Defining parameters
Level: | \( N \) | \(=\) | \( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1440.k (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 8 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(576\) | ||
Trace bound: | \(17\) | ||
Distinguishing \(T_p\): | \(7\), \(11\), \(17\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(1440, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 320 | 20 | 300 |
Cusp forms | 256 | 20 | 236 |
Eisenstein series | 64 | 0 | 64 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(1440, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
1440.2.k.a | $2$ | $11.498$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(-4\) | \(q-iq^{5}-2q^{7}-4iq^{11}+6q^{17}+4iq^{19}+\cdots\) |
1440.2.k.b | $2$ | $11.498$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(8\) | \(q+iq^{5}+4q^{7}-2iq^{11}-6iq^{13}+\cdots\) |
1440.2.k.c | $2$ | $11.498$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(8\) | \(q+iq^{5}+4q^{7}-2iq^{11}+6iq^{13}+\cdots\) |
1440.2.k.d | $4$ | $11.498$ | \(\Q(i, \sqrt{7})\) | None | \(0\) | \(0\) | \(0\) | \(-8\) | \(q-\beta _{1}q^{5}-2q^{7}+2\beta _{1}q^{11}+\beta _{3}q^{19}+\cdots\) |
1440.2.k.e | $4$ | $11.498$ | \(\Q(\zeta_{12})\) | None | \(0\) | \(0\) | \(0\) | \(4\) | \(q+\zeta_{12}q^{5}+(1-\zeta_{12}^{3})q^{7}-2\zeta_{12}q^{11}+\cdots\) |
1440.2.k.f | $6$ | $11.498$ | 6.0.399424.1 | None | \(0\) | \(0\) | \(0\) | \(-4\) | \(q+\beta _{2}q^{5}+(-1+\beta _{3})q^{7}+(\beta _{2}-\beta _{4}+\cdots)q^{11}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(1440, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(1440, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 2}\)