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Properties

Label 480.2.bh
Level $480$
Weight $2$
Character orbit 480.bh
Rep. character $\chi_{480}(367,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $24$
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.bh (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 40 \)
Character field: \(\Q(i)\)
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 224 24 200
Cusp forms 160 24 136
Eisenstein series 64 0 64

Trace form

\( 24 q + O(q^{10}) \) \( 24 q + 8 q^{17} - 8 q^{25} + 48 q^{35} + 32 q^{43} + 16 q^{51} - 8 q^{65} - 48 q^{67} - 40 q^{73} - 24 q^{81} - 80 q^{83} - 64 q^{91} - 24 q^{97} + O(q^{100}) \)

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.bh.a 480.bh 40.k $24$ $3.833$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$

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

\( S_{2}^{\mathrm{old}}(480, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 2}\)