Defining parameters
Level: | \( N \) | \(=\) | \( 3360 = 2^{5} \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3360.j (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 40 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(1536\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(11\), \(13\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(3360, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 800 | 72 | 728 |
Cusp forms | 736 | 72 | 664 |
Eisenstein series | 64 | 0 | 64 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(3360, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
3360.2.j.a | $2$ | $26.830$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(-2\) | \(-4\) | \(0\) | \(q-q^{3}+(-2+i)q^{5}-iq^{7}+q^{9}-6q^{13}+\cdots\) |
3360.2.j.b | $2$ | $26.830$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(-2\) | \(4\) | \(0\) | \(q-q^{3}+(2-i)q^{5}+iq^{7}+q^{9}+4iq^{11}+\cdots\) |
3360.2.j.c | $2$ | $26.830$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(2\) | \(-4\) | \(0\) | \(q+q^{3}+(-2-i)q^{5}-iq^{7}+q^{9}+4iq^{11}+\cdots\) |
3360.2.j.d | $2$ | $26.830$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(2\) | \(4\) | \(0\) | \(q+q^{3}+(2+i)q^{5}+iq^{7}+q^{9}+6q^{13}+\cdots\) |
3360.2.j.e | $32$ | $26.830$ | None | \(0\) | \(-32\) | \(0\) | \(0\) | ||
3360.2.j.f | $32$ | $26.830$ | None | \(0\) | \(32\) | \(0\) | \(0\) |
Decomposition of \(S_{2}^{\mathrm{old}}(3360, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(3360, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(840, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1120, [\chi])\)\(^{\oplus 2}\)