Properties

 Label 225.4.h Level $225$ Weight $4$ Character orbit 225.h Rep. character $\chi_{225}(46,\cdot)$ Character field $\Q(\zeta_{5})$ Dimension $148$ Newform subspaces $4$ Sturm bound $120$ Trace bound $2$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$225 = 3^{2} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 225.h (of order $$5$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$25$$ Character field: $$\Q(\zeta_{5})$$ Newform subspaces: $$4$$ Sturm bound: $$120$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$2$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(225, [\chi])$$.

Total New Old
Modular forms 376 156 220
Cusp forms 344 148 196
Eisenstein series 32 8 24

Trace form

 $$148 q + 5 q^{2} - 151 q^{4} + 20 q^{5} + 8 q^{7} + 74 q^{8} + O(q^{10})$$ $$148 q + 5 q^{2} - 151 q^{4} + 20 q^{5} + 8 q^{7} + 74 q^{8} + 35 q^{10} + 5 q^{11} + 117 q^{13} + 149 q^{14} - 471 q^{16} - 89 q^{17} - 43 q^{19} - 335 q^{20} - 392 q^{22} - q^{23} + 720 q^{25} - 678 q^{26} + 419 q^{28} + 349 q^{29} + 189 q^{31} - 738 q^{32} - 93 q^{34} - 50 q^{35} - 327 q^{37} - 527 q^{38} - 2050 q^{40} + 1003 q^{41} + 404 q^{43} + 1146 q^{44} + 897 q^{46} - 367 q^{47} + 6192 q^{49} + 2245 q^{50} + 1684 q^{52} - 801 q^{53} + 1345 q^{55} + 210 q^{56} - 3926 q^{58} + 513 q^{59} + 59 q^{61} + 2274 q^{62} - 1916 q^{64} + 2145 q^{65} - 1931 q^{67} - 3470 q^{68} - 4960 q^{70} + 2287 q^{71} - 3939 q^{73} - 5316 q^{74} + 3976 q^{76} - 1976 q^{77} - 689 q^{79} - 8940 q^{80} + 1806 q^{82} - 645 q^{83} - 1495 q^{85} + 105 q^{86} + 7496 q^{88} + 1307 q^{89} - 2288 q^{91} + 6882 q^{92} + 3585 q^{94} + 2795 q^{95} - 241 q^{97} + 13462 q^{98} + O(q^{100})$$

Decomposition of $$S_{4}^{\mathrm{new}}(225, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
225.4.h.a $28$ $13.275$ None $$0$$ $$0$$ $$15$$ $$-54$$
225.4.h.b $28$ $13.275$ None $$1$$ $$0$$ $$20$$ $$-16$$
225.4.h.c $28$ $13.275$ None $$4$$ $$0$$ $$-15$$ $$58$$
225.4.h.d $64$ $13.275$ None $$0$$ $$0$$ $$0$$ $$20$$

Decomposition of $$S_{4}^{\mathrm{old}}(225, [\chi])$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(225, [\chi]) \simeq$$ $$S_{4}^{\mathrm{new}}(25, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(75, [\chi])$$$$^{\oplus 2}$$