Properties

Label 215.2.p
Level 215
Weight 2
Character orbit p
Rep. character \(\chi_{215}(4,\cdot)\)
Character field \(\Q(\zeta_{14})\)
Dimension 120
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.p (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 215 \)
Character field: \(\Q(\zeta_{14})\)
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 144 144 0
Cusp forms 120 120 0
Eisenstein series 24 24 0

Trace form

\( 120q + 8q^{4} - 3q^{5} - 28q^{6} + 16q^{9} + O(q^{10}) \) \( 120q + 8q^{4} - 3q^{5} - 28q^{6} + 16q^{9} - q^{10} - 14q^{11} + 12q^{14} - q^{15} - 68q^{16} - 2q^{19} - 23q^{20} + 44q^{21} - 54q^{24} + 3q^{25} - 22q^{26} - 34q^{29} - 96q^{30} - 18q^{31} - 26q^{34} + 18q^{35} + 4q^{36} + 18q^{39} + 43q^{40} + 6q^{41} + 164q^{44} + 54q^{45} - 22q^{46} - 76q^{49} + 38q^{50} - 162q^{51} - 68q^{54} + 55q^{55} + 106q^{56} - 38q^{59} - 101q^{60} + 12q^{61} - 116q^{64} - 57q^{65} - 100q^{66} + 32q^{69} - 8q^{70} - 22q^{71} + 72q^{74} + 68q^{75} + 106q^{76} + 4q^{79} + 58q^{80} - 60q^{81} + 28q^{84} + 24q^{85} - 60q^{86} - 22q^{89} - 62q^{90} + 100q^{91} + 134q^{94} - 91q^{95} + 72q^{96} + 96q^{99} + O(q^{100}) \)

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.p.a \(120\) \(1.717\) None \(0\) \(0\) \(-3\) \(0\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database