Properties

Label 1045.4.y
Level $1045$
Weight $4$
Character orbit 1045.y
Rep. character $\chi_{1045}(151,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $960$
Sturm bound $480$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1045 = 5 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1045.y (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 209 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1045, [\chi])\).

Total New Old
Modular forms 1456 960 496
Cusp forms 1424 960 464
Eisenstein series 32 0 32

Trace form

\( 960 q - 960 q^{4} + 200 q^{6} + 2280 q^{9} + O(q^{10}) \) \( 960 q - 960 q^{4} + 200 q^{6} + 2280 q^{9} + 72 q^{11} - 3840 q^{16} + 40 q^{17} - 450 q^{19} - 608 q^{23} - 2400 q^{24} - 6000 q^{25} - 656 q^{26} + 8672 q^{36} + 1002 q^{38} + 600 q^{39} + 4636 q^{42} - 6280 q^{44} - 1240 q^{47} + 10012 q^{49} - 4170 q^{57} + 1712 q^{58} - 1800 q^{61} + 5360 q^{62} - 10824 q^{64} + 4672 q^{66} - 480 q^{68} - 360 q^{73} - 9500 q^{74} + 7208 q^{77} + 3480 q^{80} - 20476 q^{81} - 10992 q^{82} + 3700 q^{83} + 7144 q^{92} + 1872 q^{93} + 4360 q^{96} - 12952 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(1045, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1045, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1045, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(209, [\chi])\)\(^{\oplus 2}\)