Defining parameters
Level: | \( N \) | \(=\) | \( 24 = 2^{3} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 24.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 3 \) | ||
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 newform subspaces
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
\( S_{8}^{\mathrm{old}}(\Gamma_0(24)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(12))\)\(^{\oplus 2}\)