Defining parameters
Level: | \( N \) | \(=\) | \( 24 = 2^{3} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 24.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(40\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_0(24))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 40 | 5 | 35 |
Cusp forms | 32 | 5 | 27 |
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 |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(1\) |
\(+\) | \(-\) | $-$ | \(1\) |
\(-\) | \(+\) | $-$ | \(2\) |
\(-\) | \(-\) | $+$ | \(1\) |
Plus space | \(+\) | \(2\) | |
Minus space | \(-\) | \(3\) |
Trace form
Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(24))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | 3 | |||||||
24.10.a.a | $1$ | $12.361$ | \(\Q\) | None | \(0\) | \(-81\) | \(830\) | \(672\) | $+$ | $+$ | \(q-3^{4}q^{3}+830q^{5}+672q^{7}+3^{8}q^{9}+\cdots\) | |
24.10.a.b | $1$ | $12.361$ | \(\Q\) | None | \(0\) | \(81\) | \(-794\) | \(-5880\) | $-$ | $-$ | \(q+3^{4}q^{3}-794q^{5}-5880q^{7}+3^{8}q^{9}+\cdots\) | |
24.10.a.c | $1$ | $12.361$ | \(\Q\) | None | \(0\) | \(81\) | \(614\) | \(2184\) | $+$ | $-$ | \(q+3^{4}q^{3}+614q^{5}+2184q^{7}+3^{8}q^{9}+\cdots\) | |
24.10.a.d | $2$ | $12.361$ | \(\Q(\sqrt{109}) \) | None | \(0\) | \(-162\) | \(-772\) | \(-2880\) | $-$ | $+$ | \(q-3^{4}q^{3}+(-386-\beta )q^{5}+(-1440+\cdots)q^{7}+\cdots\) |
Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_0(24))\) into lower level spaces
\( S_{10}^{\mathrm{old}}(\Gamma_0(24)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(12))\)\(^{\oplus 2}\)