# Properties

 Label 363.4.p Level $363$ Weight $4$ Character orbit 363.p Rep. character $\chi_{363}(2,\cdot)$ Character field $\Q(\zeta_{110})$ Dimension $5200$ Sturm bound $176$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$363 = 3 \cdot 11^{2}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 363.p (of order $$110$$ and degree $$40$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$363$$ Character field: $$\Q(\zeta_{110})$$ Sturm bound: $$176$$

## Dimensions

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

Total New Old
Modular forms 5360 5360 0
Cusp forms 5200 5200 0
Eisenstein series 160 160 0

## Trace form

 $$5200 q - 28 q^{3} + 430 q^{4} - 177 q^{6} - 78 q^{7} + 48 q^{9} + O(q^{10})$$ $$5200 q - 28 q^{3} + 430 q^{4} - 177 q^{6} - 78 q^{7} + 48 q^{9} + 44 q^{10} + 83 q^{12} - 342 q^{13} - 564 q^{15} + 1522 q^{16} - 357 q^{18} + 372 q^{19} + 253 q^{21} + 1044 q^{22} - 1800 q^{24} - 2628 q^{25} + 254 q^{27} - 1278 q^{28} - 657 q^{30} - 1552 q^{31} - 1549 q^{33} + 580 q^{34} - 725 q^{36} - 370 q^{37} + 1328 q^{39} - 20 q^{40} + 2829 q^{42} - 88 q^{43} - 1893 q^{45} - 518 q^{46} + 929 q^{48} - 4172 q^{49} + 4632 q^{51} + 11112 q^{52} - 8294 q^{54} + 3890 q^{55} + 1764 q^{57} - 8502 q^{58} - 511 q^{60} - 738 q^{61} + 2974 q^{63} + 11382 q^{64} - 1161 q^{66} - 180 q^{67} - 3551 q^{69} - 8776 q^{70} - 4036 q^{72} - 1836 q^{73} + 5113 q^{75} + 11792 q^{76} + 1291 q^{78} + 1614 q^{79} + 2780 q^{81} + 5916 q^{82} + 7333 q^{84} + 222 q^{85} - 341 q^{87} + 13962 q^{88} - 2125 q^{90} + 342 q^{91} - 10344 q^{93} - 3640 q^{94} - 15231 q^{96} - 5728 q^{97} - 9018 q^{99} + O(q^{100})$$

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

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