Defining parameters
Level: | \( N \) | \(=\) | \( 371 = 7 \cdot 53 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 371.n (of order \(26\) and degree \(12\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 371 \) |
Character field: | \(\Q(\zeta_{26})\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(36\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(371, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 36 | 36 | 0 |
Cusp forms | 12 | 12 | 0 |
Eisenstein series | 24 | 24 | 0 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 12 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(371, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
371.1.n.a | $12$ | $0.185$ | \(\Q(\zeta_{26})\) | $D_{13}$ | \(\Q(\sqrt{-7}) \) | None | \(-2\) | \(0\) | \(0\) | \(-1\) | \(q+(-\zeta_{26}+\zeta_{26}^{6})q^{2}+(\zeta_{26}^{2}-\zeta_{26}^{7}+\cdots)q^{4}+\cdots\) |