# Properties

 Label 98.2.e Level $98$ Weight $2$ Character orbit 98.e Rep. character $\chi_{98}(15,\cdot)$ Character field $\Q(\zeta_{7})$ Dimension $36$ Newform subspaces $2$ Sturm bound $28$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$98 = 2 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 98.e (of order $$7$$ and degree $$6$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$49$$ Character field: $$\Q(\zeta_{7})$$ Newform subspaces: $$2$$ Sturm bound: $$28$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(98, [\chi])$$.

Total New Old
Modular forms 96 36 60
Cusp forms 72 36 36
Eisenstein series 24 0 24

## Trace form

 $$36q - 2q^{3} - 6q^{4} - 6q^{5} + 8q^{6} - 8q^{7} + O(q^{10})$$ $$36q - 2q^{3} - 6q^{4} - 6q^{5} + 8q^{6} - 8q^{7} - 6q^{10} + 6q^{11} - 2q^{12} - 10q^{13} - 6q^{14} - 2q^{15} - 6q^{16} - 10q^{17} - 8q^{18} - 8q^{19} + 8q^{20} - 26q^{21} + 6q^{22} + 26q^{23} - 6q^{24} - 22q^{25} - 4q^{26} - 2q^{27} - 8q^{28} - 2q^{29} - 16q^{30} - 28q^{31} - 48q^{33} - 12q^{34} - 28q^{35} + 20q^{37} - 4q^{38} + 18q^{39} + 8q^{40} - 20q^{41} + 96q^{42} - 44q^{43} + 6q^{44} + 118q^{45} + 26q^{46} + 76q^{47} + 12q^{48} + 6q^{49} - 24q^{50} + 16q^{51} + 18q^{52} + 58q^{53} + 6q^{54} + 96q^{55} + 8q^{56} - 18q^{57} + 60q^{58} - 12q^{59} - 2q^{60} + 28q^{61} - 22q^{62} + 6q^{63} - 6q^{64} - 56q^{65} - 48q^{66} - 52q^{67} + 4q^{68} - 68q^{69} - 28q^{70} - 6q^{71} - 8q^{72} - 34q^{73} - 10q^{74} - 50q^{75} - 22q^{76} - 42q^{77} + 24q^{78} - 68q^{79} + 8q^{80} - 36q^{81} - 36q^{82} + 90q^{83} + 16q^{84} - 16q^{85} + 18q^{86} - 62q^{87} + 6q^{88} + 56q^{89} - 36q^{90} + 4q^{91} - 16q^{92} + 82q^{93} + 10q^{94} - 24q^{95} - 6q^{96} + 24q^{97} - 20q^{98} + 120q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(98, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
98.2.e.a $$18$$ $$0.783$$ $$\mathbb{Q}[x]/(x^{18} - \cdots)$$ None $$-3$$ $$3$$ $$-6$$ $$-7$$ $$q-\beta _{13}q^{2}+(\beta _{1}-\beta _{14})q^{3}+(-1+\beta _{8}+\cdots)q^{4}+\cdots$$
98.2.e.b $$18$$ $$0.783$$ $$\mathbb{Q}[x]/(x^{18} + \cdots)$$ None $$3$$ $$-5$$ $$0$$ $$-1$$ $$q-\beta _{9}q^{2}+\beta _{4}q^{3}+(-1-\beta _{5}+\beta _{6}+\cdots)q^{4}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(98, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(98, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(49, [\chi])$$$$^{\oplus 2}$$