Defining parameters
Level: | \( N \) | \(=\) | \( 260 = 2^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 260.i (of order \(3\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 13 \) |
Character field: | \(\Q(\zeta_{3})\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(84\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(3\), \(19\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(260, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 96 | 8 | 88 |
Cusp forms | 72 | 8 | 64 |
Eisenstein series | 24 | 0 | 24 |
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.i.a | $2$ | $2.076$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(-1\) | \(-2\) | \(1\) | \(q+(-1+\zeta_{6})q^{3}-q^{5}+\zeta_{6}q^{7}+2\zeta_{6}q^{9}+\cdots\) |
260.2.i.b | $2$ | $2.076$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(-1\) | \(2\) | \(1\) | \(q+(-1+\zeta_{6})q^{3}+q^{5}+\zeta_{6}q^{7}+2\zeta_{6}q^{9}+\cdots\) |
260.2.i.c | $2$ | $2.076$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(1\) | \(-2\) | \(-5\) | \(q+(1-\zeta_{6})q^{3}-q^{5}-5\zeta_{6}q^{7}+2\zeta_{6}q^{9}+\cdots\) |
260.2.i.d | $2$ | $2.076$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(3\) | \(2\) | \(-3\) | \(q+(3-3\zeta_{6})q^{3}+q^{5}-3\zeta_{6}q^{7}-6\zeta_{6}q^{9}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(260, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(260, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 2}\)