Defining parameters
Level: | \( N \) | \(=\) | \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 2736.o (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 19 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(480\) | ||
Trace bound: | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(2736, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 54 | 5 | 49 |
Cusp forms | 30 | 4 | 26 |
Eisenstein series | 24 | 1 | 23 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 4 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(2736, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
2736.1.o.a | $1$ | $1.365$ | \(\Q\) | $D_{2}$ | \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-19}) \) | \(\Q(\sqrt{57}) \) | \(0\) | \(0\) | \(0\) | \(2\) | \(q+2q^{7}+q^{19}-q^{25}-2q^{43}+3q^{49}+\cdots\) |
2736.1.o.b | $1$ | $1.365$ | \(\Q\) | $D_{3}$ | \(\Q(\sqrt{-19}) \) | None | \(0\) | \(0\) | \(1\) | \(1\) | \(q+q^{5}+q^{7}-q^{11}+q^{17}-q^{19}+2q^{23}+\cdots\) |
2736.1.o.c | $2$ | $1.365$ | \(\Q(\sqrt{3}) \) | $D_{6}$ | \(\Q(\sqrt{-19}) \) | None | \(0\) | \(0\) | \(0\) | \(-2\) | \(q-\beta q^{5}-q^{7}-\beta q^{11}+\beta q^{17}+q^{19}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(2736, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(2736, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(304, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(684, [\chi])\)\(^{\oplus 3}\)