Defining parameters
Level: | \( N \) | \(=\) | \( 2156 = 2^{2} \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 2156.h (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 11 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(336\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(2156, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 43 | 7 | 36 |
Cusp forms | 19 | 7 | 12 |
Eisenstein series | 24 | 0 | 24 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 7 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(2156, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
2156.1.h.a | $1$ | $1.076$ | \(\Q\) | $D_{3}$ | \(\Q(\sqrt{-11}) \) | None | \(0\) | \(1\) | \(1\) | \(0\) | \(q+q^{3}+q^{5}+q^{11}+q^{15}-q^{23}-q^{27}+\cdots\) |
2156.1.h.b | $2$ | $1.076$ | \(\Q(\sqrt{3}) \) | $D_{6}$ | \(\Q(\sqrt{-11}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta q^{3}+\beta q^{5}+2q^{9}+q^{11}-3q^{15}+\cdots\) |
2156.1.h.c | $4$ | $1.076$ | \(\Q(\zeta_{24})^+\) | $D_{12}$ | \(\Q(\sqrt{-11}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{1}q^{3}+\beta _{3}q^{5}+(1+\beta _{2})q^{9}-q^{11}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(2156, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(2156, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(44, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(539, [\chi])\)\(^{\oplus 3}\)