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Properties

Label 480.2.bx
Level $480$
Weight $2$
Character orbit 480.bx
Rep. character $\chi_{480}(11,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $256$
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.bx (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 96 \)
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 400 256 144
Cusp forms 368 256 112
Eisenstein series 32 0 32

Trace form

\( 256 q + O(q^{10}) \) \( 256 q + 8 q^{10} + 64 q^{16} - 40 q^{24} + 48 q^{27} - 24 q^{36} + 48 q^{39} - 120 q^{42} - 64 q^{46} - 112 q^{52} - 88 q^{54} - 144 q^{58} + 32 q^{61} - 48 q^{64} + 32 q^{66} - 128 q^{67} - 56 q^{76} + 24 q^{78} - 32 q^{79} + 56 q^{84} + 80 q^{88} + 72 q^{90} - 96 q^{91} + 56 q^{94} + 168 q^{96} - 64 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
480.2.bx.a 480.bx 96.o $256$ $3.833$ None 480.2.bx.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{8}]$

Decomposition of \(S_{2}^{\mathrm{old}}(480, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(480, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 2}\)