Defining parameters
Level: | \( N \) | \(=\) | \( 6038 = 2 \cdot 3019 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6038.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(1510\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6038))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 757 | 252 | 505 |
Cusp forms | 754 | 252 | 502 |
Eisenstein series | 3 | 0 | 3 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(3019\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(57\) |
\(+\) | \(-\) | $-$ | \(69\) |
\(-\) | \(+\) | $-$ | \(72\) |
\(-\) | \(-\) | $+$ | \(54\) |
Plus space | \(+\) | \(111\) | |
Minus space | \(-\) | \(141\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6038))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | 3019 | |||||||
6038.2.a.a | $2$ | $48.214$ | \(\Q(\sqrt{5}) \) | None | \(2\) | \(-3\) | \(-5\) | \(-6\) | $-$ | $+$ | \(q+q^{2}+(-1-\beta )q^{3}+q^{4}+(-3+\beta )q^{5}+\cdots\) | |
6038.2.a.b | $54$ | $48.214$ | None | \(54\) | \(-21\) | \(-14\) | \(-44\) | $-$ | $-$ | |||
6038.2.a.c | $57$ | $48.214$ | None | \(-57\) | \(-5\) | \(-15\) | \(-28\) | $+$ | $+$ | |||
6038.2.a.d | $69$ | $48.214$ | None | \(-69\) | \(8\) | \(18\) | \(32\) | $+$ | $-$ | |||
6038.2.a.e | $70$ | $48.214$ | None | \(70\) | \(25\) | \(18\) | \(50\) | $-$ | $+$ |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6038))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(6038)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(3019))\)\(^{\oplus 2}\)