# Properties

 Label 289.4.b Level $289$ Weight $4$ Character orbit 289.b Rep. character $\chi_{289}(288,\cdot)$ Character field $\Q$ Dimension $60$ Newform subspaces $6$ Sturm bound $102$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$289 = 17^{2}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 289.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$17$$ Character field: $$\Q$$ Newform subspaces: $$6$$ Sturm bound: $$102$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(289, [\chi])$$.

Total New Old
Modular forms 86 74 12
Cusp forms 68 60 8
Eisenstein series 18 14 4

## Trace form

 $$60 q + 2 q^{2} + 222 q^{4} + 18 q^{8} - 392 q^{9} + O(q^{10})$$ $$60 q + 2 q^{2} + 222 q^{4} + 18 q^{8} - 392 q^{9} - 164 q^{13} - 12 q^{15} + 878 q^{16} - 290 q^{18} + 100 q^{19} - 144 q^{21} - 388 q^{25} + 492 q^{26} - 1202 q^{30} - 264 q^{32} + 1256 q^{33} - 1076 q^{35} - 536 q^{36} - 272 q^{38} + 882 q^{42} + 392 q^{43} - 1044 q^{47} - 1016 q^{49} + 1720 q^{50} - 932 q^{52} + 268 q^{53} - 252 q^{55} + 1032 q^{59} + 926 q^{60} - 1670 q^{64} - 1740 q^{66} + 244 q^{67} - 1688 q^{69} + 52 q^{70} + 1376 q^{72} + 188 q^{76} - 464 q^{77} + 2788 q^{81} + 2700 q^{83} - 2484 q^{84} + 3294 q^{86} - 40 q^{87} - 2120 q^{89} - 968 q^{93} - 540 q^{94} - 128 q^{98} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(289, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
289.4.b.a $2$ $17.052$ $$\Q(\sqrt{-1})$$ None $$6$$ $$0$$ $$0$$ $$0$$ $$q+3q^{2}-4iq^{3}+q^{4}+3iq^{5}-12iq^{6}+\cdots$$
289.4.b.b $6$ $17.052$ 6.0.27793984.1 None $$-2$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{2}+(\beta _{2}+\beta _{4}-\beta _{5})q^{3}+(8-\beta _{1}+\cdots)q^{4}+\cdots$$
289.4.b.c $8$ $17.052$ $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ None $$-8$$ $$0$$ $$0$$ $$0$$ $$q+(-1+\beta _{3})q^{2}-\beta _{4}q^{3}+(5-\beta _{3}-\beta _{6}+\cdots)q^{4}+\cdots$$
289.4.b.d $8$ $17.052$ $$\mathbb{Q}[x]/(x^{8} + \cdots)$$ None $$-2$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{2}+(\beta _{1}-\beta _{5}+\beta _{6})q^{3}+(3-\beta _{2}+\cdots)q^{4}+\cdots$$
289.4.b.e $12$ $17.052$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$8$$ $$0$$ $$0$$ $$0$$ $$q+(1-\beta _{6})q^{2}+\beta _{11}q^{3}+(2+2\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots$$
289.4.b.f $24$ $17.052$ None $$0$$ $$0$$ $$0$$ $$0$$

## Decomposition of $$S_{4}^{\mathrm{old}}(289, [\chi])$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(289, [\chi]) \cong$$ $$S_{4}^{\mathrm{new}}(17, [\chi])$$$$^{\oplus 2}$$