# Properties

 Label 175.3.v Level $175$ Weight $3$ Character orbit 175.v Rep. character $\chi_{175}(31,\cdot)$ Character field $\Q(\zeta_{30})$ Dimension $304$ Newform subspaces $1$ Sturm bound $60$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$175 = 5^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 175.v (of order $$30$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$175$$ Character field: $$\Q(\zeta_{30})$$ Newform subspaces: $$1$$ Sturm bound: $$60$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(175, [\chi])$$.

Total New Old
Modular forms 336 336 0
Cusp forms 304 304 0
Eisenstein series 32 32 0

## Trace form

 $$304 q - 3 q^{2} - 9 q^{3} + 69 q^{4} - 15 q^{5} - 18 q^{7} - 46 q^{8} - 105 q^{9} + O(q^{10})$$ $$304 q - 3 q^{2} - 9 q^{3} + 69 q^{4} - 15 q^{5} - 18 q^{7} - 46 q^{8} - 105 q^{9} - 15 q^{10} - 18 q^{11} - 33 q^{12} + 36 q^{14} - 80 q^{15} + 133 q^{16} - 63 q^{17} - 74 q^{18} - 9 q^{19} - 3 q^{21} - 12 q^{22} + 99 q^{23} - 66 q^{24} - 35 q^{25} - 48 q^{26} - 12 q^{28} + 48 q^{29} - 265 q^{30} + 171 q^{31} + 44 q^{32} + 252 q^{33} - 110 q^{35} + 620 q^{36} - 49 q^{37} - 210 q^{38} - 91 q^{39} - 15 q^{40} + 368 q^{42} + 444 q^{43} + 21 q^{44} - 315 q^{45} - 39 q^{46} - 219 q^{47} + 154 q^{49} - 90 q^{50} + 148 q^{51} + 138 q^{52} + 69 q^{53} - 249 q^{54} - 430 q^{56} - 1272 q^{57} - 103 q^{58} + 351 q^{59} + 35 q^{60} - 99 q^{61} + 199 q^{63} - 946 q^{64} - 35 q^{65} - 651 q^{66} - 227 q^{67} - 1842 q^{68} - 975 q^{70} - 362 q^{71} + 36 q^{72} + 33 q^{73} + 246 q^{74} + 135 q^{75} + 291 q^{77} + 202 q^{78} + 97 q^{79} + 1080 q^{80} - 103 q^{81} + 2268 q^{82} - 1209 q^{84} + 1590 q^{85} - 195 q^{86} - 153 q^{87} + 1026 q^{88} + 666 q^{89} + 538 q^{91} + 1858 q^{92} - 814 q^{93} - 489 q^{94} - 75 q^{95} + 1485 q^{96} - 868 q^{98} - 180 q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(175, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
175.3.v.a $304$ $4.768$ None $$-3$$ $$-9$$ $$-15$$ $$-18$$