Defining parameters
Level: | \( N \) | \(=\) | \( 2703 = 3 \cdot 17 \cdot 53 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 2703.g (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 2703 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(324\) | ||
Trace bound: | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(2703, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 20 | 20 | 0 |
Cusp forms | 16 | 16 | 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 | 16 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(2703, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
2703.1.g.a | $3$ | $1.349$ | \(\Q(\zeta_{14})^+\) | $D_{7}$ | \(\Q(\sqrt{-2703}) \) | None | \(-1\) | \(-3\) | \(0\) | \(0\) | \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\) |
2703.1.g.b | $3$ | $1.349$ | \(\Q(\zeta_{14})^+\) | $D_{7}$ | \(\Q(\sqrt{-2703}) \) | None | \(-1\) | \(3\) | \(0\) | \(0\) | \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\) |
2703.1.g.c | $3$ | $1.349$ | \(\Q(\zeta_{14})^+\) | $D_{7}$ | \(\Q(\sqrt{-2703}) \) | None | \(1\) | \(-3\) | \(0\) | \(0\) | \(q-\beta _{2}q^{2}-q^{3}+(\beta _{1}-\beta _{2})q^{4}+\beta _{2}q^{6}+\cdots\) |
2703.1.g.d | $3$ | $1.349$ | \(\Q(\zeta_{14})^+\) | $D_{7}$ | \(\Q(\sqrt{-2703}) \) | None | \(1\) | \(3\) | \(0\) | \(0\) | \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\) |
2703.1.g.e | $4$ | $1.349$ | \(\Q(\zeta_{8})\) | $D_{4}$ | None | \(\Q(\sqrt{901}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\zeta_{8}q^{3}-q^{4}+(\zeta_{8}+\zeta_{8}^{3})q^{5}+\zeta_{8}^{2}q^{9}+\cdots\) |