Defining parameters
Level: | \( N \) | \(=\) | \( 6 = 2 \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 20 \) |
Character orbit: | \([\chi]\) | \(=\) | 6.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(20\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{20}(\Gamma_0(6))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 21 | 3 | 18 |
Cusp forms | 17 | 3 | 14 |
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.
\(2\) | \(3\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(1\) |
\(+\) | \(-\) | $-$ | \(1\) |
\(-\) | \(-\) | $+$ | \(1\) |
Plus space | \(+\) | \(2\) | |
Minus space | \(-\) | \(1\) |
Trace form
Decomposition of \(S_{20}^{\mathrm{new}}(\Gamma_0(6))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | 3 | |||||||
6.20.a.a | $1$ | $13.729$ | \(\Q\) | None | \(-512\) | \(-19683\) | \(-3732474\) | \(-149672656\) | $+$ | $+$ | \(q-2^{9}q^{2}-3^{9}q^{3}+2^{18}q^{4}-3732474q^{5}+\cdots\) | |
6.20.a.b | $1$ | $13.729$ | \(\Q\) | None | \(-512\) | \(19683\) | \(-5849490\) | \(173530952\) | $+$ | $-$ | \(q-2^{9}q^{2}+3^{9}q^{3}+2^{18}q^{4}-5849490q^{5}+\cdots\) | |
6.20.a.c | $1$ | $13.729$ | \(\Q\) | None | \(512\) | \(19683\) | \(1953390\) | \(40488776\) | $-$ | $-$ | \(q+2^{9}q^{2}+3^{9}q^{3}+2^{18}q^{4}+1953390q^{5}+\cdots\) |
Decomposition of \(S_{20}^{\mathrm{old}}(\Gamma_0(6))\) into lower level spaces
\( S_{20}^{\mathrm{old}}(\Gamma_0(6)) \cong \) \(S_{20}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 2}\)