↑

Properties

Label 3528.2.bt
Level $3528$
Weight $2$
Character orbit 3528.bt
Rep. character $\chi_{3528}(275,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $944$
Sturm bound $1344$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3528 = 2^{3} \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3528.bt (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

\( 944 q + 2 q^{3} + 2 q^{4} + 2 q^{6} + 2 q^{9} + O(q^{10}) \) \( 944 q + 2 q^{3} + 2 q^{4} + 2 q^{6} + 2 q^{9} + 6 q^{10} + 6 q^{11} + 8 q^{12} + 2 q^{16} + 22 q^{18} + 4 q^{19} + 6 q^{20} - 8 q^{22} + 8 q^{24} - 442 q^{25} + 6 q^{26} + 8 q^{27} + 25 q^{30} + 14 q^{33} + 4 q^{34} + 36 q^{36} - 39 q^{38} - 6 q^{40} + 12 q^{41} - 8 q^{43} - 81 q^{44} - 6 q^{46} + 5 q^{48} + 3 q^{50} - 2 q^{51} - 9 q^{52} - 47 q^{54} - 28 q^{57} + 3 q^{58} + 31 q^{60} - 16 q^{64} + 26 q^{66} + 4 q^{67} + 42 q^{68} - 86 q^{72} + 4 q^{73} - 105 q^{74} - 30 q^{75} - 2 q^{76} - 5 q^{78} - 87 q^{80} - 14 q^{81} + 4 q^{82} + 72 q^{83} - 3 q^{86} + 7 q^{88} + 24 q^{89} + 49 q^{90} + 18 q^{92} + 18 q^{94} - 23 q^{96} + 4 q^{97} - 34 q^{99} + O(q^{100}) \)

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

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