Defining parameters
Level: | \( N \) | \(=\) | \( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4032.v (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 48 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(1536\) | ||
Trace bound: | \(13\) | ||
Distinguishing \(T_p\): | \(5\), \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(4032, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1600 | 96 | 1504 |
Cusp forms | 1472 | 96 | 1376 |
Eisenstein series | 128 | 0 | 128 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(4032, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
4032.2.v.a | $4$ | $32.196$ | \(\Q(\zeta_{8})\) | None | \(0\) | \(0\) | \(0\) | \(-4\) | \(q+(\zeta_{8}^{2}+\zeta_{8}^{3})q^{5}-q^{7}+(-\zeta_{8}^{2}+\zeta_{8}^{3})q^{11}+\cdots\) |
4032.2.v.b | $4$ | $32.196$ | \(\Q(\zeta_{8})\) | None | \(0\) | \(0\) | \(0\) | \(-4\) | \(q+(\zeta_{8}^{2}+\zeta_{8}^{3})q^{5}-q^{7}+(2\zeta_{8}^{2}-2\zeta_{8}^{3})q^{11}+\cdots\) |
4032.2.v.c | $12$ | $32.196$ | 12.0.\(\cdots\).1 | None | \(0\) | \(0\) | \(0\) | \(12\) | \(q+(\beta _{3}-\beta _{5})q^{5}+q^{7}+(\beta _{1}+\beta _{3}+\beta _{5}+\cdots)q^{11}+\cdots\) |
4032.2.v.d | $36$ | $32.196$ | None | \(0\) | \(0\) | \(0\) | \(36\) | ||
4032.2.v.e | $40$ | $32.196$ | None | \(0\) | \(0\) | \(0\) | \(-40\) |
Decomposition of \(S_{2}^{\mathrm{old}}(4032, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(4032, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 2}\)