Defining parameters
Level: | \( N \) | \(=\) | \( 240 = 2^{4} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 240.v (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 15 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(96\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(7\), \(11\), \(17\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(240, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 120 | 28 | 92 |
Cusp forms | 72 | 20 | 52 |
Eisenstein series | 48 | 8 | 40 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(240, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
240.2.v.a | $4$ | $1.916$ | \(\Q(\zeta_{8})\) | None | \(0\) | \(-4\) | \(4\) | \(4\) | \(q+(-1+\zeta_{8}^{2})q^{3}+(1+2\zeta_{8})q^{5}+(1+\cdots)q^{7}+\cdots\) |
240.2.v.b | $4$ | $1.916$ | \(\Q(i, \sqrt{5})\) | None | \(0\) | \(-2\) | \(0\) | \(4\) | \(q+(-1+\beta _{3})q^{3}+(-1-\beta _{1}+\beta _{3})q^{5}+\cdots\) |
240.2.v.c | $4$ | $1.916$ | \(\Q(\zeta_{8})\) | None | \(0\) | \(0\) | \(-4\) | \(4\) | \(q+(\zeta_{8}-\zeta_{8}^{3})q^{3}+(-1-2\zeta_{8})q^{5}+(1+\cdots)q^{7}+\cdots\) |
240.2.v.d | $4$ | $1.916$ | \(\Q(\zeta_{8})\) | None | \(0\) | \(4\) | \(0\) | \(-12\) | \(q+(1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+(2\zeta_{8}-\zeta_{8}^{3})q^{5}+\cdots\) |
240.2.v.e | $4$ | $1.916$ | \(\Q(\zeta_{8})\) | None | \(0\) | \(4\) | \(0\) | \(4\) | \(q+(1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+(-2\zeta_{8}-\zeta_{8}^{3})q^{5}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(240, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(240, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 2}\)