Defining parameters
Level: | \( N \) | \(=\) | \( 240 = 2^{4} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 240.f (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 5 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(96\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(7\), \(13\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(240, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 60 | 6 | 54 |
Cusp forms | 36 | 6 | 30 |
Eisenstein series | 24 | 0 | 24 |
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.f.a | $2$ | $1.916$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(-4\) | \(0\) | \(q+iq^{3}+(-2+i)q^{5}+2iq^{7}-q^{9}+\cdots\) |
240.2.f.b | $2$ | $1.916$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(2\) | \(0\) | \(q+iq^{3}+(1-2i)q^{5}-4iq^{7}-q^{9}+\cdots\) |
240.2.f.c | $2$ | $1.916$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(4\) | \(0\) | \(q+iq^{3}+(2+i)q^{5}+2iq^{7}-q^{9}-2q^{11}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(240, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(240, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 2}\)