# Properties

 Label 363.4.j Level $363$ Weight $4$ Character orbit 363.j Rep. character $\chi_{363}(32,\cdot)$ Character field $\Q(\zeta_{22})$ Dimension $1300$ Sturm bound $176$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$363 = 3 \cdot 11^{2}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 363.j (of order $$22$$ and degree $$10$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$363$$ Character field: $$\Q(\zeta_{22})$$ Sturm bound: $$176$$

## Dimensions

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

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

## Trace form

 $$1300 q - 22 q^{3} - 530 q^{4} + 77 q^{6} - 22 q^{7} - 18 q^{9} + O(q^{10})$$ $$1300 q - 22 q^{3} - 530 q^{4} + 77 q^{6} - 22 q^{7} - 18 q^{9} - 154 q^{10} - 128 q^{12} + 242 q^{13} + 414 q^{15} - 1802 q^{16} + 77 q^{18} - 22 q^{19} - 308 q^{21} - 514 q^{22} + 2310 q^{24} + 2948 q^{25} - 334 q^{27} - 22 q^{28} - 308 q^{30} + 462 q^{31} - 306 q^{33} - 670 q^{34} - 545 q^{36} + 150 q^{37} - 308 q^{39} + 576 q^{42} - 22 q^{43} + 1848 q^{45} - 22 q^{46} + 606 q^{48} + 5032 q^{49} - 4477 q^{51} - 6952 q^{52} + 8239 q^{54} - 2010 q^{55} - 3619 q^{57} + 10982 q^{58} - 3694 q^{60} - 22 q^{61} - 6974 q^{63} - 16622 q^{64} - 4474 q^{66} + 90 q^{67} + 1746 q^{69} + 686 q^{70} + 5621 q^{72} - 2134 q^{73} - 1328 q^{75} - 11902 q^{76} - 1336 q^{78} + 1826 q^{79} + 4990 q^{81} + 6194 q^{82} - 308 q^{84} + 7898 q^{85} + 286 q^{87} - 922 q^{88} - 7150 q^{90} + 1538 q^{91} + 764 q^{93} + 286 q^{96} + 1518 q^{97} + 4998 q^{99} + O(q^{100})$$

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

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