Defining parameters
Level: | \( N \) | \(=\) | \( 735 = 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 735.f (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 15 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(112\) | ||
Trace bound: | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(735, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 22 | 16 | 6 |
Cusp forms | 6 | 6 | 0 |
Eisenstein series | 16 | 10 | 6 |
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 \(S_{1}^{\mathrm{new}}(735, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
735.1.f.a | $1$ | $0.367$ | \(\Q\) | $D_{2}$ | \(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-35}) \) | \(\Q(\sqrt{21}) \) | \(0\) | \(-1\) | \(-1\) | \(0\) | \(q-q^{3}-q^{4}-q^{5}+q^{9}+q^{12}+q^{15}+\cdots\) |
735.1.f.b | $1$ | $0.367$ | \(\Q\) | $D_{2}$ | \(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-35}) \) | \(\Q(\sqrt{21}) \) | \(0\) | \(1\) | \(1\) | \(0\) | \(q+q^{3}-q^{4}+q^{5}+q^{9}-q^{12}+q^{15}+\cdots\) |
735.1.f.c | $2$ | $0.367$ | \(\Q(\sqrt{2}) \) | $D_{4}$ | \(\Q(\sqrt{-15}) \) | None | \(0\) | \(-2\) | \(2\) | \(0\) | \(q-\beta q^{2}-q^{3}+q^{4}+q^{5}+\beta q^{6}+q^{9}+\cdots\) |
735.1.f.d | $2$ | $0.367$ | \(\Q(\sqrt{2}) \) | $D_{4}$ | \(\Q(\sqrt{-15}) \) | None | \(0\) | \(2\) | \(-2\) | \(0\) | \(q-\beta q^{2}+q^{3}+q^{4}-q^{5}-\beta q^{6}+q^{9}+\cdots\) |