Defining parameters
Level: | \( N \) | \(=\) | \( 240 = 2^{4} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 240.f (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 5 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 7 \) | ||
Sturm bound: | \(192\) | ||
Trace bound: | \(11\) | ||
Distinguishing \(T_p\): | \(7\), \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(240, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 156 | 18 | 138 |
Cusp forms | 132 | 18 | 114 |
Eisenstein series | 24 | 0 | 24 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(240, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
240.4.f.a | $2$ | $14.160$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(-20\) | \(0\) | \(q+3iq^{3}+(-10-5i)q^{5}+22iq^{7}+\cdots\) |
240.4.f.b | $2$ | $14.160$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(-20\) | \(0\) | \(q-3iq^{3}+(-10+5i)q^{5}+10iq^{7}+\cdots\) |
240.4.f.c | $2$ | $14.160$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(-4\) | \(0\) | \(q-3iq^{3}+(-2-11i)q^{5}+10iq^{7}+\cdots\) |
240.4.f.d | $2$ | $14.160$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(4\) | \(0\) | \(q-3iq^{3}+(2+11i)q^{5}+2iq^{7}-9q^{9}+\cdots\) |
240.4.f.e | $2$ | $14.160$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(10\) | \(0\) | \(q+3iq^{3}+(5-10i)q^{5}+4iq^{7}-9q^{9}+\cdots\) |
240.4.f.f | $4$ | $14.160$ | \(\Q(i, \sqrt{41})\) | None | \(0\) | \(0\) | \(6\) | \(0\) | \(q-\beta _{2}q^{3}+(1-\beta _{1}-2\beta _{2}+\beta _{3})q^{5}+\cdots\) |
240.4.f.g | $4$ | $14.160$ | \(\Q(i, \sqrt{129})\) | None | \(0\) | \(0\) | \(22\) | \(0\) | \(q+3\beta _{1}q^{3}+(5+6\beta _{1}-\beta _{3})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\) |
Decomposition of \(S_{4}^{\mathrm{old}}(240, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(240, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 2}\)