Defining parameters
Level: | \( N \) | \(=\) | \( 310 = 2 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 310.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(96\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(310))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 52 | 9 | 43 |
Cusp forms | 45 | 9 | 36 |
Eisenstein series | 7 | 0 | 7 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(5\) | \(31\) | Fricke | Dim |
---|---|---|---|---|
\(+\) | \(+\) | \(+\) | \(+\) | \(2\) |
\(+\) | \(-\) | \(+\) | \(-\) | \(2\) |
\(-\) | \(+\) | \(+\) | \(-\) | \(1\) |
\(-\) | \(+\) | \(-\) | \(+\) | \(1\) |
\(-\) | \(-\) | \(-\) | \(-\) | \(3\) |
Plus space | \(+\) | \(3\) | ||
Minus space | \(-\) | \(6\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(310))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | 5 | 31 | |||||||
310.2.a.a | $1$ | $2.475$ | \(\Q\) | None | \(1\) | \(-2\) | \(-1\) | \(-4\) | $-$ | $+$ | $-$ | \(q+q^{2}-2q^{3}+q^{4}-q^{5}-2q^{6}-4q^{7}+\cdots\) | |
310.2.a.b | $1$ | $2.475$ | \(\Q\) | None | \(1\) | \(2\) | \(-1\) | \(0\) | $-$ | $+$ | $+$ | \(q+q^{2}+2q^{3}+q^{4}-q^{5}+2q^{6}+q^{8}+\cdots\) | |
310.2.a.c | $2$ | $2.475$ | \(\Q(\sqrt{3}) \) | None | \(-2\) | \(-2\) | \(-2\) | \(0\) | $+$ | $+$ | $+$ | \(q-q^{2}+(-1+\beta )q^{3}+q^{4}-q^{5}+(1+\cdots)q^{6}+\cdots\) | |
310.2.a.d | $2$ | $2.475$ | \(\Q(\sqrt{6}) \) | None | \(-2\) | \(0\) | \(2\) | \(-4\) | $+$ | $-$ | $+$ | \(q-q^{2}+\beta q^{3}+q^{4}+q^{5}-\beta q^{6}-2q^{7}+\cdots\) | |
310.2.a.e | $3$ | $2.475$ | 3.3.148.1 | None | \(3\) | \(2\) | \(3\) | \(0\) | $-$ | $-$ | $-$ | \(q+q^{2}+(1-\beta _{1})q^{3}+q^{4}+q^{5}+(1-\beta _{1}+\cdots)q^{6}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(310))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(310)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(31))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(62))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(155))\)\(^{\oplus 2}\)