# Properties

 Label 100.9.j Level $100$ Weight $9$ Character orbit 100.j Rep. character $\chi_{100}(11,\cdot)$ Character field $\Q(\zeta_{10})$ Dimension $472$ Newform subspaces $2$ Sturm bound $135$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$100 = 2^{2} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$9$$ Character orbit: $$[\chi]$$ $$=$$ 100.j (of order $$10$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$100$$ Character field: $$\Q(\zeta_{10})$$ Newform subspaces: $$2$$ Sturm bound: $$135$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{9}(100, [\chi])$$.

Total New Old
Modular forms 488 488 0
Cusp forms 472 472 0
Eisenstein series 16 16 0

## Trace form

 $$472 q - 3 q^{2} - 3 q^{4} - 176 q^{5} - 515 q^{6} + 13092 q^{8} + 249312 q^{9} + O(q^{10})$$ $$472 q - 3 q^{2} - 3 q^{4} - 176 q^{5} - 515 q^{6} + 13092 q^{8} + 249312 q^{9} + 20309 q^{10} - 35805 q^{12} - 28566 q^{13} - 33705 q^{14} - 194463 q^{16} - 193206 q^{17} + 270112 q^{18} + 165639 q^{20} + 39360 q^{21} + 140220 q^{22} + 989900 q^{24} - 761376 q^{25} - 840546 q^{26} - 2358605 q^{28} - 68886 q^{29} + 7229675 q^{30} + 1309942 q^{32} - 1866570 q^{33} - 1592211 q^{34} - 2582203 q^{36} - 4540206 q^{37} + 4012465 q^{38} + 162354 q^{40} - 5468406 q^{41} - 21337315 q^{42} + 510580 q^{44} + 9511344 q^{45} + 1721385 q^{46} + 41153690 q^{48} - 349949928 q^{49} - 65290371 q^{50} - 8175176 q^{52} - 2144526 q^{53} - 13729145 q^{54} + 7138890 q^{56} - 19745300 q^{57} + 3606634 q^{58} + 96768050 q^{60} - 15307606 q^{61} - 87505940 q^{62} - 13937508 q^{64} + 118747458 q^{65} - 69968200 q^{66} + 32716254 q^{68} - 73697610 q^{69} + 39639840 q^{70} - 199742063 q^{72} + 70429514 q^{73} - 24706596 q^{74} - 19181080 q^{76} + 111211200 q^{77} - 197089615 q^{78} - 326606016 q^{80} - 625945728 q^{81} + 72505754 q^{82} - 377672700 q^{84} + 76354258 q^{85} - 340843785 q^{86} - 29231040 q^{88} - 296838366 q^{89} + 461930399 q^{90} + 43044280 q^{92} + 241823660 q^{93} - 442380075 q^{94} - 474931550 q^{96} + 349148394 q^{97} + 25202232 q^{98} + O(q^{100})$$

## Decomposition of $$S_{9}^{\mathrm{new}}(100, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
100.9.j.a $8$ $40.738$ $$\Q(\zeta_{20})$$ $$\Q(\sqrt{-1})$$ $$-32$$ $$0$$ $$1054$$ $$0$$ $$q+(-2^{4}+2^{4}\zeta_{20}^{2}-2^{4}\zeta_{20}^{4}+2^{4}\zeta_{20}^{6}+\cdots)q^{2}+\cdots$$
100.9.j.b $464$ $40.738$ None $$29$$ $$0$$ $$-1230$$ $$0$$