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Properties

Label 175.2.q
Level $175$
Weight $2$
Character orbit 175.q
Rep. character $\chi_{175}(11,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $144$
Newform subspaces $1$
Sturm bound $40$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 175 = 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 175.q (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 175 \)
Character field: \(\Q(\zeta_{15})\)
Newform subspaces: \( 1 \)
Sturm bound: \(40\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(175, [\chi])\).

Total New Old
Modular forms 176 176 0
Cusp forms 144 144 0
Eisenstein series 32 32 0

Trace form

\( 144 q - 3 q^{2} - 3 q^{3} + 13 q^{4} - 3 q^{5} - 12 q^{6} - 22 q^{7} - 2 q^{8} + 11 q^{9} + O(q^{10}) \) \( 144 q - 3 q^{2} - 3 q^{3} + 13 q^{4} - 3 q^{5} - 12 q^{6} - 22 q^{7} - 2 q^{8} + 11 q^{9} - 3 q^{10} - 6 q^{11} - 11 q^{12} - 12 q^{13} - 6 q^{14} - 64 q^{15} + 13 q^{16} + 9 q^{17} - 18 q^{18} - 11 q^{19} - 24 q^{20} - 3 q^{21} - 52 q^{22} - 17 q^{23} + 46 q^{24} - 3 q^{25} + 44 q^{26} - 84 q^{27} + 62 q^{28} - 24 q^{29} - 27 q^{30} - 21 q^{31} - 16 q^{32} - 18 q^{33} - 36 q^{34} + 24 q^{35} - 104 q^{36} - 5 q^{37} - 12 q^{38} + 25 q^{39} + q^{40} + 38 q^{41} - 58 q^{42} + 20 q^{43} - 7 q^{44} - 45 q^{45} + 21 q^{46} - q^{47} - 12 q^{48} - 38 q^{49} + 66 q^{50} - 8 q^{51} + 50 q^{52} + 37 q^{53} + 15 q^{54} - 28 q^{55} - 60 q^{56} + 136 q^{57} + 53 q^{58} - 39 q^{59} + 9 q^{60} - 13 q^{61} + 124 q^{62} + 75 q^{63} + 42 q^{64} - 9 q^{65} + 7 q^{66} - 13 q^{67} - 110 q^{68} + 50 q^{69} - 5 q^{70} + 22 q^{71} - 18 q^{72} - 41 q^{73} - 10 q^{74} + 27 q^{75} - 276 q^{76} + 37 q^{77} + 2 q^{78} + 9 q^{79} - 94 q^{80} + 57 q^{81} - 108 q^{82} + 86 q^{83} - 29 q^{84} - 58 q^{85} - 17 q^{86} - 7 q^{87} - 26 q^{88} - 42 q^{89} + 376 q^{90} - 34 q^{91} - 62 q^{92} + 98 q^{93} - 11 q^{94} + 45 q^{95} + 13 q^{96} + 96 q^{97} - 86 q^{98} - 68 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(175, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
175.2.q.a 175.q 175.q $144$ $1.397$ None \(-3\) \(-3\) \(-3\) \(-22\) $\mathrm{SU}(2)[C_{15}]$