Defining parameters
Level: | \( N \) | \(=\) | \( 880 = 2^{4} \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 880.f (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 44 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(288\) | ||
Trace bound: | \(11\) | ||
Distinguishing \(T_p\): | \(3\), \(7\), \(19\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(880, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 156 | 24 | 132 |
Cusp forms | 132 | 24 | 108 |
Eisenstein series | 24 | 0 | 24 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(880, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
880.2.f.a | $2$ | $7.027$ | \(\Q(\sqrt{-2}) \) | None | \(0\) | \(0\) | \(-2\) | \(0\) | \(q+\beta q^{3}-q^{5}+q^{9}+(-3-\beta )q^{11}+\cdots\) |
880.2.f.b | $2$ | $7.027$ | \(\Q(\sqrt{-2}) \) | None | \(0\) | \(0\) | \(-2\) | \(0\) | \(q+\beta q^{3}-q^{5}+q^{9}+(3-\beta )q^{11}-3\beta q^{13}+\cdots\) |
880.2.f.c | $4$ | $7.027$ | \(\Q(\sqrt{-2}, \sqrt{3})\) | None | \(0\) | \(0\) | \(4\) | \(0\) | \(q-\beta _{1}q^{3}+q^{5}-2\beta _{2}q^{7}+q^{9}+(-2\beta _{1}+\cdots)q^{11}+\cdots\) |
880.2.f.d | $8$ | $7.027$ | 8.0.170772624.1 | None | \(0\) | \(0\) | \(-8\) | \(0\) | \(q+\beta _{3}q^{3}-q^{5}+\beta _{1}q^{7}+(-1-\beta _{4}+\cdots)q^{9}+\cdots\) |
880.2.f.e | $8$ | $7.027$ | 8.0.170772624.1 | None | \(0\) | \(0\) | \(8\) | \(0\) | \(q+\beta _{3}q^{3}+q^{5}+\beta _{2}q^{7}+(-1-\beta _{4}+\cdots)q^{9}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(880, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(880, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(44, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(176, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(220, [\chi])\)\(^{\oplus 3}\)