Defining parameters
Level: | \( N \) | \(=\) | \( 48 = 2^{4} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 48.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 \(M_{4}(\Gamma_0(48))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 30 | 3 | 27 |
Cusp forms | 18 | 3 | 15 |
Eisenstein series | 12 | 0 | 12 |
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 \(S_{4}^{\mathrm{new}}(\Gamma_0(48))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | 3 | |||||||
48.4.a.a | $1$ | $2.832$ | \(\Q\) | None | \(0\) | \(-3\) | \(-18\) | \(-8\) | $-$ | $+$ | \(q-3q^{3}-18q^{5}-8q^{7}+9q^{9}-6^{2}q^{11}+\cdots\) | |
48.4.a.b | $1$ | $2.832$ | \(\Q\) | None | \(0\) | \(-3\) | \(14\) | \(24\) | $+$ | $+$ | \(q-3q^{3}+14q^{5}+24q^{7}+9q^{9}+28q^{11}+\cdots\) | |
48.4.a.c | $1$ | $2.832$ | \(\Q\) | None | \(0\) | \(3\) | \(6\) | \(16\) | $-$ | $-$ | \(q+3q^{3}+6q^{5}+2^{4}q^{7}+9q^{9}-12q^{11}+\cdots\) |
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(48))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_0(48)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(12))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 2}\)