# Properties

 Label 49.2.e Level $49$ Weight $2$ Character orbit 49.e Rep. character $\chi_{49}(8,\cdot)$ Character field $\Q(\zeta_{7})$ Dimension $18$ Newform subspaces $2$ Sturm bound $9$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$49 = 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 49.e (of order $$7$$ and degree $$6$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$49$$ Character field: $$\Q(\zeta_{7})$$ Newform subspaces: $$2$$ Sturm bound: $$9$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(49, [\chi])$$.

Total New Old
Modular forms 30 30 0
Cusp forms 18 18 0
Eisenstein series 12 12 0

## Trace form

 $$18 q - 5 q^{2} - 3 q^{3} - 5 q^{4} - q^{5} - 9 q^{6} + 5 q^{8} - 14 q^{9} + O(q^{10})$$ $$18 q - 5 q^{2} - 3 q^{3} - 5 q^{4} - q^{5} - 9 q^{6} + 5 q^{8} - 14 q^{9} + 11 q^{10} - 6 q^{11} - 14 q^{12} + 7 q^{13} - 21 q^{14} - 3 q^{15} + 13 q^{16} + 4 q^{17} + 16 q^{18} - 22 q^{19} + 7 q^{20} + 21 q^{21} + 5 q^{22} - 12 q^{23} + 11 q^{24} + 14 q^{25} + 21 q^{26} + 12 q^{27} - 27 q^{29} + 40 q^{30} - 24 q^{31} - 3 q^{32} + 41 q^{33} - 37 q^{34} + 21 q^{35} + q^{36} - 26 q^{37} + 25 q^{38} - 7 q^{39} - 15 q^{40} + 21 q^{41} - 49 q^{42} + 29 q^{43} - 13 q^{44} - 55 q^{45} + 3 q^{46} - 36 q^{47} + 12 q^{48} + 14 q^{49} - 76 q^{50} + 19 q^{51} - 7 q^{52} - 20 q^{53} + 50 q^{54} - 47 q^{55} - 14 q^{56} + 11 q^{57} - 31 q^{58} + 25 q^{59} - 35 q^{60} - 15 q^{61} + 61 q^{62} + 7 q^{63} + 27 q^{64} + 49 q^{65} - 31 q^{66} + 36 q^{67} + 28 q^{68} + 5 q^{69} + 35 q^{70} - 34 q^{71} + 4 q^{72} + 46 q^{73} + 59 q^{74} - 9 q^{75} + 56 q^{77} - 7 q^{78} + 44 q^{79} + 32 q^{80} - 48 q^{81} + 14 q^{82} - 21 q^{83} + 28 q^{84} + 11 q^{85} - 3 q^{86} + 43 q^{87} + 5 q^{88} - q^{89} - 4 q^{90} - 91 q^{91} + 44 q^{92} - 65 q^{93} - 80 q^{94} - 8 q^{95} - 98 q^{96} - 28 q^{97} - 7 q^{98} - 20 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(49, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
49.2.e.a $6$ $0.391$ $$\Q(\zeta_{14})$$ None $$-3$$ $$-3$$ $$6$$ $$7$$ $$q+(-1+\zeta_{14}-\zeta_{14}^{4}+\zeta_{14}^{5})q^{2}+\cdots$$
49.2.e.b $12$ $0.391$ $$\Q(\zeta_{21})$$ None $$-2$$ $$0$$ $$-7$$ $$-7$$ $$q+(\zeta_{21}^{2}+\zeta_{21}^{4}-\zeta_{21}^{5}-\zeta_{21}^{9}+\zeta_{21}^{11})q^{2}+\cdots$$