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
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.n (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 25 \)
Character field: \(\Q(\zeta_{10})\)
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 88 56 32
Cusp forms 72 56 16
Eisenstein series 16 0 16

Trace form

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

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

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

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