# Properties

 Label 100.4.l Level $100$ Weight $4$ Character orbit 100.l Rep. character $\chi_{100}(3,\cdot)$ Character field $\Q(\zeta_{20})$ Dimension $344$ Newform subspaces $2$ Sturm bound $60$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$100 = 2^{2} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 100.l (of order $$20$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$100$$ Character field: $$\Q(\zeta_{20})$$ Newform subspaces: $$2$$ Sturm bound: $$60$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(100, [\chi])$$.

Total New Old
Modular forms 376 376 0
Cusp forms 344 344 0
Eisenstein series 32 32 0

## Trace form

 $$344 q - 8 q^{2} - 10 q^{4} - 16 q^{5} - 6 q^{6} + 34 q^{8} - 20 q^{9} + O(q^{10})$$ $$344 q - 8 q^{2} - 10 q^{4} - 16 q^{5} - 6 q^{6} + 34 q^{8} - 20 q^{9} + 64 q^{10} + 70 q^{12} - 62 q^{13} - 10 q^{14} - 6 q^{16} + 114 q^{17} - 316 q^{18} - 326 q^{20} - 12 q^{21} - 370 q^{22} - 126 q^{25} - 16 q^{26} + 870 q^{28} - 20 q^{29} + 1230 q^{30} + 622 q^{32} - 100 q^{33} - 10 q^{34} - 262 q^{36} - 346 q^{37} + 880 q^{38} + 204 q^{40} - 12 q^{41} - 470 q^{42} - 1340 q^{44} - 606 q^{45} - 6 q^{46} - 3400 q^{48} - 2206 q^{50} - 2356 q^{52} + 678 q^{53} - 3780 q^{54} - 6 q^{56} + 940 q^{57} - 1112 q^{58} + 2810 q^{60} - 12 q^{61} + 2900 q^{62} + 4820 q^{64} + 1758 q^{65} - 870 q^{66} + 2418 q^{68} - 20 q^{69} + 3030 q^{70} + 1892 q^{72} - 1962 q^{73} + 240 q^{76} - 3140 q^{77} - 3460 q^{78} - 2106 q^{80} + 4362 q^{81} - 8826 q^{82} - 11290 q^{84} + 3248 q^{85} - 6 q^{86} - 1570 q^{88} + 1410 q^{89} + 3494 q^{90} + 6130 q^{92} - 1300 q^{93} + 11030 q^{94} - 1746 q^{96} - 12626 q^{97} + 13324 q^{98} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(100, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
100.4.l.a $8$ $5.900$ $$\Q(\zeta_{20})$$ $$\Q(\sqrt{-1})$$ $$-4$$ $$0$$ $$4$$ $$0$$ $$q+(-2+2\zeta_{20}^{2}-2\zeta_{20}^{3}-2\zeta_{20}^{4}+\cdots)q^{2}+\cdots$$
100.4.l.b $336$ $5.900$ None $$-4$$ $$0$$ $$-20$$ $$0$$