Defining parameters
Level: | \( N \) | \(=\) | \( 2800 = 2^{4} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 2800.f (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 7 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(480\) | ||
Trace bound: | \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(2800, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 56 | 7 | 49 |
Cusp forms | 20 | 4 | 16 |
Eisenstein series | 36 | 3 | 33 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 4 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(2800, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
2800.1.f.a | $1$ | $1.397$ | \(\Q\) | $D_{3}$ | \(\Q(\sqrt{-7}) \) | None | \(0\) | \(0\) | \(0\) | \(-1\) | \(q-q^{7}+q^{9}+q^{11}+q^{23}-q^{29}-q^{37}+\cdots\) |
2800.1.f.b | $1$ | $1.397$ | \(\Q\) | $D_{3}$ | \(\Q(\sqrt{-7}) \) | None | \(0\) | \(0\) | \(0\) | \(1\) | \(q+q^{7}+q^{9}+q^{11}-q^{23}-q^{29}+q^{37}+\cdots\) |
2800.1.f.c | $2$ | $1.397$ | \(\Q(\sqrt{-1}) \) | $D_{3}$ | \(\Q(\sqrt{-35}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+iq^{3}+iq^{7}+q^{11}-iq^{13}+iq^{17}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(2800, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(2800, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(700, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 5}\)