Defining parameters
Level: | \( N \) | \(=\) | \( 3636 = 2^{2} \cdot 3^{2} \cdot 101 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 3636.h (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 404 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(612\) | ||
Trace bound: | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(3636, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 42 | 18 | 24 |
Cusp forms | 34 | 16 | 18 |
Eisenstein series | 8 | 2 | 6 |
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 \(S_{1}^{\mathrm{new}}(3636, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
3636.1.h.a | $2$ | $1.815$ | \(\Q(\sqrt{-1}) \) | $D_{2}$ | \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-303}) \) | \(\Q(\sqrt{303}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q-iq^{2}-q^{4}+iq^{8}-q^{13}+q^{16}+\cdots\) |
3636.1.h.b | $3$ | $1.815$ | \(\Q(\zeta_{14})^+\) | $D_{7}$ | \(\Q(\sqrt{-101}) \) | None | \(-3\) | \(0\) | \(1\) | \(-1\) | \(q-q^{2}+q^{4}+\beta _{1}q^{5}+(-1+\beta _{1}-\beta _{2})q^{7}+\cdots\) |
3636.1.h.c | $3$ | $1.815$ | \(\Q(\zeta_{14})^+\) | $D_{7}$ | \(\Q(\sqrt{-101}) \) | None | \(3\) | \(0\) | \(1\) | \(1\) | \(q+q^{2}+q^{4}+\beta _{1}q^{5}+(1-\beta _{1}+\beta _{2})q^{7}+\cdots\) |
3636.1.h.d | $8$ | $1.815$ | \(\Q(\zeta_{20})\) | $D_{10}$ | \(\Q(\sqrt{-303}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\zeta_{20}q^{2}+\zeta_{20}^{2}q^{4}-\zeta_{20}^{3}q^{8}+(-\zeta_{20}^{3}+\cdots)q^{11}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(3636, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(3636, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(404, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(1212, [\chi])\)\(^{\oplus 2}\)