Properties

Label 175.2.s
Level 175
Weight 2
Character orbit s
Rep. character \(\chi_{175}(13,\cdot)\)
Character field \(\Q(\zeta_{20})\)
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.s (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 175 \)
Character field: \(\Q(\zeta_{20})\)
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

\( 144q - 16q^{2} - 20q^{4} - 14q^{7} - 12q^{8} - 20q^{9} + O(q^{10}) \) \( 144q - 16q^{2} - 20q^{4} - 14q^{7} - 12q^{8} - 20q^{9} - 12q^{11} - 10q^{14} - 20q^{15} + 12q^{16} - 28q^{18} - 6q^{21} + 16q^{22} - 8q^{23} - 20q^{25} - 70q^{28} + 40q^{30} - 20q^{32} - 40q^{35} - 28q^{36} + 4q^{37} - 60q^{39} - 30q^{42} + 72q^{43} - 20q^{44} - 12q^{46} + 140q^{50} - 32q^{51} - 104q^{53} - 22q^{56} + 120q^{57} - 32q^{58} - 120q^{60} + 48q^{63} + 40q^{64} - 20q^{65} - 16q^{67} + 90q^{70} - 12q^{71} - 64q^{72} + 74q^{77} + 60q^{78} - 20q^{79} - 8q^{81} + 190q^{84} - 12q^{86} + 92q^{88} - 6q^{91} - 20q^{92} - 160q^{93} + 80q^{95} + 162q^{98} + O(q^{100}) \)

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.s.a \(144\) \(1.397\) None \(-16\) \(0\) \(0\) \(-14\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database