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
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

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

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

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

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database