Properties

Label 1045.4.ci
Level $1045$
Weight $4$
Character orbit 1045.ci
Rep. character $\chi_{1045}(27,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $5696$
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.ci (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1045 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 5824 5824 0
Cusp forms 5696 5696 0
Eisenstein series 128 128 0

Trace form

\( 5696 q - 18 q^{2} - 18 q^{3} - 22 q^{5} - 12 q^{6} - 48 q^{7} + O(q^{10}) \) \( 5696 q - 18 q^{2} - 18 q^{3} - 22 q^{5} - 12 q^{6} - 48 q^{7} - 48 q^{10} - 8 q^{11} - 18 q^{13} - 18 q^{15} - 11020 q^{16} + 186 q^{17} - 1792 q^{20} - 96 q^{21} + 456 q^{22} - 128 q^{23} - 14 q^{25} - 176 q^{26} - 454 q^{28} - 1216 q^{30} - 300 q^{32} + 1326 q^{33} + 338 q^{35} + 24580 q^{36} + 2100 q^{38} + 2442 q^{40} + 3960 q^{41} - 1886 q^{42} - 1672 q^{43} - 920 q^{45} - 1182 q^{47} - 3762 q^{48} + 6732 q^{51} + 78 q^{52} - 2826 q^{53} - 1166 q^{55} + 4488 q^{57} - 6848 q^{58} - 3474 q^{60} - 12 q^{61} - 2226 q^{62} - 2242 q^{63} + 704 q^{66} - 2544 q^{67} - 2592 q^{68} - 6066 q^{70} - 36 q^{71} + 10782 q^{72} - 870 q^{73} - 5408 q^{76} + 16784 q^{77} + 1044 q^{78} - 6682 q^{80} - 51956 q^{81} + 2510 q^{82} - 704 q^{83} + 4178 q^{85} - 36 q^{86} - 12440 q^{87} + 15246 q^{90} - 18864 q^{91} + 5364 q^{92} - 5398 q^{93} + 3296 q^{95} + 2832 q^{96} - 3474 q^{97} - 12132 q^{98} + O(q^{100}) \)

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

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