# Properties

 Label 4.21.b Level 4 Weight 21 Character orbit b Rep. character $$\chi_{4}(3,\cdot)$$ Character field $$\Q$$ Dimension 9 Newforms 2 Sturm bound 10 Trace bound 1

# Related objects

## Defining parameters

 Level: $$N$$ = $$4 = 2^{2}$$ Weight: $$k$$ = $$21$$ Character orbit: $$[\chi]$$ = 4.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$4$$ Character field: $$\Q$$ Newforms: $$2$$ Sturm bound: $$10$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{21}(4, [\chi])$$.

Total New Old
Modular forms 11 11 0
Cusp forms 9 9 0
Eisenstein series 2 2 0

## Trace form

 $$9q - 628q^{2} - 267504q^{4} - 738494q^{5} + 99460608q^{6} + 1103532992q^{8} - 6924577767q^{9} + O(q^{10})$$ $$9q - 628q^{2} - 267504q^{4} - 738494q^{5} + 99460608q^{6} + 1103532992q^{8} - 6924577767q^{9} + 1611884376q^{10} - 41779799040q^{12} + 147660923874q^{13} - 200556776448q^{14} + 70138216704q^{16} - 1684556709806q^{17} + 1635822350412q^{18} + 241483768096q^{20} + 33281721747456q^{21} - 31324969489920q^{22} - 47563142934528q^{24} - 567413012949q^{25} - 63229698776360q^{26} + 385881741772800q^{28} + 303916348382242q^{29} - 1063857826698240q^{30} + 454535173225472q^{32} + 1131041167426560q^{33} - 4199565255965160q^{34} + 16320708718416912q^{36} - 7415248775263806q^{37} - 19214136907706880q^{38} + 42169382228654976q^{40} - 5755597456531022q^{41} - 92697489416232960q^{42} + 157933848933319680q^{44} + 22280783580364386q^{45} - 271527229329687552q^{46} + 485296685862666240q^{48} - 37006326729654807q^{49} - 623084159258016924q^{50} + 813052968459434784q^{52} + 132739492344115714q^{53} - 1607547577815069696q^{54} + 1749313578676543488q^{56} + 440441203792112640q^{57} - 1972695284657517096q^{58} + 2279505537583872000q^{60} - 1172450092804974942q^{61} - 1243411198213386240q^{62} + 1333510659266973696q^{64} - 828610552028041948q^{65} - 21993146403409920q^{66} - 1641594099654542816q^{68} + 3450619355851659264q^{69} + 8506721176491632640q^{70} - 19477455141526114368q^{72} - 4955973119248806606q^{73} + 23508341140743382360q^{74} - 26576303558589158400q^{76} - 5280312525070141440q^{77} + 39300720744848010240q^{78} - 53478714049403538944q^{80} + 27869130702616624425q^{81} + 59306974273770046104q^{82} - 85636060864270565376q^{84} + 5624508021574984452q^{85} + 60721004056878217728q^{86} - 36088003765030440960q^{88} - 30717207683107545998q^{89} + 14470051757664399576q^{90} + 64932970344704317440q^{92} - 53255995615294218240q^{93} - 49076400009934399488q^{94} + 148896006651003076608q^{96} + 21227709255069480594q^{97} - 274458557005261496308q^{98} + O(q^{100})$$

## Decomposition of $$S_{21}^{\mathrm{new}}(4, [\chi])$$ into irreducible Hecke orbits

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
4.21.b.a $$1$$ $$10.141$$ $$\Q$$ $$\Q(\sqrt{-1})$$ $$-1024$$ $$0$$ $$-19306574$$ $$0$$ $$q-2^{10}q^{2}+2^{20}q^{4}-19306574q^{5}+\cdots$$
4.21.b.b $$8$$ $$10.141$$ $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ None $$396$$ $$0$$ $$18568080$$ $$0$$ $$q+(7^{2}+\beta _{1})q^{2}+(6-12\beta _{1}-\beta _{2})q^{3}+\cdots$$