Defining parameters
Level: | \( N \) | \(=\) | \( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 1380.bn (of order \(22\) and degree \(10\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 1380 \) |
Character field: | \(\Q(\zeta_{22})\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(288\) | ||
Trace bound: | \(10\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(1380, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 160 | 160 | 0 |
Cusp forms | 80 | 80 | 0 |
Eisenstein series | 80 | 80 | 0 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 80 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(1380, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
1380.1.bn.a | $20$ | $0.689$ | \(\Q(\zeta_{44})\) | $D_{22}$ | \(\Q(\sqrt{-5}) \) | None | \(0\) | \(0\) | \(-2\) | \(0\) | \(q+\zeta_{44}^{21}q^{2}+\zeta_{44}^{13}q^{3}-\zeta_{44}^{20}q^{4}+\cdots\) |
1380.1.bn.b | $20$ | $0.689$ | \(\Q(\zeta_{44})\) | $D_{22}$ | \(\Q(\sqrt{-15}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\zeta_{44}^{13}q^{2}+\zeta_{44}^{3}q^{3}-\zeta_{44}^{4}q^{4}+\cdots\) |
1380.1.bn.c | $20$ | $0.689$ | \(\Q(\zeta_{44})\) | $D_{22}$ | \(\Q(\sqrt{-15}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\zeta_{44}^{7}q^{2}+\zeta_{44}^{3}q^{3}+\zeta_{44}^{14}q^{4}+\cdots\) |
1380.1.bn.d | $20$ | $0.689$ | \(\Q(\zeta_{44})\) | $D_{22}$ | \(\Q(\sqrt{-5}) \) | None | \(0\) | \(0\) | \(2\) | \(0\) | \(q+\zeta_{44}^{21}q^{2}-\zeta_{44}^{15}q^{3}-\zeta_{44}^{20}q^{4}+\cdots\) |