Defining parameters
Level: | \( N \) | \(=\) | \( 180 = 2^{2} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 180.h (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 60 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(72\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(180, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 44 | 12 | 32 |
Cusp forms | 28 | 12 | 16 |
Eisenstein series | 16 | 0 | 16 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(180, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
180.2.h.a | $4$ | $1.437$ | \(\Q(\zeta_{8})\) | \(\Q(\sqrt{-1}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\zeta_{8}^{3}q^{2}+2q^{4}-\zeta_{8}^{2}q^{5}+2\zeta_{8}^{3}q^{8}+\cdots\) |
180.2.h.b | $8$ | $1.437$ | 8.0.3317760000.1 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{4}q^{2}+\beta _{3}q^{4}+(-\beta _{2}-\beta _{4}+\beta _{5}+\cdots)q^{5}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(180, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(180, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 2}\)