Properties

Label 215.2.r
Level 215
Weight 2
Character orbit r
Rep. character \(\chi_{215}(2,\cdot)\)
Character field \(\Q(\zeta_{28})\)
Dimension 240
Newform subspaces 1
Sturm bound 44
Trace bound 0

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Defining parameters

Level: \( N \) = \( 215 = 5 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 215.r (of order \(28\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 215 \)
Character field: \(\Q(\zeta_{28})\)
Newform subspaces: \( 1 \)
Sturm bound: \(44\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(215, [\chi])\).

Total New Old
Modular forms 288 288 0
Cusp forms 240 240 0
Eisenstein series 48 48 0

Trace form

\( 240q - 14q^{2} - 14q^{3} - 14q^{5} - 40q^{6} - 14q^{8} + O(q^{10}) \) \( 240q - 14q^{2} - 14q^{3} - 14q^{5} - 40q^{6} - 14q^{8} + 6q^{10} - 20q^{11} - 42q^{12} + 10q^{13} - 10q^{15} + 48q^{16} - 6q^{17} - 56q^{18} - 14q^{20} - 36q^{21} - 14q^{22} + 14q^{23} - 6q^{25} - 28q^{26} - 14q^{27} - 70q^{28} - 224q^{30} - 36q^{31} + 126q^{32} + 14q^{33} - 38q^{35} + 64q^{36} + 98q^{38} - 82q^{40} - 36q^{41} + 112q^{43} - 14q^{45} - 28q^{46} - 42q^{47} + 14q^{48} + 196q^{51} - 22q^{52} - 22q^{53} - 14q^{55} - 56q^{56} + 22q^{57} - 30q^{58} + 86q^{60} - 28q^{61} + 70q^{62} - 112q^{63} - 98q^{65} - 256q^{66} - 90q^{67} - 138q^{68} + 126q^{70} - 28q^{71} + 14q^{72} + 112q^{73} - 14q^{75} - 28q^{76} + 154q^{77} + 34q^{78} + 120q^{81} + 182q^{82} - 10q^{83} + 72q^{86} + 152q^{87} + 14q^{88} - 110q^{90} - 28q^{91} + 84q^{92} + 26q^{95} - 272q^{96} + 50q^{97} - 84q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(215, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
215.2.r.a \(240\) \(1.717\) None \(-14\) \(-14\) \(-14\) \(0\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database