Defining parameters
Level: | \( N \) | \(=\) | \( 46 = 2 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 46.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(24\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(46))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 20 | 6 | 14 |
Cusp forms | 16 | 6 | 10 |
Eisenstein series | 4 | 0 | 4 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(23\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(2\) |
\(+\) | \(-\) | $-$ | \(1\) |
\(-\) | \(+\) | $-$ | \(1\) |
\(-\) | \(-\) | $+$ | \(2\) |
Plus space | \(+\) | \(4\) | |
Minus space | \(-\) | \(2\) |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(46))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | 23 | |||||||
46.4.a.a | $1$ | $2.714$ | \(\Q\) | None | \(-2\) | \(-1\) | \(-10\) | \(-12\) | $+$ | $-$ | \(q-2q^{2}-q^{3}+4q^{4}-10q^{5}+2q^{6}+\cdots\) | |
46.4.a.b | $1$ | $2.714$ | \(\Q\) | None | \(2\) | \(-9\) | \(-20\) | \(2\) | $-$ | $+$ | \(q+2q^{2}-9q^{3}+4q^{4}-20q^{5}-18q^{6}+\cdots\) | |
46.4.a.c | $2$ | $2.714$ | \(\Q(\sqrt{41}) \) | None | \(-4\) | \(-1\) | \(10\) | \(6\) | $+$ | $+$ | \(q-2q^{2}+(1-3\beta )q^{3}+4q^{4}+(4+2\beta )q^{5}+\cdots\) | |
46.4.a.d | $2$ | $2.714$ | \(\Q(\sqrt{73}) \) | None | \(4\) | \(3\) | \(10\) | \(12\) | $-$ | $-$ | \(q+2q^{2}+(2-\beta )q^{3}+4q^{4}+(4+2\beta )q^{5}+\cdots\) |
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(46))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_0(46)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 2}\)