Properties

Label 480.3.j
Level $480$
Weight $3$
Character orbit 480.j
Rep. character $\chi_{480}(319,\cdot)$
Character field $\Q$
Dimension $24$
Newform subspaces $2$
Sturm bound $288$
Trace bound $15$

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Defining parameters

Level: \( N \) \(=\) \( 480 = 2^{5} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 480.j (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 20 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(288\)
Trace bound: \(15\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(480, [\chi])\).

Total New Old
Modular forms 208 24 184
Cusp forms 176 24 152
Eisenstein series 32 0 32

Trace form

\( 24 q + 8 q^{5} + 72 q^{9} + O(q^{10}) \) \( 24 q + 8 q^{5} + 72 q^{9} + 56 q^{25} - 80 q^{29} + 272 q^{41} + 24 q^{45} + 424 q^{49} + 80 q^{61} + 192 q^{65} + 216 q^{81} - 128 q^{85} - 16 q^{89} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(480, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
480.3.j.a 480.j 20.d $12$ $13.079$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(-\beta _{1}+\beta _{6})q^{5}+(\beta _{5}-\beta _{8}+\cdots)q^{7}+\cdots\)
480.3.j.b 480.j 20.d $12$ $13.079$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}+(-\beta _{1}+\beta _{6})q^{5}+(-\beta _{5}+\beta _{8}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(480, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(480, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 2}\)