Defining parameters
Level: | \( N \) | \(=\) | \( 21 = 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 21.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(21\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_0(21))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 20 | 8 | 12 |
Cusp forms | 16 | 8 | 8 |
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 |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(2\) |
\(+\) | \(-\) | $-$ | \(2\) |
\(-\) | \(+\) | $-$ | \(1\) |
\(-\) | \(-\) | $+$ | \(3\) |
Plus space | \(+\) | \(5\) | |
Minus space | \(-\) | \(3\) |
Trace form
Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_0(21))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 3 | 7 | |||||||
21.8.a.a | $1$ | $6.560$ | \(\Q\) | None | \(2\) | \(27\) | \(-278\) | \(-343\) | $-$ | $+$ | \(q+2q^{2}+3^{3}q^{3}-124q^{4}-278q^{5}+\cdots\) | |
21.8.a.b | $2$ | $6.560$ | \(\Q(\sqrt{1065}) \) | None | \(-9\) | \(-54\) | \(-360\) | \(686\) | $+$ | $-$ | \(q+(-4-\beta )q^{2}-3^{3}q^{3}+(154+9\beta )q^{4}+\cdots\) | |
21.8.a.c | $2$ | $6.560$ | \(\Q(\sqrt{67}) \) | None | \(12\) | \(-54\) | \(-24\) | \(-686\) | $+$ | $+$ | \(q+(6+\beta )q^{2}-3^{3}q^{3}+(176+12\beta )q^{4}+\cdots\) | |
21.8.a.d | $3$ | $6.560$ | 3.3.2910828.1 | None | \(-3\) | \(81\) | \(-114\) | \(1029\) | $-$ | $-$ | \(q+(-1+\beta _{1})q^{2}+3^{3}q^{3}+(75+\beta _{2})q^{4}+\cdots\) |
Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_0(21))\) into lower level spaces
\( S_{8}^{\mathrm{old}}(\Gamma_0(21)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 2}\)