Properties

 Label 35.3.d Level $35$ Weight $3$ Character orbit 35.d Rep. character $\chi_{35}(6,\cdot)$ Character field $\Q$ Dimension $4$ Newform subspaces $2$ Sturm bound $12$ Trace bound $2$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$35 = 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 35.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$12$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$2$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(35, [\chi])$$.

Total New Old
Modular forms 10 4 6
Cusp forms 6 4 2
Eisenstein series 4 0 4

Trace form

 $$4 q + 2 q^{2} - 6 q^{4} + 10 q^{7} - 2 q^{8} - 14 q^{9} + O(q^{10})$$ $$4 q + 2 q^{2} - 6 q^{4} + 10 q^{7} - 2 q^{8} - 14 q^{9} + 2 q^{11} - 22 q^{14} - 10 q^{15} - 22 q^{16} + 38 q^{18} + 30 q^{21} - 8 q^{22} + 68 q^{23} - 20 q^{25} - 42 q^{28} + 38 q^{29} + 40 q^{30} - 66 q^{32} - 30 q^{35} + 66 q^{36} - 28 q^{37} + 30 q^{39} + 60 q^{42} - 232 q^{43} - 12 q^{44} - 20 q^{46} + 16 q^{49} - 10 q^{50} - 270 q^{51} + 80 q^{53} + 130 q^{56} + 180 q^{57} + 208 q^{58} + 60 q^{60} - 170 q^{63} + 154 q^{64} + 150 q^{65} + 32 q^{67} - 60 q^{70} + 152 q^{71} - 218 q^{72} - 140 q^{74} + 32 q^{77} - 300 q^{78} + 38 q^{79} - 176 q^{81} - 90 q^{85} - 260 q^{86} + 44 q^{88} + 270 q^{91} - 156 q^{92} + 660 q^{93} - 262 q^{98} - 52 q^{99} + O(q^{100})$$

Decomposition of $$S_{3}^{\mathrm{new}}(35, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
35.3.d.a $2$ $0.954$ $$\Q(\sqrt{-5})$$ None $$-2$$ $$0$$ $$0$$ $$14$$ $$q-q^{2}+2\beta q^{3}-3q^{4}+\beta q^{5}-2\beta q^{6}+\cdots$$
35.3.d.b $2$ $0.954$ $$\Q(\sqrt{-5})$$ None $$4$$ $$0$$ $$0$$ $$-4$$ $$q+2q^{2}+\beta q^{3}-\beta q^{5}+2\beta q^{6}+(-2+\cdots)q^{7}+\cdots$$

Decomposition of $$S_{3}^{\mathrm{old}}(35, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(35, [\chi]) \simeq$$ $$S_{3}^{\mathrm{new}}(7, [\chi])$$$$^{\oplus 2}$$