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Properties

Label 880.2.bh
Level $880$
Weight $2$
Character orbit 880.bh
Rep. character $\chi_{880}(309,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $240$
Newform subspaces $1$
Sturm bound $288$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 880.bh (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 80 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(288\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(880, [\chi])\).

Total New Old
Modular forms 296 240 56
Cusp forms 280 240 40
Eisenstein series 16 0 16

Trace form

\( 240 q + O(q^{10}) \) \( 240 q + 12 q^{10} - 8 q^{14} - 8 q^{16} + 16 q^{19} + 28 q^{20} - 8 q^{24} + 68 q^{30} - 48 q^{31} - 56 q^{34} + 24 q^{35} - 112 q^{36} - 72 q^{40} + 8 q^{44} - 32 q^{46} + 240 q^{49} - 64 q^{50} + 16 q^{51} - 32 q^{54} - 16 q^{59} - 92 q^{60} + 32 q^{61} + 24 q^{64} + 16 q^{65} - 32 q^{69} - 48 q^{70} - 56 q^{75} + 184 q^{76} - 32 q^{79} + 8 q^{80} - 240 q^{81} + 152 q^{84} + 104 q^{86} + 52 q^{90} - 16 q^{91} - 56 q^{94} - 48 q^{95} - 152 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(880, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
880.2.bh.a 880.bh 80.q $240$ $7.027$ None 880.2.bh.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(880, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(880, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 2}\)