Defining parameters
Level: | \( N \) | \(=\) | \( 38 = 2 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 38.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(50\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_0(38))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 47 | 13 | 34 |
Cusp forms | 43 | 13 | 30 |
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.
\(2\) | \(19\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(3\) |
\(+\) | \(-\) | $-$ | \(4\) |
\(-\) | \(+\) | $-$ | \(4\) |
\(-\) | \(-\) | $+$ | \(2\) |
Plus space | \(+\) | \(5\) | |
Minus space | \(-\) | \(8\) |
Trace form
Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(38))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | 19 | |||||||
38.10.a.a | $1$ | $19.571$ | \(\Q\) | None | \(16\) | \(-119\) | \(-684\) | \(9149\) | $-$ | $-$ | \(q+2^{4}q^{2}-119q^{3}+2^{8}q^{4}-684q^{5}+\cdots\) | |
38.10.a.b | $1$ | $19.571$ | \(\Q\) | None | \(16\) | \(102\) | \(-1581\) | \(-4865\) | $-$ | $-$ | \(q+2^{4}q^{2}+102q^{3}+2^{8}q^{4}-1581q^{5}+\cdots\) | |
38.10.a.c | $3$ | $19.571$ | \(\mathbb{Q}[x]/(x^{3} - \cdots)\) | None | \(-48\) | \(3\) | \(486\) | \(-13317\) | $+$ | $+$ | \(q-2^{4}q^{2}+(1+\beta _{1})q^{3}+2^{8}q^{4}+(162+\cdots)q^{5}+\cdots\) | |
38.10.a.d | $4$ | $19.571$ | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) | None | \(-64\) | \(84\) | \(-1395\) | \(12307\) | $+$ | $-$ | \(q-2^{4}q^{2}+(21+\beta _{1})q^{3}+2^{8}q^{4}+(-350+\cdots)q^{5}+\cdots\) | |
38.10.a.e | $4$ | $19.571$ | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) | None | \(64\) | \(226\) | \(866\) | \(2670\) | $-$ | $+$ | \(q+2^{4}q^{2}+(57+\beta _{2})q^{3}+2^{8}q^{4}+(218+\cdots)q^{5}+\cdots\) |
Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_0(38))\) into lower level spaces
\( S_{10}^{\mathrm{old}}(\Gamma_0(38)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 2}\)