Defining parameters
Level: | \( N \) | \(=\) | \( 316 = 2^{2} \cdot 79 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 316.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(80\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(316))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 43 | 6 | 37 |
Cusp forms | 38 | 6 | 32 |
Eisenstein series | 5 | 0 | 5 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(79\) | Fricke | Dim |
---|---|---|---|
\(-\) | \(+\) | $-$ | \(3\) |
\(-\) | \(-\) | $+$ | \(3\) |
Plus space | \(+\) | \(3\) | |
Minus space | \(-\) | \(3\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(316))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | 79 | |||||||
316.2.a.a | $1$ | $2.523$ | \(\Q\) | None | \(0\) | \(-3\) | \(1\) | \(1\) | $-$ | $-$ | \(q-3q^{3}+q^{5}+q^{7}+6q^{9}-6q^{11}+\cdots\) | |
316.2.a.b | $1$ | $2.523$ | \(\Q\) | None | \(0\) | \(-1\) | \(1\) | \(3\) | $-$ | $+$ | \(q-q^{3}+q^{5}+3q^{7}-2q^{9}+2q^{11}+\cdots\) | |
316.2.a.c | $2$ | $2.523$ | \(\Q(\sqrt{13}) \) | None | \(0\) | \(0\) | \(-5\) | \(-2\) | $-$ | $-$ | \(q+(-2-\beta )q^{5}+(-2+2\beta )q^{7}-3q^{9}+\cdots\) | |
316.2.a.d | $2$ | $2.523$ | \(\Q(\sqrt{13}) \) | None | \(0\) | \(4\) | \(3\) | \(0\) | $-$ | $+$ | \(q+2q^{3}+(2-\beta )q^{5}+q^{9}+(1+\beta )q^{11}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(316))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(316)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(79))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(158))\)\(^{\oplus 2}\)