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Properties

Label 480.3.l
Level $480$
Weight $3$
Character orbit 480.l
Rep. character $\chi_{480}(161,\cdot)$
Character field $\Q$
Dimension $32$
Newform subspaces $2$
Sturm bound $288$
Trace bound $9$

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Defining parameters

Level: \( N \) \(=\) \( 480 = 2^{5} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 480.l (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(288\)
Trace bound: \(9\)
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 32 176
Cusp forms 176 32 144
Eisenstein series 32 0 32

Trace form

\( 32 q - 16 q^{9} + O(q^{10}) \) \( 32 q - 16 q^{9} - 32 q^{13} - 16 q^{21} - 160 q^{25} + 128 q^{33} + 160 q^{37} + 80 q^{45} + 192 q^{49} - 352 q^{57} - 224 q^{61} - 176 q^{69} + 256 q^{73} + 384 q^{81} + 320 q^{93} - 704 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.l.a 480.l 3.b $16$ $13.079$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{10}q^{3}+\beta _{5}q^{5}+(-\beta _{9}-\beta _{10})q^{7}+\cdots\)
480.3.l.b 480.l 3.b $16$ $13.079$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{5}q^{3}-\beta _{4}q^{5}+(\beta _{1}+\beta _{5})q^{7}+(1+\cdots)q^{9}+\cdots\)

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

\( S_{3}^{\mathrm{old}}(480, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 2}\)