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 $0$

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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 Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
175.3.v.a 175.v 175.v $304$ $4.768$ None \(-3\) \(-9\) \(-15\) \(-18\) $\mathrm{SU}(2)[C_{30}]$