Defining parameters
Level: | \( N \) | \(=\) | \( 3525 = 3 \cdot 5^{2} \cdot 47 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 3525.l (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 705 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(480\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(3525, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 84 | 68 | 16 |
Cusp forms | 60 | 60 | 0 |
Eisenstein series | 24 | 8 | 16 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 60 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(3525, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
3525.1.l.a | $4$ | $1.759$ | \(\Q(\zeta_{8})\) | $D_{2}$ | \(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-47}) \) | \(\Q(\sqrt{705}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\zeta_{8}q^{2}+\zeta_{8}^{3}q^{3}+3\zeta_{8}^{2}q^{4}+2q^{6}+\cdots\) |
3525.1.l.b | $8$ | $1.759$ | \(\Q(\zeta_{24})\) | $D_{6}$ | \(\Q(\sqrt{-47}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\zeta_{24}^{9}q^{2}-\zeta_{24}^{7}q^{3}+\zeta_{24}^{4}q^{6}+\cdots\) |
3525.1.l.c | $16$ | $1.759$ | \(\Q(\zeta_{40})\) | $D_{10}$ | \(\Q(\sqrt{-47}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(-\zeta_{40}^{13}+\zeta_{40}^{17})q^{2}-\zeta_{40}^{11}q^{3}+\cdots\) |
3525.1.l.d | $32$ | $1.759$ | \(\Q(\zeta_{120})\) | $D_{30}$ | \(\Q(\sqrt{-47}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(-\zeta_{120}^{41}-\zeta_{120}^{49})q^{2}+\zeta_{120}^{43}q^{3}+\cdots\) |