Defining parameters
Level: | \( N \) | \(=\) | \( 480 = 2^{5} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 480.f (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 5 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(192\) | ||
Trace bound: | \(15\) | ||
Distinguishing \(T_p\): | \(7\), \(11\), \(19\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(480, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 112 | 12 | 100 |
Cusp forms | 80 | 12 | 68 |
Eisenstein series | 32 | 0 | 32 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(480, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
480.2.f.a | $2$ | $3.833$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(-4\) | \(0\) | \(q+iq^{3}+(-2+i)q^{5}-2iq^{7}-q^{9}+\cdots\) |
480.2.f.b | $2$ | $3.833$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(-4\) | \(0\) | \(q+iq^{3}+(-2-i)q^{5}-2iq^{7}-q^{9}+\cdots\) |
480.2.f.c | $2$ | $3.833$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(2\) | \(0\) | \(q+iq^{3}+(1+2i)q^{5}+4iq^{7}-q^{9}+\cdots\) |
480.2.f.d | $2$ | $3.833$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(2\) | \(0\) | \(q+iq^{3}+(1-2i)q^{5}+4iq^{7}-q^{9}+\cdots\) |
480.2.f.e | $4$ | $3.833$ | \(\Q(i, \sqrt{5})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{1}q^{3}-\beta _{2}q^{5}-2\beta _{1}q^{7}-q^{9}-2\beta _{3}q^{11}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(480, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(480, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 2}\)