Properties

Label 480.3.c
Level $480$
Weight $3$
Character orbit 480.c
Rep. character $\chi_{480}(449,\cdot)$
Character field $\Q$
Dimension $48$
Newform subspaces $3$
Sturm bound $288$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 480 = 2^{5} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 480.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(288\)
Trace bound: \(1\)
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 48 160
Cusp forms 176 48 128
Eisenstein series 32 0 32

Trace form

\( 48 q + O(q^{10}) \) \( 48 q + 16 q^{21} + 16 q^{25} + 48 q^{45} - 176 q^{49} - 320 q^{61} + 368 q^{69} + 272 q^{81} - 192 q^{85} + O(q^{100}) \)

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.c.a 480.c 15.d $8$ $13.079$ 8.0.40960000.1 \(\Q(\sqrt{-5}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{5}q^{3}-5\beta _{1}q^{5}+(2\beta _{2}+\beta _{3}+\beta _{4}+\cdots)q^{7}+\cdots\)
480.3.c.b 480.c 15.d $16$ $13.079$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{4}q^{3}-\beta _{7}q^{5}+(\beta _{3}-\beta _{4}+\beta _{8})q^{7}+\cdots\)
480.3.c.c 480.c 15.d $24$ $13.079$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$

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

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