Properties

Label 175.2.q
Level 175
Weight 2
Character orbit q
Rep. character \(\chi_{175}(11,\cdot)\)
Character field \(\Q(\zeta_{15})\)
Dimension 144
Newforms 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: \(\Q(\zeta_{15})\)
Newforms: \( 1 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(175, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
175.2.q.a \(144\) \(1.397\) None \(-3\) \(-3\) \(-3\) \(-22\)