Defining parameters
Level: | \( N \) | \(=\) | \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 2352.d (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 3 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(448\) | ||
Trace bound: | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(2352, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 56 | 7 | 49 |
Cusp forms | 8 | 2 | 6 |
Eisenstein series | 48 | 5 | 43 |
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 \(S_{1}^{\mathrm{new}}(2352, [\chi])\) into newform subspaces
Label | Dim. | \(A\) | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
\(a_2\) | \(a_3\) | \(a_5\) | \(a_7\) | ||||||||
2352.1.d.a | \(1\) | \(1.174\) | \(\Q\) | \(D_{3}\) | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(-1\) | \(0\) | \(0\) | \(q-q^{3}+q^{9}-q^{13}+q^{19}+q^{25}-q^{27}+\cdots\) |
2352.1.d.b | \(1\) | \(1.174\) | \(\Q\) | \(D_{3}\) | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(1\) | \(0\) | \(0\) | \(q+q^{3}+q^{9}+q^{13}-q^{19}+q^{25}+q^{27}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(2352, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(2352, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(588, [\chi])\)\(^{\oplus 3}\)