Defining parameters
Level: | \( N \) | \(=\) | \( 12 = 2^{2} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 20 \) |
Character orbit: | \([\chi]\) | \(=\) | 12.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(40\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{20}(\Gamma_0(12))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 41 | 4 | 37 |
Cusp forms | 35 | 4 | 31 |
Eisenstein series | 6 | 0 | 6 |
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 |
---|---|---|---|
\(-\) | \(+\) | $-$ | \(2\) |
\(-\) | \(-\) | $+$ | \(2\) |
Plus space | \(+\) | \(2\) | |
Minus space | \(-\) | \(2\) |
Trace form
Decomposition of \(S_{20}^{\mathrm{new}}(\Gamma_0(12))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | 3 | |||||||
12.20.a.a | $2$ | $27.458$ | \(\Q(\sqrt{193153}) \) | None | \(0\) | \(-39366\) | \(624780\) | \(4667104\) | $-$ | $+$ | \(q-3^{9}q^{3}+(312390-\beta )q^{5}+(2333552+\cdots)q^{7}+\cdots\) | |
12.20.a.b | $2$ | $27.458$ | \(\mathbb{Q}[x]/(x^{2} - \cdots)\) | None | \(0\) | \(39366\) | \(-3267108\) | \(-27023984\) | $-$ | $-$ | \(q+3^{9}q^{3}+(-1633554-\beta )q^{5}+(-13511992+\cdots)q^{7}+\cdots\) |
Decomposition of \(S_{20}^{\mathrm{old}}(\Gamma_0(12))\) into lower level spaces
\( S_{20}^{\mathrm{old}}(\Gamma_0(12)) \cong \) \(S_{20}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 2}\)