Defining parameters
Level: | \( N \) | \(=\) | \( 24 = 2^{3} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 24.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(48\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_0(24))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 48 | 5 | 43 |
Cusp forms | 40 | 5 | 35 |
Eisenstein series | 8 | 0 | 8 |
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 |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(1\) |
\(+\) | \(-\) | $-$ | \(1\) |
\(-\) | \(+\) | $-$ | \(1\) |
\(-\) | \(-\) | $+$ | \(2\) |
Plus space | \(+\) | \(3\) | |
Minus space | \(-\) | \(2\) |
Trace form
Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_0(24))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | 3 | |||||||
24.12.a.a | $1$ | $18.440$ | \(\Q\) | None | \(0\) | \(-243\) | \(-7130\) | \(-19536\) | $+$ | $+$ | \(q-3^{5}q^{3}-7130q^{5}-19536q^{7}+3^{10}q^{9}+\cdots\) | |
24.12.a.b | $1$ | $18.440$ | \(\Q\) | None | \(0\) | \(-243\) | \(1190\) | \(18480\) | $-$ | $+$ | \(q-3^{5}q^{3}+1190q^{5}+18480q^{7}+3^{10}q^{9}+\cdots\) | |
24.12.a.c | $1$ | $18.440$ | \(\Q\) | None | \(0\) | \(243\) | \(1870\) | \(-72312\) | $+$ | $-$ | \(q+3^{5}q^{3}+1870q^{5}-72312q^{7}+3^{10}q^{9}+\cdots\) | |
24.12.a.d | $2$ | $18.440$ | \(\Q(\sqrt{3061}) \) | None | \(0\) | \(486\) | \(1564\) | \(37776\) | $-$ | $-$ | \(q+3^{5}q^{3}+(782-\beta )q^{5}+(18888+\beta )q^{7}+\cdots\) |
Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_0(24))\) into lower level spaces
\( S_{12}^{\mathrm{old}}(\Gamma_0(24)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 3}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 2}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(12))\)\(^{\oplus 2}\)