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Properties

Label 440.2.bu
Level $440$
Weight $2$
Character orbit 440.bu
Rep. character $\chi_{440}(13,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $544$
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.bu (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 440 \)
Character field: \(\Q(\zeta_{20})\)
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 608 608 0
Cusp forms 544 544 0
Eisenstein series 64 64 0

Trace form

\( 544 q - 10 q^{2} - 20 q^{6} - 20 q^{7} - 10 q^{8} + O(q^{10}) \) \( 544 q - 10 q^{2} - 20 q^{6} - 20 q^{7} - 10 q^{8} + 12 q^{12} - 12 q^{15} - 20 q^{16} - 20 q^{17} - 10 q^{18} - 20 q^{20} - 6 q^{22} - 32 q^{23} - 12 q^{25} + 12 q^{26} - 10 q^{28} + 30 q^{30} - 24 q^{31} - 28 q^{33} - 92 q^{36} - 42 q^{38} - 10 q^{40} - 40 q^{41} - 30 q^{42} - 140 q^{46} - 12 q^{47} - 18 q^{48} - 10 q^{50} + 30 q^{52} - 36 q^{55} + 40 q^{56} - 20 q^{57} - 10 q^{58} - 82 q^{60} - 160 q^{62} - 80 q^{63} + 28 q^{66} - 10 q^{68} + 14 q^{70} - 56 q^{71} + 140 q^{72} - 20 q^{73} + 100 q^{78} + 14 q^{80} + 48 q^{81} - 58 q^{82} - 52 q^{86} + 158 q^{88} - 100 q^{90} - 8 q^{92} - 20 q^{95} + 120 q^{96} + 20 q^{97} + O(q^{100}) \)

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.bu.a 440.bu 440.au $544$ $3.513$ None \(-10\) \(0\) \(0\) \(-20\) $\mathrm{SU}(2)[C_{20}]$