Defining parameters
Level: | \( N \) | \(=\) | \( 2475 = 3^{2} \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 2475.y (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 99 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(360\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(2475, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 36 | 18 | 18 |
Cusp forms | 12 | 6 | 6 |
Eisenstein series | 24 | 12 | 12 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 6 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(2475, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
2475.1.y.a | $2$ | $1.235$ | \(\Q(\sqrt{-3}) \) | $D_{3}$ | \(\Q(\sqrt{-11}) \) | None | \(0\) | \(1\) | \(0\) | \(0\) | \(q+\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}^{2}q^{9}+\zeta_{6}^{2}q^{11}+\cdots\) |
2475.1.y.b | $4$ | $1.235$ | \(\Q(\zeta_{12})\) | $D_{6}$ | \(\Q(\sqrt{-11}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\zeta_{12}q^{3}+\zeta_{12}^{4}q^{4}+\zeta_{12}^{2}q^{9}+\zeta_{12}^{2}q^{11}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(2475, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(2475, [\chi]) \cong \)