | \(2\) |
Plus space | \(+\) | \(3\) | |
Minus space | \(-\) | \(1\) |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(21))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 3 | 7 | |||||||
21.4.a.a | $1$ | $1.239$ | \(\Q\) | None | \(-3\) | \(-3\) | \(-18\) | \(7\) | $+$ | $-$ | \(q-3q^{2}-3q^{3}+q^{4}-18q^{5}+9q^{6}+\cdots\) | |
21.4.a.b | $1$ | $1.239$ | \(\Q\) | None | \(4\) | \(-3\) | \(-4\) | \(-7\) | $+$ | $+$ | \(q+4q^{2}-3q^{3}+8q^{4}-4q^{5}-12q^{6}+\cdots\) | |
21.4.a.c | $2$ | $1.239$ | \(\Q(\sqrt{57}) \) | None | \(-3\) | \(6\) | \(6\) | \(14\) | $-$ | $-$ | \(q+(-1-\beta )q^{2}+3q^{3}+(7+3\beta )q^{4}+\cdots\) |
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(21))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_0(21)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 2}\)