Defining parameters
Level: | \( N \) | \(=\) | \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 360.f (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 5 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(288\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(7\), \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(360, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 232 | 22 | 210 |
Cusp forms | 200 | 22 | 178 |
Eisenstein series | 32 | 0 | 32 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(360, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
360.4.f.a | $2$ | $21.241$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(-10\) | \(0\) | \(q+(-5-5i)q^{5}+2iq^{7}+28q^{11}+\cdots\) |
360.4.f.b | $2$ | $21.241$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(4\) | \(0\) | \(q+(2-11i)q^{5}+10iq^{7}+14q^{11}+\cdots\) |
360.4.f.c | $2$ | $21.241$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(20\) | \(0\) | \(q+(10+5i)q^{5}+10iq^{7}+46q^{11}+\cdots\) |
360.4.f.d | $4$ | $21.241$ | \(\Q(i, \sqrt{129})\) | None | \(0\) | \(0\) | \(-22\) | \(0\) | \(q+(-5+\beta _{1}-\beta _{3})q^{5}+(-2\beta _{1}+3\beta _{2}+\cdots)q^{7}+\cdots\) |
360.4.f.e | $4$ | $21.241$ | \(\Q(i, \sqrt{6})\) | None | \(0\) | \(0\) | \(4\) | \(0\) | \(q+(1+\beta _{2}-\beta _{3})q^{5}+(\beta _{1}-2\beta _{2})q^{7}+\cdots\) |
360.4.f.f | $8$ | $21.241$ | 8.0.\(\cdots\).2 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{4}q^{5}+\beta _{2}q^{7}+\beta _{6}q^{11}+\beta _{7}q^{13}+\cdots\) |
Decomposition of \(S_{4}^{\mathrm{old}}(360, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(360, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 2}\)