Defining parameters
Level: | \( N \) | = | \( 38 = 2 \cdot 19 \) |
Weight: | \( k \) | = | \( 2 \) |
Character orbit: | \([\chi]\) | = | 38.a (trivial) |
Character field: | \(\Q\) | ||
Newforms: | \( 2 \) | ||
Sturm bound: | \(10\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(38))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 7 | 2 | 5 |
Cusp forms | 4 | 2 | 2 |
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.
\(2\) | \(19\) | Fricke | Dim. |
---|---|---|---|
\(+\) | \(-\) | \(-\) | \(1\) |
\(-\) | \(+\) | \(-\) | \(1\) |
Plus space | \(+\) | \(0\) | |
Minus space | \(-\) | \(2\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(38))\) into irreducible Hecke orbits
Label | Dim. | \(A\) | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
\(a_2\) | \(a_3\) | \(a_5\) | \(a_7\) | 2 | 19 | |||||||
38.2.a.a | \(1\) | \(0.303\) | \(\Q\) | None | \(-1\) | \(1\) | \(0\) | \(-1\) | \(+\) | \(-\) | \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\) | |
38.2.a.b | \(1\) | \(0.303\) | \(\Q\) | None | \(1\) | \(-1\) | \(-4\) | \(3\) | \(-\) | \(+\) | \(q+q^{2}-q^{3}+q^{4}-4q^{5}-q^{6}+3q^{7}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(38))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(38)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 2}\)