Defining parameters
Level: | \( N \) | \(=\) | \( 1975 = 5^{2} \cdot 79 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 1975.d (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 79 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(200\) | ||
Trace bound: | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(1975, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 21 | 12 | 9 |
Cusp forms | 15 | 9 | 6 |
Eisenstein series | 6 | 3 | 3 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 9 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(1975, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
1975.1.d.a | $1$ | $0.986$ | \(\Q\) | $D_{2}$ | \(\Q(\sqrt{-79}) \), \(\Q(\sqrt{-395}) \) | \(\Q(\sqrt{5}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q-q^{4}+q^{9}-2q^{11}+q^{16}+2q^{19}+\cdots\) |
1975.1.d.b | $2$ | $0.986$ | \(\Q(\sqrt{-2}) \) | $D_{4}$ | \(\Q(\sqrt{-395}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta q^{3}-q^{4}-\beta q^{7}-q^{9}+\beta q^{12}+\cdots\) |
1975.1.d.c | $2$ | $0.986$ | \(\Q(\sqrt{5}) \) | $D_{5}$ | \(\Q(\sqrt{-79}) \) | None | \(1\) | \(0\) | \(0\) | \(0\) | \(q+(1-\beta )q^{2}+(1-\beta )q^{4}+q^{8}+q^{9}+\cdots\) |
1975.1.d.d | $4$ | $0.986$ | \(\Q(\zeta_{20})^+\) | $D_{10}$ | \(\Q(\sqrt{-79}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-\beta _{1}-\beta _{3})q^{8}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(1975, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(1975, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(79, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(395, [\chi])\)\(^{\oplus 2}\)