Properties

Label 528.2.br
Level $528$
Weight $2$
Character orbit 528.br
Rep. character $\chi_{528}(59,\cdot)$
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.br (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

\( 736 q - 6 q^{3} - 12 q^{4} - 6 q^{6} - 24 q^{7} + O(q^{10}) \) \( 736 q - 6 q^{3} - 12 q^{4} - 6 q^{6} - 24 q^{7} - 32 q^{10} - 16 q^{12} - 12 q^{13} - 44 q^{16} + 2 q^{18} - 12 q^{19} - 4 q^{21} + 24 q^{22} - 38 q^{24} - 6 q^{27} - 4 q^{28} + 2 q^{30} - 16 q^{33} - 48 q^{34} - 22 q^{36} - 12 q^{37} - 12 q^{39} - 12 q^{40} + 38 q^{42} - 64 q^{43} + 4 q^{45} + 44 q^{46} + 14 q^{48} - 160 q^{49} - 18 q^{51} - 28 q^{52} + 84 q^{54} - 64 q^{55} - 44 q^{58} - 106 q^{60} - 12 q^{61} + 60 q^{64} - 58 q^{66} - 96 q^{67} + 12 q^{69} - 120 q^{70} + 116 q^{72} + 2 q^{75} - 160 q^{76} - 76 q^{78} - 12 q^{81} - 56 q^{82} - 36 q^{84} - 52 q^{85} - 32 q^{87} - 236 q^{88} - 12 q^{90} - 28 q^{91} - 18 q^{93} - 92 q^{94} - 38 q^{96} - 24 q^{97} + 42 q^{99} + O(q^{100}) \)

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.br.a 528.br 528.ar $736$ $4.216$ None \(0\) \(-6\) \(0\) \(-24\) $\mathrm{SU}(2)[C_{20}]$