Defining parameters
Level: | \( N \) | \(=\) | \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 684.h (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 19 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(120\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(684, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 21 | 3 | 18 |
Cusp forms | 9 | 3 | 6 |
Eisenstein series | 12 | 0 | 12 |
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 \(S_{1}^{\mathrm{new}}(684, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
684.1.h.a | $1$ | $0.341$ | \(\Q\) | $D_{3}$ | \(\Q(\sqrt{-19}) \) | None | \(0\) | \(0\) | \(1\) | \(-1\) | \(q+q^{5}-q^{7}+q^{11}+q^{17}+q^{19}-2q^{23}+\cdots\) |
684.1.h.b | $2$ | $0.341$ | \(\Q(\sqrt{3}) \) | $D_{6}$ | \(\Q(\sqrt{-19}) \) | None | \(0\) | \(0\) | \(0\) | \(2\) | \(q-\beta q^{5}+q^{7}+\beta q^{11}+\beta q^{17}-q^{19}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(684, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(684, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(228, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(342, [\chi])\)\(^{\oplus 2}\)