Properties

Label 1560.2.fk
Level $1560$
Weight $2$
Character orbit 1560.fk
Rep. character $\chi_{1560}(149,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1312$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 1560 = 2^{3} \cdot 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1560.fk (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1560 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1560, [\chi])\).

Total New Old
Modular forms 1376 1376 0
Cusp forms 1312 1312 0
Eisenstein series 64 64 0

Trace form

\( 1312 q - 24 q^{4} - 16 q^{6} - 8 q^{9} + O(q^{10}) \) \( 1312 q - 24 q^{4} - 16 q^{6} - 8 q^{9} - 12 q^{10} - 20 q^{15} + 8 q^{16} - 52 q^{24} - 6 q^{30} - 32 q^{31} - 32 q^{34} - 12 q^{36} + 8 q^{39} + 8 q^{40} + 48 q^{46} - 48 q^{49} - 28 q^{54} + 24 q^{55} - 12 q^{60} + 8 q^{66} + 16 q^{76} - 64 q^{79} - 8 q^{81} - 76 q^{84} - 120 q^{94} + 68 q^{96} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1560, [\chi])\) into newform subspaces

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