Defining parameters
Level: | \( N \) | \(=\) | \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 1200.bj (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 60 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(240\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(1200, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 96 | 12 | 84 |
Cusp forms | 24 | 12 | 12 |
Eisenstein series | 72 | 0 | 72 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 12 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(1200, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
1200.1.bj.a | $4$ | $0.599$ | \(\Q(\zeta_{8})\) | $D_{2}$ | \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-5}) \) | \(\Q(\sqrt{15}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\zeta_{8}q^{3}-\zeta_{8}^{3}q^{7}+\zeta_{8}^{2}q^{9}-2q^{21}+\cdots\) |
1200.1.bj.b | $8$ | $0.599$ | \(\Q(\zeta_{24})\) | $D_{6}$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\zeta_{24}^{3}q^{3}+\zeta_{24}^{9}q^{7}+\zeta_{24}^{6}q^{9}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(1200, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(1200, [\chi]) \cong \)