Properties

Label 175.2.n
Level 175
Weight 2
Character orbit n
Rep. character \(\chi_{175}(29,\cdot)\)
Character field \(\Q(\zeta_{10})\)
Dimension 56
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.n (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 25 \)
Character field: \(\Q(\zeta_{10})\)
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 88 56 32
Cusp forms 72 56 16
Eisenstein series 16 0 16

Trace form

\( 56q + 12q^{4} - 6q^{5} + 6q^{9} + O(q^{10}) \) \( 56q + 12q^{4} - 6q^{5} + 6q^{9} - 4q^{10} + 8q^{11} - 40q^{12} - 4q^{14} - 18q^{15} - 32q^{16} + 12q^{19} + 12q^{20} + 4q^{21} - 30q^{22} + 10q^{23} - 28q^{24} + 4q^{25} + 12q^{26} + 30q^{27} - 2q^{29} + 28q^{30} + 12q^{31} + 20q^{33} + 2q^{35} - 14q^{36} - 70q^{37} - 70q^{38} - 4q^{39} - 30q^{40} + 4q^{41} + 50q^{42} + 22q^{44} - 52q^{45} - 4q^{46} - 10q^{47} + 30q^{48} - 56q^{49} - 54q^{50} - 44q^{51} - 20q^{53} + 54q^{54} - 2q^{55} + 12q^{56} + 10q^{58} - 6q^{59} + 16q^{60} - 4q^{61} + 50q^{62} + 20q^{63} + 24q^{64} - 18q^{65} - 74q^{66} + 10q^{67} - 78q^{69} + 8q^{70} - 8q^{71} + 140q^{72} + 40q^{73} + 60q^{74} - 8q^{75} + 52q^{76} - 20q^{77} - 90q^{78} + 124q^{80} - 72q^{81} - 30q^{83} - 12q^{84} + 96q^{85} - 20q^{86} + 30q^{87} + 140q^{88} + 38q^{89} - 8q^{90} + 8q^{91} + 80q^{92} + 88q^{94} - 70q^{95} - 28q^{96} - 30q^{97} + 60q^{99} + O(q^{100}) \)

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.n.a \(56\) \(1.397\) None \(0\) \(0\) \(-6\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(175, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(175, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database