Defining parameters
Level: | \( N \) | \(=\) | \( 75 = 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 75.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 5 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(80\) | ||
Trace bound: | \(4\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{8}(75, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 76 | 20 | 56 |
Cusp forms | 64 | 20 | 44 |
Eisenstein series | 12 | 0 | 12 |
Trace form
Decomposition of \(S_{8}^{\mathrm{new}}(75, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
75.8.b.a | $2$ | $23.429$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+22iq^{2}+3^{3}iq^{3}-356q^{4}-594q^{6}+\cdots\) |
75.8.b.b | $2$ | $23.429$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+13iq^{2}-3^{3}iq^{3}-41q^{4}+351q^{6}+\cdots\) |
75.8.b.c | $2$ | $23.429$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+6iq^{2}+3^{3}iq^{3}+92q^{4}-162q^{6}+\cdots\) |
75.8.b.d | $4$ | $23.429$ | \(\Q(i, \sqrt{601})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(\beta _{1}-3\beta _{2})q^{2}+3^{3}\beta _{2}q^{3}+(-38+\cdots)q^{4}+\cdots\) |
75.8.b.e | $4$ | $23.429$ | \(\Q(i, \sqrt{31})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(-4\beta _{1}-\beta _{3})q^{2}-3^{3}\beta _{1}q^{3}+(-12+\cdots)q^{4}+\cdots\) |
75.8.b.f | $6$ | $23.429$ | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(-\beta _{2}+2\beta _{4})q^{2}-3^{3}\beta _{4}q^{3}+(-51+\cdots)q^{4}+\cdots\) |
Decomposition of \(S_{8}^{\mathrm{old}}(75, [\chi])\) into lower level spaces
\( S_{8}^{\mathrm{old}}(75, [\chi]) \cong \) \(S_{8}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 2}\)