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Properties

Label 440.2.bd
Level $440$
Weight $2$
Character orbit 440.bd
Rep. character $\chi_{440}(69,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $272$
Newform subspaces $1$
Sturm bound $144$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 440 = 2^{3} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 440.bd (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 440 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 1 \)
Sturm bound: \(144\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(440, [\chi])\).

Total New Old
Modular forms 304 304 0
Cusp forms 272 272 0
Eisenstein series 32 32 0

Trace form

\( 272 q - 6 q^{4} + 2 q^{6} - 72 q^{9} + O(q^{10}) \) \( 272 q - 6 q^{4} + 2 q^{6} - 72 q^{9} - 12 q^{10} - 18 q^{14} + 6 q^{15} - 34 q^{16} + 4 q^{20} - 10 q^{24} - 6 q^{25} + 44 q^{26} - 38 q^{30} - 12 q^{31} - 40 q^{34} + 16 q^{36} - 20 q^{39} - 12 q^{40} - 12 q^{41} - 42 q^{44} + 42 q^{46} + 32 q^{49} - 18 q^{50} - 64 q^{54} - 34 q^{55} - 32 q^{56} - 46 q^{60} - 18 q^{64} + 4 q^{65} - 34 q^{66} + 22 q^{70} + 4 q^{71} - 20 q^{74} - 36 q^{76} + 28 q^{79} + 74 q^{80} - 24 q^{81} + 68 q^{84} - 18 q^{86} - 32 q^{89} + 32 q^{90} - 96 q^{94} - 86 q^{95} + 110 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(440, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
440.2.bd.a 440.bd 440.ad $272$ $3.513$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$