# Properties

 Label 83.7.b Level $83$ Weight $7$ Character orbit 83.b Rep. character $\chi_{83}(82,\cdot)$ Character field $\Q$ Dimension $41$ Newform subspaces $3$ Sturm bound $49$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$83$$ Weight: $$k$$ $$=$$ $$7$$ Character orbit: $$[\chi]$$ $$=$$ 83.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$83$$ Character field: $$\Q$$ Newform subspaces: $$3$$ Sturm bound: $$49$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$, $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{7}(83, [\chi])$$.

Total New Old
Modular forms 43 43 0
Cusp forms 41 41 0
Eisenstein series 2 2 0

## Trace form

 $$41 q + 18 q^{3} - 1150 q^{4} + 262 q^{7} + 11255 q^{9} + O(q^{10})$$ $$41 q + 18 q^{3} - 1150 q^{4} + 262 q^{7} + 11255 q^{9} + 2058 q^{10} - 998 q^{11} + 2542 q^{12} + 16682 q^{16} + 12194 q^{17} - 34164 q^{21} + 26574 q^{23} - 132691 q^{25} + 69298 q^{26} + 51660 q^{27} + 13948 q^{28} - 35418 q^{29} + 15200 q^{30} - 81746 q^{31} - 130788 q^{33} - 201072 q^{36} - 27650 q^{37} + 60478 q^{38} - 73434 q^{40} - 149862 q^{41} + 165158 q^{44} - 388934 q^{48} + 744219 q^{49} + 121164 q^{51} + 668362 q^{59} - 850010 q^{61} + 495730 q^{63} + 732086 q^{64} + 1043648 q^{65} - 82256 q^{68} - 147292 q^{69} - 3597600 q^{70} - 698790 q^{75} + 1440724 q^{77} + 953724 q^{78} + 4374157 q^{81} + 509677 q^{83} + 1340702 q^{84} + 18150 q^{86} + 314356 q^{87} + 1165418 q^{90} - 1855466 q^{92} + 1165124 q^{93} - 5928444 q^{94} + 1075920 q^{95} - 5590658 q^{99} + O(q^{100})$$

## Decomposition of $$S_{7}^{\mathrm{new}}(83, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
83.7.b.a $1$ $19.094$ $$\Q$$ $$\Q(\sqrt{-83})$$ $$0$$ $$-29$$ $$0$$ $$-61$$ $$q-29q^{3}+2^{6}q^{4}-61q^{7}+112q^{9}+\cdots$$
83.7.b.b $2$ $19.094$ $$\Q(\sqrt{249})$$ $$\Q(\sqrt{-83})$$ $$0$$ $$29$$ $$0$$ $$61$$ $$q+(15+\beta )q^{3}+2^{6}q^{4}+(23-15\beta )q^{7}+\cdots$$
83.7.b.c $38$ $19.094$ None $$0$$ $$18$$ $$0$$ $$262$$