Defining parameters
Level: | \( N \) | \(=\) | \( 2015 = 5 \cdot 13 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 2015.bq (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 2015 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(224\) | ||
Trace bound: | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(2015, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 24 | 24 | 0 |
Cusp forms | 16 | 16 | 0 |
Eisenstein series | 8 | 8 | 0 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 8 | 8 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(2015, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
2015.1.bq.a | $2$ | $1.006$ | \(\Q(\sqrt{-3}) \) | $D_{3}$ | \(\Q(\sqrt{-155}) \) | None | \(0\) | \(-2\) | \(2\) | \(0\) | \(q-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}+q^{5}+3\zeta_{6}^{2}q^{9}+\cdots\) |
2015.1.bq.b | $2$ | $1.006$ | \(\Q(\sqrt{-3}) \) | $D_{3}$ | \(\Q(\sqrt{-155}) \) | None | \(0\) | \(2\) | \(2\) | \(0\) | \(q+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}+q^{5}+3\zeta_{6}^{2}q^{9}+\cdots\) |
2015.1.bq.c | $4$ | $1.006$ | \(\Q(\zeta_{12})\) | $A_{4}$ | None | None | \(0\) | \(-2\) | \(0\) | \(0\) | \(q+\zeta_{12}q^{2}+\zeta_{12}^{4}q^{3}+\zeta_{12}^{3}q^{5}+\zeta_{12}^{5}q^{6}+\cdots\) |
2015.1.bq.d | $4$ | $1.006$ | \(\Q(\zeta_{12})\) | $D_{6}$ | \(\Q(\sqrt{-155}) \) | None | \(0\) | \(0\) | \(-4\) | \(0\) | \(q-\zeta_{12}^{2}q^{4}-q^{5}+\zeta_{12}^{2}q^{9}+\zeta_{12}^{5}q^{13}+\cdots\) |
2015.1.bq.e | $4$ | $1.006$ | \(\Q(\zeta_{12})\) | $A_{4}$ | None | None | \(0\) | \(2\) | \(0\) | \(0\) | \(q-\zeta_{12}q^{2}-\zeta_{12}^{4}q^{3}-\zeta_{12}^{3}q^{5}+\zeta_{12}^{5}q^{6}+\cdots\) |