Defining parameters
Level: | \( N \) | \(=\) | \( 2075 = 5^{2} \cdot 83 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 2075.d (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 415 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(210\) | ||
Trace bound: | \(29\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(2075, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 22 | 10 | 12 |
Cusp forms | 16 | 8 | 8 |
Eisenstein series | 6 | 2 | 4 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 8 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(2075, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
2075.1.d.a | $2$ | $1.036$ | \(\Q(\sqrt{-1}) \) | $D_{3}$ | \(\Q(\sqrt{-83}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-iq^{3}-q^{4}-iq^{7}-3q^{9}-q^{11}+\cdots\) |
2075.1.d.b | $2$ | $1.036$ | \(\Q(\sqrt{-1}) \) | $D_{3}$ | \(\Q(\sqrt{-83}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-iq^{3}-q^{4}+iq^{7}-q^{11}+iq^{12}+\cdots\) |
2075.1.d.c | $2$ | $1.036$ | \(\Q(\sqrt{-1}) \) | $D_{3}$ | \(\Q(\sqrt{-83}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+iq^{3}-q^{4}-iq^{7}-q^{11}-iq^{12}+\cdots\) |
2075.1.d.d | $2$ | $1.036$ | \(\Q(\sqrt{-1}) \) | $D_{3}$ | \(\Q(\sqrt{-83}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-iq^{3}-q^{4}-iq^{7}+q^{11}+iq^{12}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(2075, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(2075, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(415, [\chi])\)\(^{\oplus 2}\)