Defining parameters
Level: | \( N \) | \(=\) | \( 2015 = 5 \cdot 13 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 2015.h (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 2015 \) |
Character field: | \(\Q\) | ||
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 | 32 | 32 | 0 |
Cusp forms | 28 | 28 | 0 |
Eisenstein series | 4 | 4 | 0 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 28 | 0 | 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.h.a | $4$ | $1.006$ | \(\Q(\zeta_{8})\) | $D_{4}$ | \(\Q(\sqrt{-155}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(\zeta_{8}-\zeta_{8}^{3})q^{3}-q^{4}+\zeta_{8}^{2}q^{5}+q^{9}+\cdots\) |
2015.1.h.b | $6$ | $1.006$ | \(\Q(\zeta_{26})^+\) | $D_{13}$ | \(\Q(\sqrt{-2015}) \) | None | \(-1\) | \(-1\) | \(6\) | \(-1\) | \(q-\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots\) |
2015.1.h.c | $6$ | $1.006$ | \(\Q(\zeta_{26})^+\) | $D_{13}$ | \(\Q(\sqrt{-2015}) \) | None | \(-1\) | \(1\) | \(6\) | \(-1\) | \(q-\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots\) |
2015.1.h.d | $6$ | $1.006$ | \(\Q(\zeta_{26})^+\) | $D_{13}$ | \(\Q(\sqrt{-2015}) \) | None | \(1\) | \(-1\) | \(-6\) | \(1\) | \(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots\) |
2015.1.h.e | $6$ | $1.006$ | \(\Q(\zeta_{26})^+\) | $D_{13}$ | \(\Q(\sqrt{-2015}) \) | None | \(1\) | \(1\) | \(-6\) | \(1\) | \(q+\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots\) |