# Properties

 Label 363.4.f Level $363$ Weight $4$ Character orbit 363.f Rep. character $\chi_{363}(161,\cdot)$ Character field $\Q(\zeta_{10})$ Dimension $400$ Sturm bound $176$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$363 = 3 \cdot 11^{2}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 363.f (of order $$10$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$33$$ Character field: $$\Q(\zeta_{10})$$ Sturm bound: $$176$$

## Dimensions

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

Total New Old
Modular forms 576 464 112
Cusp forms 480 400 80
Eisenstein series 96 64 32

## Trace form

 $$400 q + q^{3} - 362 q^{4} - 45 q^{6} + 10 q^{7} + 49 q^{9} + O(q^{10})$$ $$400 q + q^{3} - 362 q^{4} - 45 q^{6} + 10 q^{7} + 49 q^{9} + 178 q^{12} + 10 q^{13} - 63 q^{15} - 1590 q^{16} - 225 q^{18} + 460 q^{19} + 565 q^{24} + 2498 q^{25} + 583 q^{27} - 1190 q^{28} - 910 q^{30} - 876 q^{31} - 372 q^{34} - 2597 q^{36} + 30 q^{37} + 1075 q^{39} + 90 q^{40} + 3240 q^{42} + 3758 q^{45} - 430 q^{46} + 96 q^{48} + 2014 q^{49} + 210 q^{51} + 4270 q^{52} - 1800 q^{57} + 5434 q^{58} - 538 q^{60} - 650 q^{61} - 3945 q^{63} - 10266 q^{64} - 9100 q^{67} - 4510 q^{69} - 2624 q^{70} + 1640 q^{72} - 3860 q^{73} + 7506 q^{75} + 13608 q^{78} + 3550 q^{79} + 2093 q^{81} + 6412 q^{82} + 7080 q^{84} + 8230 q^{85} - 9220 q^{90} + 3598 q^{91} - 7189 q^{93} - 3530 q^{94} - 14890 q^{96} - 7200 q^{97} + O(q^{100})$$

## 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

$$S_{4}^{\mathrm{old}}(363, [\chi]) \cong$$ $$S_{4}^{\mathrm{new}}(33, [\chi])$$$$^{\oplus 2}$$