Defining parameters
Level: | \( N \) | \(=\) | \( 1152 = 2^{7} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 1152.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 8 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(192\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(1152, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 42 | 3 | 39 |
Cusp forms | 10 | 3 | 7 |
Eisenstein series | 32 | 0 | 32 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 3 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(1152, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
1152.1.b.a | $1$ | $0.575$ | \(\Q\) | $D_{2}$ | \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-2}) \) | \(\Q(\sqrt{2}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q+2q^{17}+q^{25}-2q^{41}+q^{49}-2q^{73}+\cdots\) |
1152.1.b.b | $2$ | $0.575$ | \(\Q(\sqrt{-1}) \) | $D_{2}$ | \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-6}) \) | \(\Q(\sqrt{6}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q-iq^{5}-3q^{25}-iq^{29}+q^{49}+iq^{53}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(1152, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(1152, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(384, [\chi])\)\(^{\oplus 2}\)