# Properties

 Label 115.2.g Level $115$ Weight $2$ Character orbit 115.g Rep. character $\chi_{115}(6,\cdot)$ Character field $\Q(\zeta_{11})$ Dimension $80$ Newform subspaces $3$ Sturm bound $24$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$115 = 5 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 115.g (of order $$11$$ and degree $$10$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$23$$ Character field: $$\Q(\zeta_{11})$$ Newform subspaces: $$3$$ Sturm bound: $$24$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(115, [\chi])$$.

Total New Old
Modular forms 140 80 60
Cusp forms 100 80 20
Eisenstein series 40 0 40

## Trace form

 $$80q - 4q^{2} - 16q^{4} - 2q^{5} - 14q^{6} - 4q^{7} - 18q^{8} - 12q^{9} + O(q^{10})$$ $$80q - 4q^{2} - 16q^{4} - 2q^{5} - 14q^{6} - 4q^{7} - 18q^{8} - 12q^{9} - 6q^{10} - 16q^{11} - 6q^{12} - 4q^{13} - 12q^{14} - 4q^{15} - 4q^{16} + 6q^{17} - 42q^{18} + 6q^{19} - 6q^{20} + 22q^{21} + 16q^{22} - 18q^{23} + 96q^{24} - 8q^{25} - 10q^{26} + 30q^{27} - 48q^{28} - 24q^{29} - 8q^{30} - 8q^{31} - 16q^{32} - 48q^{33} - 22q^{34} + 16q^{35} + 8q^{36} - 40q^{37} + 22q^{38} - 20q^{39} + 58q^{40} - 6q^{41} - 104q^{42} + 56q^{43} - 30q^{44} + 40q^{45} + 104q^{46} - 64q^{47} + 86q^{48} + 8q^{49} + 18q^{50} + 20q^{51} - 66q^{52} - 28q^{53} + 12q^{54} + 28q^{55} + 80q^{56} - 14q^{57} + 68q^{58} - 4q^{59} + 10q^{60} - 12q^{61} + 70q^{62} + 18q^{63} - 62q^{64} - 24q^{65} - 92q^{66} - 32q^{67} + 112q^{68} - 96q^{69} - 12q^{70} - 66q^{71} + 18q^{72} - 4q^{73} - 38q^{74} - 24q^{76} + 90q^{77} + 158q^{78} + 40q^{79} - 30q^{80} - 60q^{81} + 78q^{82} + 86q^{83} + 134q^{84} - 18q^{85} - 102q^{86} + 152q^{87} - 16q^{88} + 28q^{89} - 42q^{90} - 68q^{91} + 42q^{92} + 148q^{93} + 32q^{94} - 16q^{95} - 162q^{96} + 56q^{97} - 12q^{98} + 104q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(115, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
115.2.g.a $$10$$ $$0.918$$ $$\Q(\zeta_{22})$$ None $$5$$ $$1$$ $$1$$ $$5$$ $$q+(\zeta_{22}+\zeta_{22}^{3}-\zeta_{22}^{4}+\zeta_{22}^{5}+\zeta_{22}^{7}+\cdots)q^{2}+\cdots$$
115.2.g.b $$20$$ $$0.918$$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None $$-4$$ $$1$$ $$2$$ $$-4$$ $$q+(-1+\beta _{2}+\beta _{3}+\beta _{4}+\beta _{6}+\beta _{8}+\cdots)q^{2}+\cdots$$
115.2.g.c $$50$$ $$0.918$$ None $$-5$$ $$-2$$ $$-5$$ $$-5$$

## Decomposition of $$S_{2}^{\mathrm{old}}(115, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(115, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(23, [\chi])$$$$^{\oplus 2}$$