Defining parameters
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.h (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 36 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(72\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(108, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 120 | 40 | 80 |
Cusp forms | 96 | 32 | 64 |
Eisenstein series | 24 | 8 | 16 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(108, [\chi])\) into newform subspaces
Label | Dim. | \(A\) | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
\(a_2\) | \(a_3\) | \(a_5\) | \(a_7\) | ||||||
108.4.h.a | \(8\) | \(6.372\) | 8.0.\(\cdots\).1 | None | \(3\) | \(0\) | \(-66\) | \(0\) | \(q+\beta _{7}q^{2}+(2\beta _{2}-2\beta _{3}-2\beta _{4}+\beta _{6}+\cdots)q^{4}+\cdots\) |
108.4.h.b | \(24\) | \(6.372\) | None | \(0\) | \(0\) | \(72\) | \(0\) |
Decomposition of \(S_{4}^{\mathrm{old}}(108, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(108, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 2}\)