# Properties

 Label 102.2.i Level $102$ Weight $2$ Character orbit 102.i Rep. character $\chi_{102}(5,\cdot)$ Character field $\Q(\zeta_{16})$ Dimension $48$ Newform subspaces $2$ Sturm bound $36$ Trace bound $11$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$102 = 2 \cdot 3 \cdot 17$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 102.i (of order $$16$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$51$$ Character field: $$\Q(\zeta_{16})$$ Newform subspaces: $$2$$ Sturm bound: $$36$$ Trace bound: $$11$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(102, [\chi])$$.

Total New Old
Modular forms 176 48 128
Cusp forms 112 48 64
Eisenstein series 64 0 64

## Trace form

 $$48 q + O(q^{10})$$ $$48 q - 8 q^{12} - 48 q^{15} - 32 q^{18} - 48 q^{21} - 8 q^{24} - 32 q^{25} - 32 q^{31} - 32 q^{37} + 32 q^{39} + 48 q^{42} - 16 q^{43} + 64 q^{45} + 32 q^{46} + 64 q^{49} + 64 q^{51} + 32 q^{52} + 56 q^{54} + 64 q^{55} + 72 q^{57} + 32 q^{58} + 32 q^{60} + 32 q^{61} + 8 q^{66} - 32 q^{69} - 32 q^{70} - 128 q^{73} - 48 q^{75} - 64 q^{79} - 8 q^{81} - 128 q^{82} - 64 q^{85} + 48 q^{87} - 32 q^{88} - 128 q^{91} + 64 q^{93} - 64 q^{94} - 32 q^{97} + 40 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(102, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
102.2.i.a $24$ $0.814$ None $$0$$ $$0$$ $$0$$ $$0$$
102.2.i.b $24$ $0.814$ None $$0$$ $$0$$ $$0$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(102, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(102, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(51, [\chi])$$$$^{\oplus 2}$$