Defining parameters
Level: | \( N \) | \(=\) | \( 36 = 2^{2} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 36.h (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 36 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(24\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(36, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 40 | 40 | 0 |
Cusp forms | 32 | 32 | 0 |
Eisenstein series | 8 | 8 | 0 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(36, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
36.4.h.a | $8$ | $2.124$ | 8.0.\(\cdots\).1 | None | \(-3\) | \(0\) | \(66\) | \(0\) | \(q-\beta _{7}q^{2}+(-\beta _{2}+\beta _{5})q^{3}+(2\beta _{2}-2\beta _{3}+\cdots)q^{4}+\cdots\) |
36.4.h.b | $24$ | $2.124$ | None | \(0\) | \(0\) | \(-72\) | \(0\) |