Properties

Label 1960.2.bf
Level $1960$
Weight $2$
Character orbit 1960.bf
Rep. character $\chi_{1960}(949,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $464$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 1960 = 2^{3} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1960.bf (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 280 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1960, [\chi])\).

Total New Old
Modular forms 704 496 208
Cusp forms 640 464 176
Eisenstein series 64 32 32

Trace form

\( 464 q + 2 q^{4} - 212 q^{9} + O(q^{10}) \) \( 464 q + 2 q^{4} - 212 q^{9} - 6 q^{10} - 28 q^{15} - 2 q^{16} + 24 q^{20} + 8 q^{24} + 2 q^{25} + 14 q^{26} - 6 q^{30} + 28 q^{31} - 24 q^{34} - 124 q^{36} + 16 q^{39} + 32 q^{40} + 16 q^{41} - 58 q^{44} + 30 q^{46} - 20 q^{50} - 8 q^{54} + 28 q^{55} + 22 q^{60} - 148 q^{64} + 12 q^{65} + 44 q^{66} - 64 q^{71} + 78 q^{74} + 36 q^{76} + 4 q^{79} + 40 q^{80} - 160 q^{81} + 56 q^{86} - 4 q^{89} + 96 q^{90} + 22 q^{94} - 26 q^{95} - 80 q^{96} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1960, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1960, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1960, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 2}\)