# Properties

 Label 7.7.b Level $7$ Weight $7$ Character orbit 7.b Rep. character $\chi_{7}(6,\cdot)$ Character field $\Q$ Dimension $3$ Newform subspaces $2$ Sturm bound $4$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$7$$ Weight: $$k$$ $$=$$ $$7$$ Character orbit: $$[\chi]$$ $$=$$ 7.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$4$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{7}(7, [\chi])$$.

Total New Old
Modular forms 5 5 0
Cusp forms 3 3 0
Eisenstein series 2 2 0

## Trace form

 $$3 q - 7 q^{2} + 17 q^{4} - 77 q^{7} + 601 q^{8} - 1893 q^{9} + O(q^{10})$$ $$3 q - 7 q^{2} + 17 q^{4} - 77 q^{7} + 601 q^{8} - 1893 q^{9} + 3710 q^{11} - 5215 q^{14} + 4080 q^{15} - 13087 q^{16} + 27537 q^{18} - 28560 q^{21} + 3674 q^{22} - 13258 q^{23} + 42795 q^{25} - 5831 q^{28} + 1070 q^{29} - 32640 q^{30} - 16983 q^{32} + 28560 q^{35} + 12393 q^{36} + 107198 q^{37} - 199920 q^{39} + 228480 q^{42} - 63778 q^{43} + 33354 q^{44} - 280414 q^{46} - 46893 q^{49} - 76735 q^{50} + 538560 q^{51} - 102466 q^{53} + 281281 q^{56} - 281520 q^{57} - 369334 q^{58} - 598773 q^{63} + 684721 q^{64} + 199920 q^{65} + 936558 q^{67} - 228480 q^{70} - 611290 q^{71} - 1650831 q^{72} + 862714 q^{74} - 440482 q^{77} + 1599360 q^{78} - 140490 q^{79} + 994563 q^{81} - 538560 q^{85} - 1642214 q^{86} + 65050 q^{88} - 1399440 q^{91} - 386478 q^{92} + 2480640 q^{93} + 281520 q^{95} + 2375177 q^{98} - 861330 q^{99} + O(q^{100})$$

## Decomposition of $$S_{7}^{\mathrm{new}}(7, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
7.7.b.a $1$ $1.610$ $$\Q$$ $$\Q(\sqrt{-7})$$ $$9$$ $$0$$ $$0$$ $$-343$$ $$q+9q^{2}+17q^{4}-7^{3}q^{7}-423q^{8}+\cdots$$
7.7.b.b $2$ $1.610$ $$\Q(\sqrt{-510})$$ None $$-16$$ $$0$$ $$0$$ $$266$$ $$q-8q^{2}+\beta q^{3}-\beta q^{5}-8\beta q^{6}+(133+\cdots)q^{7}+\cdots$$