Defining parameters
Level: | \( N \) | \(=\) | \( 2700 = 2^{2} \cdot 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 2700.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 15 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(540\) | ||
Trace bound: | \(19\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(2700, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 82 | 4 | 78 |
Cusp forms | 28 | 4 | 24 |
Eisenstein series | 54 | 0 | 54 |
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 \(S_{1}^{\mathrm{new}}(2700, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
2700.1.b.a | $2$ | $1.347$ | \(\Q(\sqrt{-1}) \) | $D_{3}$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-iq^{7}-iq^{13}-q^{19}-q^{31}+iq^{37}+\cdots\) |
2700.1.b.b | $2$ | $1.347$ | \(\Q(\sqrt{-1}) \) | $D_{3}$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-iq^{7}+iq^{13}+q^{19}+q^{31}-iq^{37}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(2700, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(2700, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(675, [\chi])\)\(^{\oplus 3}\)