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Properties

Label 1560.4.w
Level $1560$
Weight $4$
Character orbit 1560.w
Rep. character $\chi_{1560}(781,\cdot)$
Character field $\Q$
Dimension $288$
Sturm bound $1344$

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Defining parameters

Level: \( N \) \(=\) \( 1560 = 2^{3} \cdot 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1560.w (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Sturm bound: \(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1560, [\chi])\).

Total New Old
Modular forms 1016 288 728
Cusp forms 1000 288 712
Eisenstein series 16 0 16

Trace form

\( 288 q + 8 q^{2} + 52 q^{4} - 12 q^{6} + 112 q^{7} - 136 q^{8} - 2592 q^{9} + O(q^{10}) \) \( 288 q + 8 q^{2} + 52 q^{4} - 12 q^{6} + 112 q^{7} - 136 q^{8} - 2592 q^{9} + 60 q^{10} + 280 q^{14} - 120 q^{15} + 12 q^{16} - 72 q^{18} + 448 q^{22} + 1312 q^{23} + 228 q^{24} - 7200 q^{25} - 168 q^{28} - 528 q^{31} - 712 q^{32} + 480 q^{34} - 468 q^{36} + 60 q^{40} + 1344 q^{44} - 784 q^{46} + 14112 q^{49} - 200 q^{50} + 108 q^{54} - 3136 q^{56} - 3192 q^{58} - 660 q^{60} + 608 q^{62} - 1008 q^{63} - 284 q^{64} - 1368 q^{66} + 32 q^{68} + 1080 q^{70} - 5920 q^{71} + 1224 q^{72} - 744 q^{74} - 112 q^{76} + 3312 q^{79} + 23328 q^{81} + 3912 q^{82} - 3528 q^{84} - 8064 q^{86} + 9688 q^{88} - 540 q^{90} - 1440 q^{92} - 4248 q^{94} + 348 q^{96} + 7112 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1560, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1560, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1560, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(520, [\chi])\)\(^{\oplus 2}\)