Defining parameters
Level: | \( N \) | \(=\) | \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 756.h (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 84 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(144\) | ||
Trace bound: | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(756, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 24 | 4 | 20 |
Cusp forms | 12 | 4 | 8 |
Eisenstein series | 12 | 0 | 12 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 4 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(756, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
756.1.h.a | $1$ | $0.377$ | \(\Q\) | $D_{3}$ | \(\Q(\sqrt{-21}) \) | None | \(-1\) | \(0\) | \(-1\) | \(-1\) | \(q-q^{2}+q^{4}-q^{5}-q^{7}-q^{8}+q^{10}+\cdots\) |
756.1.h.b | $1$ | $0.377$ | \(\Q\) | $D_{3}$ | \(\Q(\sqrt{-21}) \) | None | \(-1\) | \(0\) | \(1\) | \(1\) | \(q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-q^{10}+\cdots\) |
756.1.h.c | $1$ | $0.377$ | \(\Q\) | $D_{3}$ | \(\Q(\sqrt{-21}) \) | None | \(1\) | \(0\) | \(-1\) | \(1\) | \(q+q^{2}+q^{4}-q^{5}+q^{7}+q^{8}-q^{10}+\cdots\) |
756.1.h.d | $1$ | $0.377$ | \(\Q\) | $D_{3}$ | \(\Q(\sqrt{-21}) \) | None | \(1\) | \(0\) | \(1\) | \(-1\) | \(q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(756, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(756, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 2}\)