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Properties

Label 3528.2.ex
Level $3528$
Weight $2$
Character orbit 3528.ex
Rep. character $\chi_{3528}(5,\cdot)$
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.ex (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

\( 8016 q - 21 q^{2} - 5 q^{4} - 8 q^{6} - 12 q^{7} - 26 q^{9} + O(q^{10}) \) \( 8016 q - 21 q^{2} - 5 q^{4} - 8 q^{6} - 12 q^{7} - 26 q^{9} - 22 q^{10} + 44 q^{12} - 108 q^{14} - 26 q^{15} - 5 q^{16} - 19 q^{18} - 21 q^{20} - q^{22} - 36 q^{23} - 2 q^{24} - 668 q^{25} + 6 q^{26} - 20 q^{28} - 4 q^{30} - 21 q^{32} - 22 q^{33} - 13 q^{34} - 26 q^{36} + 54 q^{38} - 20 q^{39} + 11 q^{40} - 42 q^{41} + 28 q^{42} + 9 q^{44} - 30 q^{46} - 30 q^{47} - 9 q^{48} - 12 q^{49} - 51 q^{50} - 28 q^{52} - 47 q^{54} - 56 q^{55} - 39 q^{56} + 10 q^{57} - 4 q^{58} - 63 q^{60} + 30 q^{62} + 44 q^{63} - 20 q^{64} - 42 q^{65} - 14 q^{66} - 3 q^{68} + 20 q^{70} - 32 q^{72} - 44 q^{73} - 6 q^{74} + 37 q^{76} + 93 q^{78} - 24 q^{79} + 57 q^{80} - 66 q^{81} - 28 q^{82} + 71 q^{84} + 36 q^{86} - 22 q^{87} - 16 q^{88} + 24 q^{89} + 124 q^{90} + 15 q^{92} - 7 q^{94} - 42 q^{95} + 38 q^{96} + 45 q^{98} + O(q^{100}) \)

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.