# Properties

 Label 21.7.f Level $21$ Weight $7$ Character orbit 21.f Rep. character $\chi_{21}(10,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $16$ Newform subspaces $2$ Sturm bound $18$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$21 = 3 \cdot 7$$ Weight: $$k$$ $$=$$ $$7$$ Character orbit: $$[\chi]$$ $$=$$ 21.f (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$2$$ Sturm bound: $$18$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{7}(21, [\chi])$$.

Total New Old
Modular forms 36 16 20
Cusp forms 28 16 12
Eisenstein series 8 0 8

## Trace form

 $$16 q - 10 q^{2} - 346 q^{4} - 336 q^{5} + 92 q^{7} + 2872 q^{8} + 1944 q^{9} + O(q^{10})$$ $$16 q - 10 q^{2} - 346 q^{4} - 336 q^{5} + 92 q^{7} + 2872 q^{8} + 1944 q^{9} - 3150 q^{10} - 1384 q^{11} + 710 q^{14} + 4536 q^{15} - 8810 q^{16} + 1680 q^{17} + 2430 q^{18} - 42840 q^{19} + 17496 q^{21} + 86028 q^{22} - 11296 q^{23} - 51030 q^{24} + 5236 q^{25} - 6678 q^{26} + 81622 q^{28} + 24224 q^{29} + 33048 q^{30} - 49308 q^{31} - 116004 q^{32} - 20412 q^{33} - 268296 q^{35} - 168156 q^{36} + 19036 q^{37} + 426174 q^{38} + 122472 q^{39} + 126882 q^{40} + 228744 q^{42} - 399920 q^{43} - 96300 q^{44} - 81648 q^{45} + 414300 q^{46} + 566160 q^{47} - 286568 q^{49} - 251668 q^{50} + 114696 q^{51} - 951132 q^{52} - 554008 q^{53} - 114824 q^{56} - 114696 q^{57} + 380298 q^{58} + 1628592 q^{59} + 283338 q^{60} + 25368 q^{61} - 54432 q^{63} + 968180 q^{64} - 803208 q^{65} - 1163484 q^{66} - 774808 q^{67} - 2437596 q^{68} + 1493922 q^{70} + 1668032 q^{71} + 348948 q^{72} + 524412 q^{73} + 752590 q^{74} + 1061424 q^{75} + 738320 q^{77} - 565380 q^{78} + 51860 q^{79} - 1247232 q^{80} - 472392 q^{81} - 1213632 q^{82} - 2459160 q^{84} + 1678464 q^{85} - 1486178 q^{86} + 551124 q^{87} - 61554 q^{88} - 2759232 q^{89} - 2656272 q^{91} + 565656 q^{92} + 1167372 q^{93} - 2553768 q^{94} + 568320 q^{95} + 6923070 q^{96} + 9242096 q^{98} - 672624 q^{99} + O(q^{100})$$

## Decomposition of $$S_{7}^{\mathrm{new}}(21, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
21.7.f.a $$8$$ $$4.831$$ $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ None $$-5$$ $$-108$$ $$-294$$ $$-656$$ $$q+(-1-\beta _{1}+\beta _{2})q^{2}+(-18+9\beta _{2}+\cdots)q^{3}+\cdots$$
21.7.f.b $$8$$ $$4.831$$ $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ None $$-5$$ $$108$$ $$-42$$ $$748$$ $$q+(-\beta _{1}-\beta _{2})q^{2}+(9+9\beta _{2})q^{3}+(-43+\cdots)q^{4}+\cdots$$

## Decomposition of $$S_{7}^{\mathrm{old}}(21, [\chi])$$ into lower level spaces

$$S_{7}^{\mathrm{old}}(21, [\chi]) \cong$$ $$S_{7}^{\mathrm{new}}(7, [\chi])$$$$^{\oplus 2}$$