Properties

 Label 100.3.b Level $100$ Weight $3$ Character orbit 100.b Rep. character $\chi_{100}(51,\cdot)$ Character field $\Q$ Dimension $16$ Newform subspaces $6$ Sturm bound $45$ Trace bound $2$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$100 = 2^{2} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 100.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$4$$ Character field: $$\Q$$ Newform subspaces: $$6$$ Sturm bound: $$45$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$3$$, $$13$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(100, [\chi])$$.

Total New Old
Modular forms 36 22 14
Cusp forms 24 16 8
Eisenstein series 12 6 6

Trace form

 $$16q + 2q^{2} + 6q^{4} + 2q^{6} + 8q^{8} - 32q^{9} + O(q^{10})$$ $$16q + 2q^{2} + 6q^{4} + 2q^{6} + 8q^{8} - 32q^{9} - 40q^{12} + 16q^{13} - 28q^{14} - 14q^{16} + 24q^{17} - 22q^{18} - 56q^{21} + 80q^{22} + 142q^{24} + 60q^{26} + 40q^{28} + 32q^{29} - 128q^{32} - 80q^{33} - 130q^{34} - 112q^{36} - 16q^{37} - 80q^{38} + 112q^{41} + 120q^{42} + 90q^{44} - 68q^{46} + 8q^{49} - 56q^{52} + 176q^{53} - 26q^{54} + 52q^{56} + 36q^{58} - 168q^{61} + 80q^{62} - 174q^{64} + 90q^{66} + 136q^{68} + 104q^{69} + 72q^{72} - 264q^{73} - 240q^{74} + 90q^{76} - 240q^{77} + 80q^{78} + 200q^{81} - 116q^{82} + 44q^{84} + 352q^{86} - 160q^{88} - 88q^{89} + 120q^{92} + 400q^{93} + 272q^{94} + 302q^{96} + 264q^{97} - 102q^{98} + O(q^{100})$$

Decomposition of $$S_{3}^{\mathrm{new}}(100, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
100.3.b.a $$1$$ $$2.725$$ $$\Q$$ $$\Q(\sqrt{-1})$$ $$-2$$ $$0$$ $$0$$ $$0$$ $$q-2q^{2}+4q^{4}-8q^{8}+9q^{9}+24q^{13}+\cdots$$
100.3.b.b $$1$$ $$2.725$$ $$\Q$$ $$\Q(\sqrt{-1})$$ $$2$$ $$0$$ $$0$$ $$0$$ $$q+2q^{2}+4q^{4}+8q^{8}+9q^{9}-24q^{13}+\cdots$$
100.3.b.c $$2$$ $$2.725$$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-5})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}+2iq^{3}-4q^{4}-8q^{6}+2iq^{7}+\cdots$$
100.3.b.d $$4$$ $$2.725$$ 4.0.8405.1 None $$-1$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{2}+(-\beta _{1}-\beta _{2})q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots$$
100.3.b.e $$4$$ $$2.725$$ 4.0.8405.1 None $$1$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{2}+(\beta _{1}+\beta _{2})q^{3}+(1-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots$$
100.3.b.f $$4$$ $$2.725$$ $$\Q(\zeta_{10})$$ None $$2$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{10}q^{2}+\zeta_{10}^{2}q^{3}+(-1+\zeta_{10}+\cdots)q^{4}+\cdots$$

Decomposition of $$S_{3}^{\mathrm{old}}(100, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(100, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(20, [\chi])$$$$^{\oplus 2}$$