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Properties

Label 528.2.bs
Level $528$
Weight $2$
Character orbit 528.bs
Rep. character $\chi_{528}(37,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $384$
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.bs (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 176 \)
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 800 384 416
Cusp forms 736 384 352
Eisenstein series 64 0 64

Trace form

\( 384 q + 8 q^{4} + O(q^{10}) \) \( 384 q + 8 q^{4} + 8 q^{11} - 16 q^{12} - 28 q^{14} - 8 q^{16} + 12 q^{18} - 16 q^{20} - 60 q^{22} + 60 q^{26} + 24 q^{28} + 32 q^{29} - 24 q^{30} - 40 q^{34} - 48 q^{37} + 56 q^{38} - 40 q^{40} + 16 q^{43} + 24 q^{44} - 32 q^{46} + 96 q^{49} + 96 q^{50} - 80 q^{52} + 48 q^{53} - 56 q^{56} + 8 q^{58} - 32 q^{59} - 24 q^{60} - 16 q^{63} + 128 q^{64} - 24 q^{66} - 16 q^{67} - 56 q^{68} - 8 q^{70} - 12 q^{72} - 204 q^{74} + 48 q^{75} - 128 q^{76} - 16 q^{77} - 120 q^{78} + 80 q^{79} - 172 q^{80} + 96 q^{81} - 100 q^{82} - 120 q^{83} - 72 q^{84} - 80 q^{86} - 72 q^{88} - 24 q^{90} + 104 q^{91} - 104 q^{92} - 12 q^{94} - 60 q^{96} - 352 q^{98} - 32 q^{99} + O(q^{100}) \)

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.bs.a 528.bs 176.w $384$ $4.216$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{20}]$

Decomposition of \(S_{2}^{\mathrm{old}}(528, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(528, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(176, [\chi])\)\(^{\oplus 2}\)