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Properties

Label 528.2.x
Level $528$
Weight $2$
Character orbit 528.x
Rep. character $\chi_{528}(197,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $184$
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.x (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 528 \)
Character field: \(\Q(i)\)
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 200 200 0
Cusp forms 184 184 0
Eisenstein series 16 16 0

Trace form

\( 184 q - 4 q^{3} - 8 q^{4} + O(q^{10}) \) \( 184 q - 4 q^{3} - 8 q^{4} - 4 q^{12} - 8 q^{15} + 24 q^{16} - 24 q^{22} - 4 q^{27} - 16 q^{31} - 4 q^{33} - 24 q^{34} + 12 q^{36} - 8 q^{37} - 48 q^{42} - 24 q^{45} + 16 q^{48} + 120 q^{49} - 40 q^{58} + 36 q^{60} - 56 q^{64} - 20 q^{66} - 72 q^{67} - 16 q^{69} - 40 q^{70} + 28 q^{75} + 56 q^{78} - 8 q^{81} - 32 q^{82} - 96 q^{88} - 16 q^{91} - 16 q^{93} - 16 q^{97} - 52 q^{99} + O(q^{100}) \)

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.x.a 528.x 528.x $184$ $4.216$ None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$