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Properties

Label 528.2.bo
Level $528$
Weight $2$
Character orbit 528.bo
Rep. character $\chi_{528}(29,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $736$
Newform subspaces $1$
Sturm bound $192$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 528 = 2^{4} \cdot 3 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 528.bo (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 528 \)
Character field: \(\Q(\zeta_{20})\)
Newform subspaces: \( 1 \)
Sturm bound: \(192\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(528, [\chi])\).

Total New Old
Modular forms 800 800 0
Cusp forms 736 736 0
Eisenstein series 64 64 0

Trace form

\( 736 q - 6 q^{3} - 12 q^{4} - 10 q^{6} + O(q^{10}) \) \( 736 q - 6 q^{3} - 12 q^{4} - 10 q^{6} - 16 q^{12} - 20 q^{13} - 12 q^{15} - 44 q^{16} - 10 q^{18} - 20 q^{19} - 56 q^{22} - 10 q^{24} - 6 q^{27} - 20 q^{28} - 10 q^{30} - 24 q^{31} - 16 q^{33} - 16 q^{34} - 22 q^{36} - 12 q^{37} - 20 q^{40} + 38 q^{42} + 4 q^{45} - 60 q^{46} - 26 q^{48} - 160 q^{49} - 10 q^{51} + 20 q^{52} + 20 q^{58} + 94 q^{60} - 20 q^{61} - 20 q^{63} - 84 q^{64} + 10 q^{66} + 32 q^{67} - 24 q^{69} - 120 q^{70} - 160 q^{72} - 38 q^{75} - 76 q^{78} - 40 q^{79} - 12 q^{81} - 88 q^{82} + 60 q^{84} - 20 q^{85} - 204 q^{88} - 100 q^{90} + 116 q^{91} + 6 q^{93} - 140 q^{94} - 10 q^{96} - 24 q^{97} + 42 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(528, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
528.2.bo.a 528.bo 528.ao $736$ $4.216$ None \(0\) \(-6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{20}]$