# Properties

 Label 21.22.c Level $21$ Weight $22$ Character orbit 21.c Rep. character $\chi_{21}(20,\cdot)$ Character field $\Q$ Dimension $54$ Newform subspaces $2$ Sturm bound $58$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$21 = 3 \cdot 7$$ Weight: $$k$$ $$=$$ $$22$$ Character orbit: $$[\chi]$$ $$=$$ 21.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$21$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$58$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{22}(21, [\chi])$$.

Total New Old
Modular forms 58 58 0
Cusp forms 54 54 0
Eisenstein series 4 4 0

## Trace form

 $$54q - 54525956q^{4} + 298304168q^{7} - 10770061710q^{9} + O(q^{10})$$ $$54q - 54525956q^{4} + 298304168q^{7} - 10770061710q^{9} - 687153165468q^{15} + 45037875412612q^{16} + 36759093002772q^{18} - 21361304207298q^{21} + 228880341648112q^{22} + 3548494642823562q^{25} - 2685628339220812q^{28} - 2422487119598196q^{30} + 50795822386155600q^{36} + 4299402242744668q^{37} - 9657429075015348q^{39} - 125754675449474820q^{42} + 277691869261125616q^{43} - 1124214920076830456q^{46} + 906809781130583982q^{49} + 4341973540932052200q^{51} - 4914506248901334432q^{57} - 10814528487339424568q^{58} + 13643758017961015644q^{60} - 26425051438882828836q^{63} - 12033810960284129284q^{64} - 11658587217124746000q^{67} + 73727169165159410040q^{70} + 39846964674222889428q^{72} + 45848199464273536260q^{78} + 535346775587250893472q^{79} + 454337585225870025006q^{81} - 585257506869205373580q^{84} - 570842672309470848672q^{85} - 1060053674241923431168q^{88} - 13967188170478076112q^{91} - 3089212290687116419284q^{93} + 1525182290356701596928q^{99} + O(q^{100})$$

## Decomposition of $$S_{22}^{\mathrm{new}}(21, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
21.22.c.a $$2$$ $$58.690$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ $$0$$ $$0$$ $$0$$ $$-1123983020$$ $$q+3^{8}\zeta_{6}q^{3}+2^{21}q^{4}+(-561991510+\cdots)q^{7}+\cdots$$
21.22.c.b $$52$$ $$58.690$$ None $$0$$ $$0$$ $$0$$ $$1422287188$$