# Properties

 Label 363.4.i Level $363$ Weight $4$ Character orbit 363.i Rep. character $\chi_{363}(34,\cdot)$ Character field $\Q(\zeta_{11})$ Dimension $660$ Sturm bound $176$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$363 = 3 \cdot 11^{2}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 363.i (of order $$11$$ and degree $$10$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$121$$ Character field: $$\Q(\zeta_{11})$$ Sturm bound: $$176$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(363, [\chi])$$.

Total New Old
Modular forms 1340 660 680
Cusp forms 1300 660 640
Eisenstein series 40 0 40

## Trace form

 $$660 q + 4 q^{2} - 284 q^{4} + 16 q^{5} + 12 q^{6} + 32 q^{7} - 36 q^{8} + 5940 q^{9} + O(q^{10})$$ $$660 q + 4 q^{2} - 284 q^{4} + 16 q^{5} + 12 q^{6} + 32 q^{7} - 36 q^{8} + 5940 q^{9} + 220 q^{10} + 308 q^{11} + 24 q^{12} - 236 q^{13} - 516 q^{14} - 60 q^{15} - 1228 q^{16} - 152 q^{17} + 36 q^{18} - 8 q^{19} + 636 q^{20} + 84 q^{21} - 836 q^{22} + 1484 q^{23} + 324 q^{24} - 1646 q^{25} - 284 q^{26} + 192 q^{28} + 120 q^{29} - 336 q^{30} - 800 q^{31} - 364 q^{32} - 66 q^{33} + 464 q^{34} - 920 q^{35} - 2556 q^{36} - 1664 q^{37} + 800 q^{38} + 336 q^{39} - 5112 q^{40} + 760 q^{41} - 876 q^{42} - 200 q^{43} + 3366 q^{44} + 144 q^{45} + 464 q^{46} + 672 q^{47} + 816 q^{48} - 5926 q^{49} + 7508 q^{50} + 624 q^{51} + 1914 q^{52} - 5884 q^{53} + 108 q^{54} - 3872 q^{55} - 1234 q^{56} - 84 q^{57} - 946 q^{58} - 768 q^{59} - 624 q^{60} + 1180 q^{61} + 3458 q^{62} + 288 q^{63} - 8464 q^{64} - 176 q^{65} - 264 q^{66} - 732 q^{67} - 1000 q^{68} - 720 q^{69} + 8396 q^{70} + 2184 q^{71} - 324 q^{72} + 1388 q^{73} - 2256 q^{74} - 1152 q^{75} + 23318 q^{76} + 176 q^{77} - 7974 q^{78} + 7712 q^{79} + 4472 q^{80} + 53460 q^{81} + 1820 q^{82} - 264 q^{83} + 2880 q^{84} + 1488 q^{85} + 1372 q^{86} - 1368 q^{87} + 10252 q^{88} - 2720 q^{89} + 1980 q^{90} - 2140 q^{91} - 12200 q^{92} + 960 q^{93} - 31856 q^{94} + 168 q^{95} - 4836 q^{96} + 420 q^{97} - 44 q^{98} + 2772 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(363, [\chi])$$ into newform subspaces

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

## Decomposition of $$S_{4}^{\mathrm{old}}(363, [\chi])$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(363, [\chi]) \cong$$ $$S_{4}^{\mathrm{new}}(121, [\chi])$$$$^{\oplus 2}$$