# Properties

 Label 35.4.e Level $35$ Weight $4$ Character orbit 35.e Rep. character $\chi_{35}(11,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $16$ Newform subspaces $3$ Sturm bound $16$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$35 = 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 35.e (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$3$$ Sturm bound: $$16$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(35, [\chi])$$.

Total New Old
Modular forms 28 16 12
Cusp forms 20 16 4
Eisenstein series 8 0 8

## Trace form

 $$16 q + 2 q^{2} + 12 q^{3} - 42 q^{4} + 10 q^{5} + 8 q^{6} - 68 q^{7} + 36 q^{8} - 42 q^{9} + O(q^{10})$$ $$16 q + 2 q^{2} + 12 q^{3} - 42 q^{4} + 10 q^{5} + 8 q^{6} - 68 q^{7} + 36 q^{8} - 42 q^{9} + 20 q^{10} - 30 q^{11} + 34 q^{12} + 48 q^{13} + 70 q^{14} + 40 q^{15} - 86 q^{16} + 132 q^{17} + 48 q^{18} - 18 q^{19} - 280 q^{20} + 242 q^{21} + 688 q^{22} - 248 q^{23} - 728 q^{24} - 200 q^{25} - 278 q^{26} - 840 q^{27} + 770 q^{28} - 444 q^{29} + 140 q^{30} - 168 q^{31} + 98 q^{32} + 320 q^{33} + 824 q^{34} - 110 q^{35} + 2028 q^{36} + 820 q^{37} - 96 q^{38} + 188 q^{39} + 240 q^{40} - 384 q^{41} - 2970 q^{42} - 768 q^{43} - 890 q^{44} + 600 q^{45} - 142 q^{46} + 624 q^{47} + 164 q^{48} + 866 q^{49} - 100 q^{50} - 268 q^{51} + 668 q^{52} + 4 q^{53} + 72 q^{54} - 640 q^{55} - 1464 q^{56} + 1448 q^{57} - 1842 q^{58} - 1188 q^{59} - 810 q^{60} - 2434 q^{61} + 360 q^{62} + 2660 q^{63} - 588 q^{64} - 110 q^{65} - 1988 q^{66} + 448 q^{67} + 4696 q^{68} + 3324 q^{69} + 1600 q^{70} + 3952 q^{71} + 1472 q^{72} + 1156 q^{73} + 2270 q^{74} + 300 q^{75} + 852 q^{76} - 1512 q^{77} - 11000 q^{78} + 240 q^{79} + 1280 q^{80} + 788 q^{81} - 2050 q^{82} - 5280 q^{83} - 876 q^{84} - 1280 q^{85} + 3104 q^{86} - 1684 q^{87} - 3680 q^{88} - 1778 q^{89} + 540 q^{90} - 2124 q^{91} - 292 q^{92} + 780 q^{93} + 2210 q^{94} - 300 q^{95} - 6404 q^{96} + 1744 q^{97} + 7654 q^{98} + 2172 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(35, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
35.4.e.a $2$ $2.065$ $$\Q(\sqrt{-3})$$ None $$-3$$ $$2$$ $$-5$$ $$-28$$ $$q-3\zeta_{6}q^{2}+(2-2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$$
35.4.e.b $4$ $2.065$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$6$$ $$2$$ $$-10$$ $$22$$ $$q+(\beta _{1}-3\beta _{2}+\beta _{3})q^{2}+(1+3\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots$$
35.4.e.c $10$ $2.065$ $$\mathbb{Q}[x]/(x^{10} - \cdots)$$ None $$-1$$ $$8$$ $$25$$ $$-62$$ $$q+(\beta _{1}-\beta _{2})q^{2}+(-\beta _{3}-\beta _{5}+2\beta _{6}+\cdots)q^{3}+\cdots$$

## Decomposition of $$S_{4}^{\mathrm{old}}(35, [\chi])$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(35, [\chi]) \simeq$$ $$S_{4}^{\mathrm{new}}(7, [\chi])$$$$^{\oplus 2}$$