Properties

Label 3528.2.bf
Level $3528$
Weight $2$
Character orbit 3528.bf
Rep. character $\chi_{3528}(619,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $944$
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.bf (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 504 \)
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 976 400
Cusp forms 1312 944 368
Eisenstein series 64 32 32

Trace form

\( 944 q + 2 q^{2} + 6 q^{3} + 2 q^{4} + 6 q^{6} - 16 q^{8} + 2 q^{9} + O(q^{10}) \) \( 944 q + 2 q^{2} + 6 q^{3} + 2 q^{4} + 6 q^{6} - 16 q^{8} + 2 q^{9} + 6 q^{10} - 2 q^{11} - 12 q^{12} + 2 q^{16} + 12 q^{17} - 20 q^{18} + 12 q^{19} - 24 q^{20} + 12 q^{24} - 442 q^{25} - 3 q^{30} + 62 q^{32} + 6 q^{33} + 6 q^{34} - 4 q^{36} + 33 q^{38} - 12 q^{40} - 8 q^{43} - 3 q^{44} + 10 q^{46} + 9 q^{48} - 45 q^{50} - 42 q^{51} - 21 q^{52} + 51 q^{54} - 4 q^{57} - 5 q^{58} + 15 q^{60} - 16 q^{64} - 36 q^{65} - 36 q^{66} + 4 q^{67} - 12 q^{68} + 10 q^{72} + 12 q^{73} - 49 q^{74} + 6 q^{75} + 12 q^{76} + 77 q^{78} + 63 q^{80} - 14 q^{81} + 12 q^{82} - 60 q^{83} + 41 q^{86} - 9 q^{88} + 36 q^{89} + 33 q^{90} + 54 q^{92} + 45 q^{96} + 2 q^{99} + O(q^{100}) \)

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

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