Defining parameters
Level: | \( N \) | \(=\) | \( 240 = 2^{4} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 240.y (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 80 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(96\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(7\), \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(240, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 104 | 48 | 56 |
Cusp forms | 88 | 48 | 40 |
Eisenstein series | 16 | 0 | 16 |
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.y.a | $2$ | $1.916$ | \(\Q(\sqrt{-1}) \) | None | \(-2\) | \(-2\) | \(-2\) | \(-2\) | \(q+(-1-i)q^{2}-q^{3}+2iq^{4}+(-1+\cdots)q^{5}+\cdots\) |
240.2.y.b | $2$ | $1.916$ | \(\Q(\sqrt{-1}) \) | None | \(-2\) | \(2\) | \(-2\) | \(6\) | \(q+(-1-i)q^{2}+q^{3}+2iq^{4}+(-1+\cdots)q^{5}+\cdots\) |
240.2.y.c | $2$ | $1.916$ | \(\Q(\sqrt{-1}) \) | None | \(2\) | \(-2\) | \(2\) | \(6\) | \(q+(1+i)q^{2}-q^{3}+2iq^{4}+(1-2i)q^{5}+\cdots\) |
240.2.y.d | $6$ | $1.916$ | 6.0.399424.1 | None | \(0\) | \(6\) | \(6\) | \(-2\) | \(q+\beta _{3}q^{2}+q^{3}+(-\beta _{1}-\beta _{5})q^{4}+(1+\cdots)q^{5}+\cdots\) |
240.2.y.e | $16$ | $1.916$ | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) | None | \(2\) | \(16\) | \(-4\) | \(-4\) | \(q+\beta _{7}q^{2}+q^{3}+(-1+\beta _{2}-\beta _{3}-\beta _{4}+\cdots)q^{4}+\cdots\) |
240.2.y.f | $20$ | $1.916$ | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) | None | \(0\) | \(-20\) | \(0\) | \(-4\) | \(q+\beta _{13}q^{2}-q^{3}-\beta _{3}q^{4}+\beta _{7}q^{5}-\beta _{13}q^{6}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(240, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(240, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 2}\)