Defining parameters
Level: | \( N \) | \(=\) | \( 24 = 2^{3} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 22 \) |
Character orbit: | \([\chi]\) | \(=\) | 24.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(88\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{22}(\Gamma_0(24))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 88 | 11 | 77 |
Cusp forms | 80 | 11 | 69 |
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. |
---|---|---|---|
\(+\) | \(+\) | \(+\) | \(3\) |
\(+\) | \(-\) | \(-\) | \(3\) |
\(-\) | \(+\) | \(-\) | \(3\) |
\(-\) | \(-\) | \(+\) | \(2\) |
Plus space | \(+\) | \(5\) | |
Minus space | \(-\) | \(6\) |
Trace form
Decomposition of \(S_{22}^{\mathrm{new}}(\Gamma_0(24))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | 3 | |||||||
24.22.a.a | $2$ | $67.075$ | \(\Q(\sqrt{537541}) \) | None | \(0\) | \(118098\) | \(21948620\) | \(-659451408\) | $-$ | $-$ | \(q+3^{10}q^{3}+(10974310-5\beta )q^{5}+(-329725704+\cdots)q^{7}+\cdots\) | |
24.22.a.b | $3$ | $67.075$ | \(\mathbb{Q}[x]/(x^{3} - \cdots)\) | None | \(0\) | \(-177147\) | \(-4833126\) | \(271431024\) | $-$ | $+$ | \(q-3^{10}q^{3}+(-1611042-\beta _{1})q^{5}+\cdots\) | |
24.22.a.c | $3$ | $67.075$ | \(\mathbb{Q}[x]/(x^{3} - \cdots)\) | None | \(0\) | \(-177147\) | \(2080026\) | \(-1205282064\) | $+$ | $+$ | \(q-3^{10}q^{3}+(693342+\beta _{1})q^{5}+(-401760688+\cdots)q^{7}+\cdots\) | |
24.22.a.d | $3$ | $67.075$ | \(\mathbb{Q}[x]/(x^{3} - \cdots)\) | None | \(0\) | \(177147\) | \(5280498\) | \(852542376\) | $+$ | $-$ | \(q+3^{10}q^{3}+(1760166-\beta _{1})q^{5}+(284180792+\cdots)q^{7}+\cdots\) |
Decomposition of \(S_{22}^{\mathrm{old}}(\Gamma_0(24))\) into lower level spaces
\( S_{22}^{\mathrm{old}}(\Gamma_0(24)) \cong \) \(S_{22}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 3}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 2}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_0(12))\)\(^{\oplus 2}\)