Defining parameters
| Level: | \( N \) | \(=\) | \( 440 = 2^{3} \cdot 5 \cdot 11 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 440.b (of order \(2\) and degree \(1\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 5 \) |
| Character field: | \(\Q\) | ||
| Newform subspaces: | \( 4 \) | ||
| Sturm bound: | \(144\) | ||
| Trace bound: | \(5\) | ||
| Distinguishing \(T_p\): | \(3\), \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(440, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 80 | 14 | 66 |
| Cusp forms | 64 | 14 | 50 |
| Eisenstein series | 16 | 0 | 16 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(440, [\chi])\) into newform subspaces
| Label | Dim. | \(A\) | Field | CM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|
| $a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
| 440.2.b.a | $2$ | $3.513$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(-2\) | \(0\) | \(q+iq^{3}+(-1+i)q^{5}+iq^{7}-q^{9}+\cdots\) |
| 440.2.b.b | $2$ | $3.513$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(2\) | \(0\) | \(q+iq^{3}+(1-i)q^{5}-2iq^{7}-q^{9}+q^{11}+\cdots\) |
| 440.2.b.c | $2$ | $3.513$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(4\) | \(0\) | \(q+iq^{3}+(2+i)q^{5}+iq^{7}+2q^{9}-q^{11}+\cdots\) |
| 440.2.b.d | $8$ | $3.513$ | 8.0.\(\cdots\).2 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{1}q^{3}+\beta _{3}q^{5}+(\beta _{1}-\beta _{3}-\beta _{4})q^{7}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(440, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(440, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(110, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(220, [\chi])\)\(^{\oplus 2}\)