Defining parameters
Level: | \( N \) | \(=\) | \( 480 = 2^{5} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 480.d (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 40 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(192\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(13\) |
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.d.a | $6$ | $3.833$ | 6.0.839056.1 | None | \(0\) | \(-6\) | \(0\) | \(0\) | \(q-q^{3}-\beta _{2}q^{5}-\beta _{1}q^{7}+q^{9}+(\beta _{1}+\beta _{5})q^{11}+\cdots\) |
480.2.d.b | $6$ | $3.833$ | 6.0.839056.1 | None | \(0\) | \(6\) | \(0\) | \(0\) | \(q+q^{3}+\beta _{4}q^{5}+\beta _{1}q^{7}+q^{9}+(\beta _{1}+\beta _{5})q^{11}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(480, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(480, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 2}\)