Defining parameters
Level: | \( N \) | \(=\) | \( 260 = 2^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 260.bf (of order \(12\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 65 \) |
Character field: | \(\Q(\zeta_{12})\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(84\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(260, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 192 | 28 | 164 |
Cusp forms | 144 | 28 | 116 |
Eisenstein series | 48 | 0 | 48 |
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.bf.a | $4$ | $2.076$ | \(\Q(\zeta_{12})\) | None | \(0\) | \(-2\) | \(8\) | \(4\) | \(q+(-1+\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+(2+\zeta_{12}^{3})q^{5}+\cdots\) |
260.2.bf.b | $4$ | $2.076$ | \(\Q(\zeta_{12})\) | None | \(0\) | \(4\) | \(-4\) | \(2\) | \(q+(1-\zeta_{12})q^{3}+(-1+2\zeta_{12}^{3})q^{5}+\cdots\) |
260.2.bf.c | $20$ | $2.076$ | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) | None | \(0\) | \(-2\) | \(-6\) | \(-6\) | \(q+(-1-\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5}+\cdots)q^{3}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(260, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(260, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(130, [\chi])\)\(^{\oplus 2}\)