Properties

 Label 154.2.i Level $154$ Weight $2$ Character orbit 154.i Rep. character $\chi_{154}(87,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $16$ 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.i (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$77$$ Character field: $$\Q(\zeta_{6})$$ 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 56 16 40
Cusp forms 40 16 24
Eisenstein series 16 0 16

Trace form

 $$16 q + 8 q^{4} - 12 q^{5} + 16 q^{9} + O(q^{10})$$ $$16 q + 8 q^{4} - 12 q^{5} + 16 q^{9} + 8 q^{11} - 8 q^{14} - 8 q^{15} - 8 q^{16} - 8 q^{22} + 16 q^{23} - 36 q^{26} - 12 q^{31} - 24 q^{33} + 32 q^{36} - 16 q^{37} + 12 q^{38} + 12 q^{42} - 8 q^{44} - 108 q^{45} + 24 q^{47} + 8 q^{49} - 28 q^{53} - 4 q^{56} - 12 q^{58} + 60 q^{59} - 4 q^{60} - 16 q^{64} + 48 q^{66} + 12 q^{67} + 60 q^{70} + 8 q^{71} + 60 q^{75} + 44 q^{77} - 16 q^{78} + 12 q^{80} - 8 q^{81} + 20 q^{86} - 4 q^{88} + 96 q^{89} - 36 q^{91} + 32 q^{92} - 44 q^{93} + 56 q^{99} + O(q^{100})$$

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.i.a $16$ $1.230$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$-12$$ $$0$$ $$q+\beta _{1}q^{2}+(-\beta _{3}+\beta _{4}+\beta _{13})q^{3}+\beta _{10}q^{4}+\cdots$$

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

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