# Properties

 Label 98.4.c Level $98$ Weight $4$ Character orbit 98.c Rep. character $\chi_{98}(67,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $20$ Newform subspaces $8$ Sturm bound $56$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$98 = 2 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 98.c (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$8$$ Sturm bound: $$56$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(98, [\chi])$$.

Total New Old
Modular forms 100 20 80
Cusp forms 68 20 48
Eisenstein series 32 0 32

## Trace form

 $$20q - 6q^{3} - 40q^{4} - 2q^{5} + 16q^{6} - 168q^{9} + O(q^{10})$$ $$20q - 6q^{3} - 40q^{4} - 2q^{5} + 16q^{6} - 168q^{9} - 32q^{10} - 30q^{11} - 24q^{12} + 8q^{13} - 68q^{15} - 160q^{16} + 110q^{17} + 40q^{18} + 142q^{19} + 16q^{20} + 512q^{22} + 26q^{23} - 32q^{24} - 520q^{25} - 272q^{26} - 396q^{27} - 824q^{29} + 264q^{30} + 98q^{31} + 250q^{33} + 32q^{34} + 1344q^{36} + 874q^{37} - 264q^{38} + 1604q^{39} - 128q^{40} + 1080q^{41} - 1272q^{43} - 120q^{44} - 164q^{45} + 248q^{46} + 30q^{47} + 192q^{48} - 2720q^{50} - 250q^{51} - 16q^{52} - 150q^{53} + 184q^{54} - 1516q^{55} + 1908q^{57} + 480q^{58} + 202q^{59} + 136q^{60} - 658q^{61} + 208q^{62} + 1280q^{64} + 1540q^{65} + 640q^{66} - 986q^{67} + 440q^{68} + 676q^{69} + 2288q^{71} + 160q^{72} - 18q^{73} - 1280q^{74} + 296q^{75} - 1136q^{76} - 2432q^{78} - 3078q^{79} - 32q^{80} - 1150q^{81} + 912q^{82} - 688q^{83} + 3236q^{85} - 1256q^{86} - 676q^{87} - 1024q^{88} - 1890q^{89} - 800q^{90} - 208q^{92} - 5210q^{93} + 744q^{94} + 1142q^{95} - 128q^{96} + 4248q^{97} - 6560q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(98, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
98.4.c.a $$2$$ $$5.782$$ $$\Q(\sqrt{-3})$$ None $$-2$$ $$-5$$ $$-9$$ $$0$$ $$q-2\zeta_{6}q^{2}+(-5+5\zeta_{6})q^{3}+(-4+4\zeta_{6})q^{4}+\cdots$$
98.4.c.b $$2$$ $$5.782$$ $$\Q(\sqrt{-3})$$ None $$-2$$ $$-2$$ $$-12$$ $$0$$ $$q-2\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{3}+(-4+4\zeta_{6})q^{4}+\cdots$$
98.4.c.c $$2$$ $$5.782$$ $$\Q(\sqrt{-3})$$ None $$-2$$ $$2$$ $$12$$ $$0$$ $$q-2\zeta_{6}q^{2}+(2-2\zeta_{6})q^{3}+(-4+4\zeta_{6})q^{4}+\cdots$$
98.4.c.d $$2$$ $$5.782$$ $$\Q(\sqrt{-3})$$ None $$2$$ $$-8$$ $$14$$ $$0$$ $$q+2\zeta_{6}q^{2}+(-8+8\zeta_{6})q^{3}+(-4+4\zeta_{6})q^{4}+\cdots$$
98.4.c.e $$2$$ $$5.782$$ $$\Q(\sqrt{-3})$$ None $$2$$ $$-1$$ $$7$$ $$0$$ $$q+2\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-4+4\zeta_{6})q^{4}+\cdots$$
98.4.c.f $$2$$ $$5.782$$ $$\Q(\sqrt{-3})$$ None $$2$$ $$8$$ $$-14$$ $$0$$ $$q+2\zeta_{6}q^{2}+(8-8\zeta_{6})q^{3}+(-4+4\zeta_{6})q^{4}+\cdots$$
98.4.c.g $$4$$ $$5.782$$ $$\Q(\sqrt{-3}, \sqrt{22})$$ None $$-4$$ $$0$$ $$0$$ $$0$$ $$q+(-2-2\beta _{2})q^{2}+(\beta _{1}+\beta _{3})q^{3}+4\beta _{2}q^{4}+\cdots$$
98.4.c.h $$4$$ $$5.782$$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$4$$ $$0$$ $$0$$ $$0$$ $$q+(2+2\beta _{2})q^{2}+(5\beta _{1}+5\beta _{3})q^{3}+4\beta _{2}q^{4}+\cdots$$

## Decomposition of $$S_{4}^{\mathrm{old}}(98, [\chi])$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(98, [\chi]) \cong$$ $$S_{4}^{\mathrm{new}}(7, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(14, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(49, [\chi])$$$$^{\oplus 2}$$