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Properties

Label 480.2.br
Level $480$
Weight $2$
Character orbit 480.br
Rep. character $\chi_{480}(173,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $368$
Newform subspaces $1$
Sturm bound $192$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 480 = 2^{5} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 480.br (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 480 \)
Character field: \(\Q(\zeta_{8})\)
Newform subspaces: \( 1 \)
Sturm bound: \(192\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(480, [\chi])\).

Total New Old
Modular forms 400 400 0
Cusp forms 368 368 0
Eisenstein series 32 32 0

Trace form

\( 368 q - 4 q^{3} - 8 q^{6} + O(q^{10}) \) \( 368 q - 4 q^{3} - 8 q^{6} - 8 q^{10} - 4 q^{12} - 8 q^{13} - 16 q^{16} + 4 q^{18} + 16 q^{19} - 8 q^{21} + 8 q^{22} + 32 q^{24} - 8 q^{25} - 4 q^{27} + 24 q^{28} - 16 q^{30} - 32 q^{31} - 8 q^{33} - 8 q^{34} - 8 q^{36} - 8 q^{37} - 8 q^{40} + 20 q^{42} + 24 q^{43} - 4 q^{45} - 16 q^{46} - 56 q^{48} - 272 q^{49} - 8 q^{51} - 24 q^{52} - 56 q^{54} + 24 q^{55} - 40 q^{58} - 20 q^{60} + 16 q^{61} - 8 q^{63} - 40 q^{66} - 8 q^{67} - 24 q^{69} + 48 q^{70} - 96 q^{72} - 16 q^{75} - 72 q^{76} - 88 q^{78} + 48 q^{82} + 56 q^{84} - 8 q^{85} - 120 q^{87} + 104 q^{88} - 12 q^{90} - 16 q^{91} - 16 q^{93} - 40 q^{96} - 16 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(480, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
480.2.br.a 480.br 480.ar $368$ $3.833$ None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{8}]$