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Properties

Label 440.2.bs
Level $440$
Weight $2$
Character orbit 440.bs
Rep. character $\chi_{440}(3,\cdot)$
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.bs (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

\( 544 q - 6 q^{2} - 12 q^{3} - 12 q^{6} - 6 q^{8} + O(q^{10}) \) \( 544 q - 6 q^{2} - 12 q^{3} - 12 q^{6} - 6 q^{8} - 32 q^{11} - 44 q^{12} - 20 q^{16} - 12 q^{17} - 2 q^{18} + 40 q^{20} - 22 q^{22} - 12 q^{25} - 52 q^{26} - 36 q^{27} + 10 q^{28} - 50 q^{30} + 4 q^{32} - 4 q^{33} - 12 q^{35} - 92 q^{36} + 14 q^{38} - 10 q^{40} - 24 q^{41} - 30 q^{42} - 96 q^{43} - 84 q^{46} + 6 q^{48} + 14 q^{50} - 24 q^{51} - 14 q^{52} - 168 q^{56} - 36 q^{57} + 6 q^{58} - 50 q^{60} + 96 q^{62} - 32 q^{65} - 28 q^{66} - 32 q^{67} + 50 q^{68} + 14 q^{70} - 140 q^{72} - 12 q^{73} - 12 q^{75} - 16 q^{76} + 76 q^{78} - 66 q^{80} + 48 q^{81} + 46 q^{82} - 132 q^{83} - 68 q^{86} + 158 q^{88} + 160 q^{90} + 8 q^{91} - 156 q^{92} - 64 q^{96} - 44 q^{97} + 124 q^{98} + O(q^{100}) \)

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.bs.a 440.bs 440.as $544$ $3.513$ None \(-6\) \(-12\) \(0\) \(0\) $\mathrm{SU}(2)[C_{20}]$