Defining parameters
Level: | \( N \) | \(=\) | \( 3960 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3960.ba (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 165 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(1728\) | ||
Trace bound: | \(11\) | ||
Distinguishing \(T_p\): | \(7\), \(29\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(3960, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 896 | 72 | 824 |
Cusp forms | 832 | 72 | 760 |
Eisenstein series | 64 | 0 | 64 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(3960, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
3960.2.ba.a | $4$ | $31.621$ | \(\Q(\zeta_{8})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(-\zeta_{8}-2\zeta_{8}^{3})q^{5}+(-\zeta_{8}+\zeta_{8}^{3})q^{7}+\cdots\) |
3960.2.ba.b | $4$ | $31.621$ | \(\Q(\zeta_{8})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(-2\zeta_{8}-\zeta_{8}^{3})q^{5}+(-\zeta_{8}+\zeta_{8}^{3})q^{7}+\cdots\) |
3960.2.ba.c | $64$ | $31.621$ | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{2}^{\mathrm{old}}(3960, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(3960, [\chi]) \cong \)