Defining parameters
Level: | \( N \) | \(=\) | \( 260 = 2^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 260.p (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 260 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(84\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(3\), \(7\), \(37\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(260, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 92 | 92 | 0 |
Cusp forms | 76 | 76 | 0 |
Eisenstein series | 16 | 16 | 0 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(260, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
260.2.p.a | $2$ | $2.076$ | \(\Q(\sqrt{-1}) \) | \(\Q(\sqrt{-1}) \) | \(-2\) | \(0\) | \(4\) | \(0\) | \(q+(-1+i)q^{2}-2iq^{4}+(2+i)q^{5}+\cdots\) |
260.2.p.b | $2$ | $2.076$ | \(\Q(\sqrt{-1}) \) | \(\Q(\sqrt{-1}) \) | \(2\) | \(0\) | \(-4\) | \(0\) | \(q+(1-i)q^{2}-2iq^{4}+(-2-i)q^{5}+\cdots\) |
260.2.p.c | $8$ | $2.076$ | 8.0.3317760000.5 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(-\beta _{1}-\beta _{5})q^{5}+\cdots\) |
260.2.p.d | $64$ | $2.076$ | None | \(0\) | \(0\) | \(0\) | \(0\) |