Properties

Label 175.3.w
Level $175$
Weight $3$
Character orbit 175.w
Rep. character $\chi_{175}(2,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $608$
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.w (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 175 \)
Character field: \(\Q(\zeta_{60})\)
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 672 672 0
Cusp forms 608 608 0
Eisenstein series 64 64 0

Trace form

\( 608 q - 8 q^{2} - 8 q^{3} - 10 q^{4} - 6 q^{5} - 24 q^{6} - 14 q^{7} - 4 q^{8} - 10 q^{9} + O(q^{10}) \) \( 608 q - 8 q^{2} - 8 q^{3} - 10 q^{4} - 6 q^{5} - 24 q^{6} - 14 q^{7} - 4 q^{8} - 10 q^{9} - 24 q^{10} - 6 q^{11} + 36 q^{12} - 32 q^{13} - 20 q^{14} - 92 q^{15} - 262 q^{16} - 102 q^{17} - 6 q^{18} - 10 q^{19} + 32 q^{20} - 12 q^{21} + 16 q^{22} + 56 q^{23} + 6 q^{25} - 16 q^{26} - 116 q^{27} + 34 q^{28} - 240 q^{29} + 166 q^{30} - 6 q^{31} - 140 q^{32} - 126 q^{33} - 40 q^{34} + 330 q^{35} - 568 q^{36} - 54 q^{37} + 304 q^{38} - 410 q^{39} + 148 q^{40} - 24 q^{41} + 350 q^{42} - 324 q^{43} - 10 q^{44} + 414 q^{45} - 6 q^{46} + 198 q^{47} - 68 q^{48} - 440 q^{50} - 16 q^{51} + 88 q^{52} + 382 q^{53} - 10 q^{54} - 248 q^{55} + 52 q^{56} + 584 q^{57} - 8 q^{58} - 410 q^{59} + 828 q^{60} - 6 q^{61} - 1656 q^{62} - 782 q^{63} + 860 q^{64} - 142 q^{65} + 138 q^{66} - 208 q^{67} + 378 q^{68} - 740 q^{69} - 140 q^{70} - 24 q^{71} - 498 q^{72} - 390 q^{73} + 360 q^{75} + 64 q^{76} + 692 q^{77} + 860 q^{78} - 10 q^{79} + 314 q^{80} - 402 q^{81} + 168 q^{82} + 400 q^{83} + 3580 q^{84} - 184 q^{85} - 6 q^{86} + 204 q^{87} - 1042 q^{88} - 760 q^{89} - 940 q^{90} - 12 q^{91} - 1412 q^{92} - 662 q^{93} - 10 q^{94} - 242 q^{95} - 54 q^{96} - 528 q^{97} - 262 q^{98} + O(q^{100}) \)

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.w.a 175.w 175.w $608$ $4.768$ None \(-8\) \(-8\) \(-6\) \(-14\) $\mathrm{SU}(2)[C_{60}]$