Defining parameters
| Level: | \( N \) | = | \( 24 = 2^{3} \cdot 3 \) |
| Weight: | \( k \) | = | \( 8 \) |
| Character orbit: | \([\chi]\) | = | 24.a (trivial) |
| Character field: | \(\Q\) | ||
| Newforms: | \( 3 \) | ||
| Sturm bound: | \(32\) | ||
| Trace bound: | \(5\) | ||
| Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_0(24))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 32 | 3 | 29 |
| Cusp forms | 24 | 3 | 21 |
| 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. |
|---|---|---|---|
| \(+\) | \(+\) | \(+\) | \(1\) |
| \(+\) | \(-\) | \(-\) | \(1\) |
| \(-\) | \(-\) | \(+\) | \(1\) |
| Plus space | \(+\) | \(2\) | |
| Minus space | \(-\) | \(1\) | |
Trace form
Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_0(24))\) into irreducible Hecke orbits
| Label | Dim. | \(A\) | Field | CM | Traces | A-L signs | $q$-expansion | |||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(a_2\) | \(a_3\) | \(a_5\) | \(a_7\) | 2 | 3 | |||||||
| 24.8.a.a | \(1\) | \(7.497\) | \(\Q\) | None | \(0\) | \(-27\) | \(-26\) | \(1056\) | \(+\) | \(+\) | \(q-3^{3}q^{3}-26q^{5}+1056q^{7}+3^{6}q^{9}+\cdots\) | |
| 24.8.a.b | \(1\) | \(7.497\) | \(\Q\) | None | \(0\) | \(27\) | \(-530\) | \(120\) | \(+\) | \(-\) | \(q+3^{3}q^{3}-530q^{5}+120q^{7}+3^{6}q^{9}+\cdots\) | |
| 24.8.a.c | \(1\) | \(7.497\) | \(\Q\) | None | \(0\) | \(27\) | \(110\) | \(504\) | \(-\) | \(-\) | \(q+3^{3}q^{3}+110q^{5}+504q^{7}+3^{6}q^{9}+\cdots\) | |
Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_0(24))\) into lower level spaces
\( S_{8}^{\mathrm{old}}(\Gamma_0(24)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(12))\)\(^{\oplus 2}\)