Defining parameters
Level: | \( N \) | \(=\) | \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 1575.cp (of order \(12\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 315 \) |
Character field: | \(\Q(\zeta_{12})\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(240\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(1575, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 56 | 24 | 32 |
Cusp forms | 8 | 8 | 0 |
Eisenstein series | 48 | 16 | 32 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 0 | 8 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(1575, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
1575.1.cp.a | $8$ | $0.786$ | \(\Q(\zeta_{24})\) | $A_{4}$ | None | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\zeta_{24}^{11}q^{2}-\zeta_{24}^{9}q^{3}-\zeta_{24}^{8}q^{6}+\cdots\) |