# Properties

 Label 154.2.n Level $154$ Weight $2$ Character orbit 154.n Rep. character $\chi_{154}(17,\cdot)$ Character field $\Q(\zeta_{30})$ Dimension $64$ Newform subspaces $1$ Sturm bound $48$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$154 = 2 \cdot 7 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 154.n (of order $$30$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$77$$ Character field: $$\Q(\zeta_{30})$$ Newform subspaces: $$1$$ Sturm bound: $$48$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(154, [\chi])$$.

Total New Old
Modular forms 224 64 160
Cusp forms 160 64 96
Eisenstein series 64 0 64

## Trace form

 $$64 q - 8 q^{4} + 12 q^{5} - 10 q^{7} + 4 q^{9} + O(q^{10})$$ $$64 q - 8 q^{4} + 12 q^{5} - 10 q^{7} + 4 q^{9} - 8 q^{11} - 2 q^{14} - 12 q^{15} + 8 q^{16} - 30 q^{17} + 8 q^{22} - 16 q^{23} - 20 q^{25} - 24 q^{26} + 10 q^{28} + 20 q^{29} - 18 q^{31} - 126 q^{33} + 30 q^{35} - 32 q^{36} + 16 q^{37} - 12 q^{38} + 20 q^{39} - 30 q^{40} - 2 q^{42} - 2 q^{44} + 108 q^{45} - 24 q^{47} - 78 q^{49} - 60 q^{51} + 8 q^{53} + 4 q^{56} - 80 q^{57} - 28 q^{58} - 60 q^{59} + 4 q^{60} + 30 q^{61} + 50 q^{63} + 16 q^{64} + 72 q^{66} - 32 q^{67} + 30 q^{68} - 10 q^{70} - 8 q^{71} + 20 q^{72} + 90 q^{73} + 20 q^{74} + 180 q^{75} + 46 q^{77} + 96 q^{78} + 30 q^{79} + 18 q^{80} + 48 q^{81} + 60 q^{82} + 40 q^{84} + 140 q^{85} + 10 q^{86} + 14 q^{88} - 36 q^{89} + 106 q^{91} + 28 q^{92} + 94 q^{93} - 120 q^{94} - 70 q^{95} + 104 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(154, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
154.2.n.a $64$ $1.230$ None $$0$$ $$0$$ $$12$$ $$-10$$

## Decomposition of $$S_{2}^{\mathrm{old}}(154, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(154, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(77, [\chi])$$$$^{\oplus 2}$$