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Properties

Label 440.4.g
Level $440$
Weight $4$
Character orbit 440.g
Rep. character $\chi_{440}(221,\cdot)$
Character field $\Q$
Dimension $120$
Sturm bound $288$

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Defining parameters

Level: \( N \) \(=\) \( 440 = 2^{3} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 440.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Sturm bound: \(288\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(440, [\chi])\).

Total New Old
Modular forms 220 120 100
Cusp forms 212 120 92
Eisenstein series 8 0 8

Trace form

\( 120 q - 12 q^{4} + 72 q^{6} + 12 q^{8} - 1080 q^{9} + O(q^{10}) \) \( 120 q - 12 q^{4} + 72 q^{6} + 12 q^{8} - 1080 q^{9} - 60 q^{10} - 376 q^{12} - 48 q^{14} + 120 q^{15} - 160 q^{16} + 232 q^{18} - 20 q^{20} - 552 q^{23} - 728 q^{24} - 3000 q^{25} + 252 q^{26} + 380 q^{28} + 528 q^{31} - 1120 q^{32} - 688 q^{34} - 1288 q^{36} - 800 q^{38} - 1200 q^{39} - 240 q^{40} - 1240 q^{42} - 308 q^{44} - 256 q^{46} + 1880 q^{47} + 1432 q^{48} + 4440 q^{49} - 1836 q^{52} + 248 q^{54} - 440 q^{55} + 2792 q^{56} + 672 q^{57} + 2560 q^{58} + 660 q^{60} - 1528 q^{62} + 80 q^{63} + 132 q^{64} - 1100 q^{66} + 1620 q^{68} - 620 q^{70} + 112 q^{71} + 3652 q^{72} - 864 q^{73} + 1872 q^{74} + 576 q^{76} - 3680 q^{78} - 2832 q^{79} - 880 q^{80} + 8488 q^{81} + 1432 q^{82} - 848 q^{84} - 2012 q^{86} + 8112 q^{87} + 848 q^{89} + 4500 q^{90} - 1928 q^{92} + 1288 q^{94} + 10984 q^{96} + 3168 q^{97} + 10512 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(440, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(440, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(440, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(88, [\chi])\)\(^{\oplus 2}\)