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Properties

Label 3528.2.gb
Level $3528$
Weight $2$
Character orbit 3528.gb
Rep. character $\chi_{3528}(205,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $8016$
Sturm bound $1344$

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Defining parameters

Level: \( N \) \(=\) \( 3528 = 2^{3} \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3528.gb (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3528 \)
Character field: \(\Q(\zeta_{42})\)
Sturm bound: \(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3528, [\chi])\).

Total New Old
Modular forms 8112 8112 0
Cusp forms 8016 8016 0
Eisenstein series 96 96 0

Trace form

\( 8016 q - 8 q^{2} - 8 q^{4} - 12 q^{6} - 12 q^{7} - 20 q^{8} - 26 q^{9} + O(q^{10}) \) \( 8016 q - 8 q^{2} - 8 q^{4} - 12 q^{6} - 12 q^{7} - 20 q^{8} - 26 q^{9} - 30 q^{10} - 32 q^{12} - 70 q^{14} - 26 q^{15} - 8 q^{16} - 52 q^{17} - 20 q^{18} - 13 q^{20} - 9 q^{22} - 10 q^{23} - 26 q^{24} + 1294 q^{25} - 24 q^{26} - 20 q^{28} - 9 q^{30} + 12 q^{31} + 2 q^{32} - 50 q^{33} - 7 q^{34} + 14 q^{36} - 45 q^{38} - 14 q^{39} - 15 q^{40} - 10 q^{41} - 17 q^{42} - 45 q^{44} - 22 q^{46} - 56 q^{47} - 25 q^{48} - 12 q^{49} - 3 q^{50} + 11 q^{52} + 44 q^{54} - 60 q^{55} - 253 q^{56} - 50 q^{57} + 3 q^{58} - 226 q^{60} - 74 q^{62} - 78 q^{63} - 20 q^{64} - 36 q^{65} + 173 q^{66} - 38 q^{68} - 15 q^{70} - 40 q^{71} + 17 q^{72} - 52 q^{73} + 59 q^{74} + 27 q^{76} - 51 q^{78} + 12 q^{79} - 3 q^{80} + 78 q^{81} - 28 q^{82} - 169 q^{84} - 33 q^{86} - 32 q^{87} - 21 q^{88} - 60 q^{89} - 147 q^{90} + 83 q^{92} - 16 q^{94} + 34 q^{95} + 247 q^{96} - 24 q^{97} + 55 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3528, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.