Defining parameters
Level: | \( N \) | \(=\) | \( 416 = 2^{5} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 416.h (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 104 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(56\) | ||
Trace bound: | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(416, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 16 | 4 | 12 |
Cusp forms | 8 | 2 | 6 |
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 | 2 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(416, [\chi])\) into newform subspaces
Label | Dim. | \(A\) | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
\(a_2\) | \(a_3\) | \(a_5\) | \(a_7\) | ||||||||
416.1.h.a | \(1\) | \(0.208\) | \(\Q\) | \(D_{3}\) | \(\Q(\sqrt{-26}) \) | None | \(0\) | \(1\) | \(-1\) | \(1\) | \(q+q^{3}-q^{5}+q^{7}+q^{13}-q^{15}-q^{17}+\cdots\) |
416.1.h.b | \(1\) | \(0.208\) | \(\Q\) | \(D_{3}\) | \(\Q(\sqrt{-26}) \) | None | \(0\) | \(1\) | \(1\) | \(-1\) | \(q+q^{3}+q^{5}-q^{7}-q^{13}+q^{15}-q^{17}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(416, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(416, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 3}\)