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Properties

Label 3528.2.cs
Level $3528$
Weight $2$
Character orbit 3528.cs
Rep. character $\chi_{3528}(589,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $964$
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.cs (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 72 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 1376 1004 372
Cusp forms 1312 964 348
Eisenstein series 64 40 24

Trace form

\( 964 q + q^{2} + q^{4} + 7 q^{6} - 26 q^{8} + 4 q^{9} + O(q^{10}) \) \( 964 q + q^{2} + q^{4} + 7 q^{6} - 26 q^{8} + 4 q^{9} + 8 q^{10} + 4 q^{12} - 14 q^{15} + q^{16} + 8 q^{17} + 18 q^{18} + 2 q^{20} - q^{22} - 10 q^{23} + 7 q^{24} + 444 q^{25} + 36 q^{26} + 48 q^{30} + 2 q^{31} - 19 q^{32} + 2 q^{33} - 3 q^{34} - 49 q^{36} + 3 q^{38} + 22 q^{39} - 10 q^{40} + 6 q^{41} - 26 q^{44} + 12 q^{46} - 18 q^{47} - 15 q^{48} - 7 q^{50} + 18 q^{52} + 5 q^{54} + 28 q^{55} - 36 q^{57} - 4 q^{58} + 20 q^{62} + 10 q^{64} + 22 q^{65} - 46 q^{66} - 39 q^{68} + 16 q^{71} + 69 q^{72} + 8 q^{73} + 60 q^{74} + 3 q^{76} - 40 q^{78} + 2 q^{79} + 8 q^{80} + 16 q^{81} + 18 q^{82} + 23 q^{86} + 62 q^{87} + 5 q^{88} - 8 q^{89} + 108 q^{90} - 14 q^{92} - 6 q^{94} + 84 q^{95} + 50 q^{96} + 2 q^{97} + O(q^{100}) \)

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.

Decomposition of \(S_{2}^{\mathrm{old}}(3528, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3528, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 2}\)